From a6dad51ad585a235dc7bfe89ba1b488037642b9a Mon Sep 17 00:00:00 2001
From: Simon Rochester <simon.rochester@gmail.com>
Date: Sun, 21 Aug 2011 17:33:33 -0700
Subject: xmds2 model of Gena's 4-level system. GenerateGenasSystem.nb:
 generate evolution  equations GenasSystemPlots: code for reading output data,
   converting complex field amplitudes to   rotation angle/ellipticity, and
 plotting

---
 xmds2/Genas_system/GenasSystemPlots.nb    |  458 +++++
 xmds2/Genas_system/Genas_system.xmds      |  218 +++
 xmds2/Genas_system/GenerateGenasSystem.nb | 2722 +++++++++++++++++++++++++++++
 xmds2/Genas_system/Makefile               |   37 +
 4 files changed, 3435 insertions(+)
 create mode 100755 xmds2/Genas_system/GenasSystemPlots.nb
 create mode 100755 xmds2/Genas_system/Genas_system.xmds
 create mode 100755 xmds2/Genas_system/GenerateGenasSystem.nb
 create mode 100755 xmds2/Genas_system/Makefile

diff --git a/xmds2/Genas_system/GenasSystemPlots.nb b/xmds2/Genas_system/GenasSystemPlots.nb
new file mode 100755
index 0000000..c347101
--- /dev/null
+++ b/xmds2/Genas_system/GenasSystemPlots.nb
@@ -0,0 +1,458 @@
+(* Content-type: application/mathematica *)
+
+(*** Wolfram Notebook File ***)
+(* http://www.wolfram.com/nb *)
+
+(* CreatedBy='Mathematica 7.0' *)
+
+(*CacheID: 234*)
+(* Internal cache information:
+NotebookFileLineBreakTest
+NotebookFileLineBreakTest
+NotebookDataPosition[       145,          7]
+NotebookDataLength[     15335,        449]
+NotebookOptionsPosition[     14375,        415]
+NotebookOutlinePosition[     14740,        431]
+CellTagsIndexPosition[     14697,        428]
+WindowFrame->Normal*)
+
+(* Beginning of Notebook Content *)
+Notebook[{
+
+Cell[CellGroupData[{
+Cell["Functions for field parameterization conversion", "Section"],
+
+Cell[BoxData[
+ RowBox[{
+  RowBox[{
+   RowBox[{"Ax", "[", 
+    RowBox[{
+     RowBox[{"{", 
+      RowBox[{"0", ",", "0"}], "}"}], ",", "ComplexAmplitude"}], "]"}], "=", 
+   "0"}], ";"}]], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+  RowBox[{"Ax", "[", 
+   RowBox[{
+    RowBox[{"{", 
+     RowBox[{"Ex_", ",", "Ey_"}], "}"}], ",", "ComplexAmplitude"}], "]"}], ":=", 
+  FractionBox[
+   RowBox[{"Abs", "[", "Ex", "]"}], 
+   SqrtBox[
+    RowBox[{
+     SuperscriptBox[
+      RowBox[{"Abs", "[", "Ex", "]"}], "2"], "+", 
+     SuperscriptBox[
+      RowBox[{"Abs", "[", "Ey", "]"}], "2"]}]]]}]], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+  RowBox[{
+   RowBox[{"Ay", "[", 
+    RowBox[{
+     RowBox[{"{", 
+      RowBox[{"0", ",", "0"}], "}"}], ",", "ComplexAmplitude"}], "]"}], "=", 
+   "0"}], ";"}]], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+  RowBox[{"Ay", "[", 
+   RowBox[{
+    RowBox[{"{", 
+     RowBox[{"Ex_", ",", "Ey_"}], "}"}], ",", "ComplexAmplitude"}], "]"}], ":=", 
+  FractionBox[
+   RowBox[{"Abs", "[", "Ey", "]"}], 
+   SqrtBox[
+    RowBox[{
+     SuperscriptBox[
+      RowBox[{"Abs", "[", "Ex", "]"}], "2"], "+", 
+     SuperscriptBox[
+      RowBox[{"Abs", "[", "Ey", "]"}], "2"]}]]]}]], "Input"],
+
+Cell[BoxData[{
+ RowBox[{
+  RowBox[{
+   RowBox[{"\[Phi]", "[", 
+    RowBox[{
+     RowBox[{"{", 
+      RowBox[{"0", ",", "Ey_"}], "}"}], ",", "ComplexAmplitude"}], "]"}], "=",
+    "0"}], ";"}], "\[IndentingNewLine]", 
+ RowBox[{
+  RowBox[{
+   RowBox[{"\[Phi]", "[", 
+    RowBox[{
+     RowBox[{"{", 
+      RowBox[{"Ex_", ",", "0"}], "}"}], ",", "ComplexAmplitude"}], "]"}], "=",
+    "0"}], ";"}]}], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+  RowBox[{"\[Phi]", "[", 
+   RowBox[{
+    RowBox[{"{", 
+     RowBox[{"Ex_", ",", "Ey_"}], "}"}], ",", "ComplexAmplitude"}], "]"}], ":=", 
+  RowBox[{"Arg", "[", 
+   RowBox[{
+    FractionBox["Ey", 
+     RowBox[{"Abs", "[", "Ey", "]"}]], 
+    FractionBox[
+     RowBox[{"Abs", "[", "Ex", "]"}], "Ex"]}], "]"}]}]], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+  RowBox[{"AmplitudePhase", "[", 
+   RowBox[{
+    RowBox[{"{", 
+     RowBox[{"Ex_", ",", "Ey_"}], "}"}], ",", "ComplexAmplitude"}], "]"}], ":=", 
+  RowBox[{
+   RowBox[{
+    RowBox[{"{", 
+     RowBox[{
+      RowBox[{"Ax", "[", 
+       RowBox[{"#1", ",", "#2"}], "]"}], ",", 
+      RowBox[{"Ay", "[", 
+       RowBox[{"#1", ",", "#2"}], "]"}], ",", 
+      RowBox[{"\[Phi]", "[", 
+       RowBox[{"#1", ",", "#2"}], "]"}]}], "}"}], "&"}], "[", 
+   RowBox[{
+    RowBox[{"{", 
+     RowBox[{"Ex", ",", "Ey"}], "}"}], ",", "ComplexAmplitude"}], 
+   "]"}]}]], "Input"],
+
+Cell[BoxData[{
+ RowBox[{
+  RowBox[{"S1", "[", 
+   RowBox[{
+    RowBox[{"{", 
+     RowBox[{"Ax_", ",", "Ay_", ",", "\[Phi]_"}], "}"}], ",", 
+    "AmplitudePhase"}], "]"}], ":=", 
+  RowBox[{
+   SuperscriptBox["Ax", "2"], "-", 
+   SuperscriptBox["Ay", "2"]}]}], "\[IndentingNewLine]", 
+ RowBox[{
+  RowBox[{"S2", "[", 
+   RowBox[{
+    RowBox[{"{", 
+     RowBox[{"Ax_", ",", "Ay_", ",", "\[Phi]_"}], "}"}], ",", 
+    "AmplitudePhase"}], "]"}], ":=", 
+  RowBox[{"2", "Ax", " ", "Ay", " ", 
+   RowBox[{"Cos", "[", "\[Phi]", "]"}]}]}], "\[IndentingNewLine]", 
+ RowBox[{
+  RowBox[{"S3", "[", 
+   RowBox[{
+    RowBox[{"{", 
+     RowBox[{"Ax_", ",", "Ay_", ",", "\[Phi]_"}], "}"}], ",", 
+    "AmplitudePhase"}], "]"}], ":=", 
+  RowBox[{"2", "Ax", " ", "Ay", " ", 
+   RowBox[{"Sin", "[", "\[Phi]", "]"}]}]}]}], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+  RowBox[{"Stokes", "[", 
+   RowBox[{
+    RowBox[{"{", 
+     RowBox[{"Ax_", ",", "Ay_", ",", "\[Phi]_"}], "}"}], ",", 
+    "AmplitudePhase"}], "]"}], ":=", 
+  RowBox[{
+   RowBox[{
+    RowBox[{"{", 
+     RowBox[{
+      RowBox[{"S1", "[", 
+       RowBox[{"#1", ",", "#2"}], "]"}], ",", 
+      RowBox[{"S2", "[", 
+       RowBox[{"#1", ",", "#2"}], "]"}], ",", 
+      RowBox[{"S3", "[", 
+       RowBox[{"#1", ",", "#2"}], "]"}]}], "}"}], "&"}], "[", 
+   RowBox[{
+    RowBox[{"{", 
+     RowBox[{"Ax", ",", "Ay", ",", "\[Phi]"}], "}"}], ",", "AmplitudePhase"}],
+    "]"}]}]], "Input"],
+
+Cell[BoxData[{
+ RowBox[{
+  RowBox[{"\[Alpha]", "[", 
+   RowBox[{
+    RowBox[{"{", 
+     RowBox[{"S1_", ",", "S2_", ",", "S3_"}], "}"}], ",", "Stokes"}], "]"}], ":=", 
+  RowBox[{
+   FractionBox["1", "2"], 
+   RowBox[{"ArcTan", "[", 
+    RowBox[{"S1", ",", "S2"}], "]"}]}]}], "\[IndentingNewLine]", 
+ RowBox[{
+  RowBox[{"\[Epsilon]", "[", 
+   RowBox[{
+    RowBox[{"{", 
+     RowBox[{"S1_", ",", "S2_", ",", "S3_"}], "}"}], ",", "Stokes"}], "]"}], ":=", 
+  RowBox[{
+   FractionBox["1", "2"], 
+   RowBox[{"ArcSin", "[", "S3", "]"}]}]}]}], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+  RowBox[{"AngleEllipticity", "[", 
+   RowBox[{
+    RowBox[{"{", 
+     RowBox[{"S1_", ",", "S2_", ",", "S3_"}], "}"}], ",", "Stokes"}], "]"}], ":=", 
+  RowBox[{
+   RowBox[{
+    RowBox[{"{", 
+     RowBox[{
+      RowBox[{"\[Alpha]", "[", 
+       RowBox[{"#1", ",", "#2"}], "]"}], ",", 
+      RowBox[{"\[Epsilon]", "[", 
+       RowBox[{"#1", ",", "#2"}], "]"}]}], "}"}], "&"}], "[", 
+   RowBox[{
+    RowBox[{"{", 
+     RowBox[{"S1", ",", "S2", ",", "S3"}], "}"}], ",", "Stokes"}], 
+   "]"}]}]], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+  RowBox[{"AngleEllipticity", "[", 
+   RowBox[{
+    RowBox[{"{", 
+     RowBox[{"Ax_", ",", "Ay_", ",", "\[Phi]_"}], "}"}], ",", 
+    "AmplitudePhase"}], "]"}], ":=", 
+  RowBox[{"AngleEllipticity", "[", 
+   RowBox[{
+    RowBox[{"Stokes", "[", 
+     RowBox[{
+      RowBox[{"{", 
+       RowBox[{"Ax", ",", "Ay", ",", "\[Phi]"}], "}"}], ",", 
+      "AmplitudePhase"}], "]"}], ",", "Stokes"}], "]"}]}]], "Input"],
+
+Cell[BoxData[
+ RowBox[{
+  RowBox[{"AngleEllipticity", "[", 
+   RowBox[{
+    RowBox[{"{", 
+     RowBox[{"Ex_", ",", "Ey_"}], "}"}], ",", "ComplexAmplitude"}], "]"}], ":=", 
+  RowBox[{"AngleEllipticity", "[", 
+   RowBox[{
+    RowBox[{"AmplitudePhase", "[", 
+     RowBox[{
+      RowBox[{"{", 
+       RowBox[{"Ex", ",", "Ey"}], "}"}], ",", "ComplexAmplitude"}], "]"}], 
+    ",", "AmplitudePhase"}], "]"}]}]], "Input"]
+}, Open  ]],
+
+Cell[CellGroupData[{
+
+Cell["Read and plot data", "Section"],
+
+Cell["\<\
+SetDirectory[NotebookDirectory[]];
+fpDat = OpenRead[\"Genas_system_mg0.dat\",BinaryFormat -> True];
+z1Len = BinaryRead[fpDat, \"UnsignedInteger32\", ByteOrdering->-1];
+z1 = Flatten[BinaryReadList[fpDat, {\"Real64\"}, z1Len, ByteOrdering->-1]];
+t1Len = BinaryRead[fpDat, \"UnsignedInteger32\", ByteOrdering->-1];
+t1 = Flatten[BinaryReadList[fpDat, {\"Real64\"}, t1Len, ByteOrdering->-1]];
+Exreout1Len = BinaryRead[fpDat, \"UnsignedInteger32\", ByteOrdering->-1];
+Exreout1 = Flatten[Table[BinaryReadList[fpDat, {\"Real64\"}, t1Len, \
+ByteOrdering->-1],{j1,1,z1Len}],{{1},{2,3}}];
+Eximout1Len = BinaryRead[fpDat, \"UnsignedInteger32\", ByteOrdering->-1];
+Eximout1 = Flatten[Table[BinaryReadList[fpDat, {\"Real64\"}, t1Len, \
+ByteOrdering->-1],{j1,1,z1Len}],{{1},{2,3}}];
+Eyreout1Len = BinaryRead[fpDat, \"UnsignedInteger32\", ByteOrdering->-1];
+Eyreout1 = Flatten[Table[BinaryReadList[fpDat, {\"Real64\"}, t1Len, \
+ByteOrdering->-1],{j1,1,z1Len}],{{1},{2,3}}];
+Eyimout1Len = BinaryRead[fpDat, \"UnsignedInteger32\", ByteOrdering->-1];
+Eyimout1 = Flatten[Table[BinaryReadList[fpDat, {\"Real64\"}, t1Len, \
+ByteOrdering->-1],{j1,1,z1Len}],{{1},{2,3}}];
+Close[fpDat];
+ResetDirectory[];
+SetDirectory[NotebookDirectory[]];
+fpDat = OpenRead[\"Genas_system_mg1.dat\",BinaryFormat -> True];
+z2Len = BinaryRead[fpDat, \"UnsignedInteger32\", ByteOrdering->-1];
+z2 = Flatten[BinaryReadList[fpDat, {\"Real64\"}, z2Len, ByteOrdering->-1]];
+t2Len = BinaryRead[fpDat, \"UnsignedInteger32\", ByteOrdering->-1];
+t2 = Flatten[BinaryReadList[fpDat, {\"Real64\"}, t2Len, ByteOrdering->-1]];
+r11out2Len = BinaryRead[fpDat, \"UnsignedInteger32\", ByteOrdering->-1];
+r11out2 = Flatten[Table[BinaryReadList[fpDat, {\"Real64\"}, t2Len, \
+ByteOrdering->-1],{j1,1,z2Len}],{{1},{2,3}}];
+r22out2Len = BinaryRead[fpDat, \"UnsignedInteger32\", ByteOrdering->-1];
+r22out2 = Flatten[Table[BinaryReadList[fpDat, {\"Real64\"}, t2Len, \
+ByteOrdering->-1],{j1,1,z2Len}],{{1},{2,3}}];
+r33out2Len = BinaryRead[fpDat, \"UnsignedInteger32\", ByteOrdering->-1];
+r33out2 = Flatten[Table[BinaryReadList[fpDat, {\"Real64\"}, t2Len, \
+ByteOrdering->-1],{j1,1,z2Len}],{{1},{2,3}}];
+r44out2Len = BinaryRead[fpDat, \"UnsignedInteger32\", ByteOrdering->-1];
+r44out2 = Flatten[Table[BinaryReadList[fpDat, {\"Real64\"}, t2Len, \
+ByteOrdering->-1],{j1,1,z2Len}],{{1},{2,3}}];
+r12reout2Len = BinaryRead[fpDat, \"UnsignedInteger32\", ByteOrdering->-1];
+r12reout2 = Flatten[Table[BinaryReadList[fpDat, {\"Real64\"}, t2Len, \
+ByteOrdering->-1],{j1,1,z2Len}],{{1},{2,3}}];
+r12imout2Len = BinaryRead[fpDat, \"UnsignedInteger32\", ByteOrdering->-1];
+r12imout2 = Flatten[Table[BinaryReadList[fpDat, {\"Real64\"}, t2Len, \
+ByteOrdering->-1],{j1,1,z2Len}],{{1},{2,3}}];
+r13reout2Len = BinaryRead[fpDat, \"UnsignedInteger32\", ByteOrdering->-1];
+r13reout2 = Flatten[Table[BinaryReadList[fpDat, {\"Real64\"}, t2Len, \
+ByteOrdering->-1],{j1,1,z2Len}],{{1},{2,3}}];
+r13imout2Len = BinaryRead[fpDat, \"UnsignedInteger32\", ByteOrdering->-1];
+r13imout2 = Flatten[Table[BinaryReadList[fpDat, {\"Real64\"}, t2Len, \
+ByteOrdering->-1],{j1,1,z2Len}],{{1},{2,3}}];
+r14reout2Len = BinaryRead[fpDat, \"UnsignedInteger32\", ByteOrdering->-1];
+r14reout2 = Flatten[Table[BinaryReadList[fpDat, {\"Real64\"}, t2Len, \
+ByteOrdering->-1],{j1,1,z2Len}],{{1},{2,3}}];
+r14imout2Len = BinaryRead[fpDat, \"UnsignedInteger32\", ByteOrdering->-1];
+r14imout2 = Flatten[Table[BinaryReadList[fpDat, {\"Real64\"}, t2Len, \
+ByteOrdering->-1],{j1,1,z2Len}],{{1},{2,3}}];
+r23reout2Len = BinaryRead[fpDat, \"UnsignedInteger32\", ByteOrdering->-1];
+r23reout2 = Flatten[Table[BinaryReadList[fpDat, {\"Real64\"}, t2Len, \
+ByteOrdering->-1],{j1,1,z2Len}],{{1},{2,3}}];
+r23imout2Len = BinaryRead[fpDat, \"UnsignedInteger32\", ByteOrdering->-1];
+r23imout2 = Flatten[Table[BinaryReadList[fpDat, {\"Real64\"}, t2Len, \
+ByteOrdering->-1],{j1,1,z2Len}],{{1},{2,3}}];
+r24reout2Len = BinaryRead[fpDat, \"UnsignedInteger32\", ByteOrdering->-1];
+r24reout2 = Flatten[Table[BinaryReadList[fpDat, {\"Real64\"}, t2Len, \
+ByteOrdering->-1],{j1,1,z2Len}],{{1},{2,3}}];
+r24imout2Len = BinaryRead[fpDat, \"UnsignedInteger32\", ByteOrdering->-1];
+r24imout2 = Flatten[Table[BinaryReadList[fpDat, {\"Real64\"}, t2Len, \
+ByteOrdering->-1],{j1,1,z2Len}],{{1},{2,3}}];
+r34reout2Len = BinaryRead[fpDat, \"UnsignedInteger32\", ByteOrdering->-1];
+r34reout2 = Flatten[Table[BinaryReadList[fpDat, {\"Real64\"}, t2Len, \
+ByteOrdering->-1],{j1,1,z2Len}],{{1},{2,3}}];
+r34imout2Len = BinaryRead[fpDat, \"UnsignedInteger32\", ByteOrdering->-1];
+r34imout2 = Flatten[Table[BinaryReadList[fpDat, {\"Real64\"}, t2Len, \
+ByteOrdering->-1],{j1,1,z2Len}],{{1},{2,3}}];
+Close[fpDat];
+ResetDirectory[];
+
+declaredVariables={\"z1\", \"t1\", \"Exreout1\", \"Eximout1\", \"Eyreout1\", \
+\"Eyimout1\", \"z2\", \"t2\", \"r11out2\", \"r22out2\", \"r33out2\", \
+\"r44out2\", \"r12reout2\", \"r12imout2\", \"r13reout2\", \"r13imout2\", \
+\"r14reout2\", \"r14imout2\", \"r23reout2\", \"r23imout2\", \"r24reout2\", \
+\"r24imout2\", \"r34reout2\", \"r34imout2\"}
+\
+\>", "Input"],
+
+Cell[BoxData[{
+ RowBox[{
+  RowBox[{"Exout1", "=", 
+   RowBox[{"Exreout1", "+", 
+    RowBox[{"\[ImaginaryI]", " ", "Eximout1"}]}]}], 
+  ";"}], "\[IndentingNewLine]", 
+ RowBox[{
+  RowBox[{"Eyout1", "=", 
+   RowBox[{"Eyreout1", "+", 
+    RowBox[{"\[ImaginaryI]", " ", "Eyimout1"}]}]}], 
+  ";"}], "\[IndentingNewLine]", 
+ RowBox[{"ListAnimate", "@", 
+  RowBox[{"Table", "[", "\[IndentingNewLine]", 
+   RowBox[{
+    RowBox[{
+     RowBox[{"intens", "=", 
+      RowBox[{
+       RowBox[{
+        RowBox[{".5", " ", 
+         SuperscriptBox["10", 
+          RowBox[{"-", "7"}]], 
+         RowBox[{"Abs", "[", "#", "]"}]}], "&"}], "/@", 
+       RowBox[{"Transpose", "@", 
+        RowBox[{"{", 
+         RowBox[{
+          RowBox[{"Exout1", "[", 
+           RowBox[{"[", 
+            RowBox[{"All", ",", "i"}], "]"}], "]"}], ",", 
+          RowBox[{"Eyout1", "[", 
+           RowBox[{"[", 
+            RowBox[{"All", ",", "i"}], "]"}], "]"}]}], "}"}]}]}]}], ";", 
+     "\[IndentingNewLine]", 
+     RowBox[{"mask", "=", 
+      RowBox[{
+       RowBox[{
+        RowBox[{"If", "[", 
+         RowBox[{
+          RowBox[{"#", "<", ".1"}], ",", "Null", ",", "1"}], "]"}], "&"}], "/@", 
+       RowBox[{"intens", "[", 
+        RowBox[{"[", 
+         RowBox[{"All", ",", "1"}], "]"}], "]"}]}]}], ";", 
+     "\[IndentingNewLine]", 
+     RowBox[{"alep", "=", 
+      RowBox[{
+       RowBox[{
+        RowBox[{"AngleEllipticity", "[", 
+         RowBox[{"#", ",", "ComplexAmplitude"}], "]"}], "&"}], "/@", 
+       RowBox[{"Transpose", "@", 
+        RowBox[{"{", 
+         RowBox[{
+          RowBox[{"Exout1", "[", 
+           RowBox[{"[", 
+            RowBox[{"All", ",", "i"}], "]"}], "]"}], ",", 
+          RowBox[{"Eyout1", "[", 
+           RowBox[{"[", 
+            RowBox[{"All", ",", "i"}], "]"}], "]"}]}], "}"}]}]}]}], ";", 
+     RowBox[{"ListLinePlot", "[", 
+      RowBox[{
+       RowBox[{"{", 
+        RowBox[{
+         RowBox[{"Transpose", "[", 
+          RowBox[{"{", 
+           RowBox[{"z1", ",", 
+            RowBox[{"mask", " ", 
+             RowBox[{"alep", "[", 
+              RowBox[{"[", 
+               RowBox[{"All", ",", "1"}], "]"}], "]"}]}]}], "}"}], "]"}], ",", 
+         RowBox[{"Transpose", "[", 
+          RowBox[{"{", 
+           RowBox[{"z1", ",", 
+            RowBox[{"intens", "[", 
+             RowBox[{"[", 
+              RowBox[{"All", ",", "1"}], "]"}], "]"}]}], "}"}], "]"}]}], 
+        "}"}], ",", 
+       RowBox[{"PlotRange", "\[Rule]", 
+        RowBox[{"{", 
+         RowBox[{
+          RowBox[{
+           RowBox[{"-", "\[Pi]"}], "/", "2"}], ",", 
+          RowBox[{"\[Pi]", "/", "2"}]}], "}"}]}]}], "]"}]}], ",", 
+    RowBox[{"{", 
+     RowBox[{"i", ",", "1", ",", 
+      RowBox[{"Length", "[", "t1", "]"}], ",", "1"}], "}"}]}], 
+   "]"}]}]}], "Input"]
+}, Open  ]]
+},
+WindowSize->{844, 920},
+WindowMargins->{{-4, Automatic}, {2, Automatic}},
+ShowSelection->True,
+FrontEndVersion->"7.0 for Microsoft Windows (64-bit) (February 18, 2009)",
+StyleDefinitions->"Default.nb"
+]
+(* End of Notebook Content *)
+
+(* Internal cache information *)
+(*CellTagsOutline
+CellTagsIndex->{}
+*)
+(*CellTagsIndex
+CellTagsIndex->{}
+*)
+(*NotebookFileOutline
+Notebook[{
+Cell[CellGroupData[{
+Cell[567, 22, 66, 0, 71, "Section"],
+Cell[636, 24, 194, 7, 31, "Input"],
+Cell[833, 33, 388, 13, 57, "Input"],
+Cell[1224, 48, 194, 7, 31, "Input"],
+Cell[1421, 57, 388, 13, 57, "Input"],
+Cell[1812, 72, 403, 14, 52, "Input"],
+Cell[2218, 88, 342, 11, 49, "Input"],
+Cell[2563, 101, 582, 19, 52, "Input"],
+Cell[3148, 122, 807, 25, 72, "Input"],
+Cell[3958, 149, 602, 20, 52, "Input"],
+Cell[4563, 171, 543, 17, 83, "Input"],
+Cell[5109, 190, 524, 17, 31, "Input"],
+Cell[5636, 209, 431, 13, 52, "Input"],
+Cell[6070, 224, 413, 12, 52, "Input"]
+}, Open  ]],
+Cell[CellGroupData[{
+Cell[6520, 241, 37, 0, 71, "Section"],
+Cell[6560, 243, 5029, 84, 1017, "Input"],
+Cell[11592, 329, 2767, 83, 177, "Input"]
+}, Open  ]]
+}
+]
+*)
+
+(* End of internal cache information *)
diff --git a/xmds2/Genas_system/Genas_system.xmds b/xmds2/Genas_system/Genas_system.xmds
new file mode 100755
index 0000000..e855e4f
--- /dev/null
+++ b/xmds2/Genas_system/Genas_system.xmds
@@ -0,0 +1,218 @@
+<?xml version="1.0"?>
+<simulation xmds-version="2">
+
+	<name>Genas_system</name>
+	
+	<author>Eugeniy Mikhailov and Simon Rochester</author>
+	<description>
+		License GPL.
+
+		Solving 4 level atom in 0->1 configuration,
+		with field propagation along spatial axis Z
+		no Doppler broadening
+
+		We are solving 
+			dE/dz+(1/c)*dE/dt=i*eta*rho_ij,  where j level is higher then i.
+			Note that E is actually a Rabi frequency of electromagnetic field not the EM field
+		in xmds terms it looks like
+			dE_dz = i*eta*rhoij - 1/c*L[E], here we moved t dependence to Fourier space
+
+		VERY IMPORTANT: all Rabi frequency should be given in [1/s], if you want to
+		normalize it to something else look drho/dt equation.
+		No need to renormalizes eta as long as its express through i
+		the upper level decay rate in the same units as Rabi frequency.
+	</description>
+
+	<features>
+		<globals>
+			<![CDATA[
+				const double pi = M_PI; 
+				const double c=3.e8;
+				const double lambda=794.7e-9; //wavelength in m
+				const double N=1e6*(1e6);    //number of particles per cubic m i.e. density
+				const double Gamma=6*(2*M_PI*1e6);  // characteristic decay rate of upper level used for eta  calculations expressed in [1/s]
+				const double eta = 3*lambda*lambda*N*Gamma/16.0/M_PI;  // eta constant in the wave equation for Rabi frequency. Units are [1/(m s)]
+
+				// repopulation rate (atoms flying in/out the laser beam)  in [1/s]
+				const double gt=0.01*(2*M_PI*1e6);
+				// Natural linewidth  of upper state in [1/s]
+				const double g0=1.*(2*M_PI*1e6);
+
+				complex  Exc, Eyc; // Complex-conjugated Rabi frequency
+
+				complex  r21, r31, r41, r32, r42, r43, r44;   // density matrix elements
+			]]>
+		</globals>
+		<benchmark />
+		<arguments>
+			<!-- Real and imaginary parts of complex Rabi frequency in [1/s] -->
+			<argument name="ExReo" type="real" default_value="(3.+0.001)*(2*M_PI*1.e6)" />
+			<argument name="ExImo" type="real" default_value="0." />
+			<argument name="EyReo" type="real" default_value="0." />
+			<argument name="EyImo" type="real" default_value="(3.-0.001)*(2*M_PI*1.e6)" />
+			<!-- light detuning in [1/s] -->
+			<argument name="delta"  type="real" default_value="3.0*(2*M_PI*1e6)" />
+			<!--shift of upper-state M=0 sublevel-->
+			<argument name="delta0" type="real" default_value="1.*(2*M_PI*1e6)" />
+			<!--Static B-field Larmor frequency-->
+			<argument name="OL" type="real" default_value="4.*(2*M_PI*1e6)" />
+			<!--rf Rabi frequency-->
+			<argument name="Orf" type="real" default_value="0.1*(2*M_PI*1e6)" />
+			<!--rf frequency-->
+			<argument name="orf" type="real" default_value="4.*(2*M_PI*1e6)" />	
+		</arguments>
+		<bing />
+		<fftw plan="patient" />
+		<openmp />
+		<auto_vectorise />
+	</features>
+
+	<!-- 'z' and 't' to have dimensions [m] and [s]   -->
+	<geometry>
+		<propagation_dimension> z </propagation_dimension>
+		<transverse_dimensions>
+			<dimension name="t" lattice="1000" domain="(-1.5e-7, 2.5e-7)" />
+		</transverse_dimensions>
+	</geometry>
+
+	<!-- Rabi frequency --> 
+	<vector name="E_field" type="complex" initial_space="t">
+		<components>Ex Ey</components>
+		<initialisation>
+			<![CDATA[
+				// Initial (at starting 'z' position) electromagnetic field does not depend on detuning
+				// as well as time
+				Ex=(ExReo+i*ExImo)*exp(-pow( ((t-0.0)/1e-7),2) );
+				Ey=(EyReo+i*EyImo)*exp(-pow( ((t-0.0)/1e-7),2) );
+			]]>
+		</initialisation>
+	</vector>
+
+	<vector name="density_matrix" type="complex" initial_space="t">
+		<components>r11 r22 r33 r12 r13 r14 r23 r24 r34 r44</components>
+		<initialisation>
+			<![CDATA[
+				r11 = 1; r22 = 0; r33 = 0; r44 = 0;
+				r12 = 0; r13 = 0; r14 = 0;
+				r23 = 0; r24 = 0;
+				r34 = 0;
+			]]>
+		</initialisation>
+	</vector>
+
+	<vector name="rfField" type="real">
+		<components> rf </components>
+		<initialisation>
+		  <![CDATA[
+			rf = Orf*sin(orf*t);
+		  ]]>
+		</initialisation>
+	</vector>	
+	
+	<sequence>
+		<integrate algorithm="ARK45" tolerance="0.05e-7" interval="1e1">
+			<samples>200 200</samples>
+			<operators>
+				<operator kind="cross_propagation" algorithm="SI" propagation_dimension="t">
+					<integration_vectors>density_matrix</integration_vectors>
+					<dependencies>E_field rfField</dependencies>
+					<boundary_condition kind="left">
+						<![CDATA[
+							r11 = 1; r22 = 0; r33 = 0; r44 = 0;
+							r12 = 0; r13 = 0; r14 = 0;
+							r23 = 0; r24 = 0;
+							r34 = 0;
+						]]>
+					</boundary_condition>
+					<![CDATA[
+						Exc = conj(Ex);
+						Eyc = conj(Ey);
+
+						r21=conj(r12);
+						r31=conj(r13);
+						r41=conj(r14);
+						r32=conj(r23);
+						r42=conj(r24);
+						r43=conj(r34);
+
+						// Equations of motions according to Simon's mathematica code
+						dr11_dt = gt - gt*r11 + (-Ey - Ex*i)*r12 + i*(Ex + Ey*i)*r14 + i*(Exc + Eyc*i)*r21 + (-Eyc - Exc*i)*r41 + g0*(r22 + r33 + r44);
+						dr12_dt = (2*(Eyc - Exc*i)*r11 - i*((2*delta - (g0 + 2*gt)*i - 2*OL - 2*rf)*r12 - 2*(Exc + Eyc*i)*r22 + 2*(Exc - Eyc*i)*r42))/2.;
+						dr13_dt = (-g0/2. - gt - delta*i + delta0*i)*r13 + i*(Exc + Eyc*i)*r23 + (-Eyc - Exc*i)*r43;
+						dr14_dt = -(i*((2*delta - (g0 + 2*gt)*i + 2*OL + 2*rf)*r14 - 2*(Exc + Eyc*i)*r24 - 2*(Exc - Eyc*i)*(r11 - r44)))/2.;
+						dr22_dt = (Ey + Ex*i)*r12 + (Eyc - Exc*i)*r21 - (g0 + gt)*r22;
+						dr23_dt = (Ey + Ex*i)*r13 + i*(delta0 + i*(g0 + gt + i*OL) - rf)*r23;
+						dr24_dt = (Ey + Ex*i)*r14 + (Eyc + Exc*i)*r21 - (g0 + gt + 2*i*OL + 2*i*rf)*r24;
+						dr33_dt = -((g0 + gt)*r33);
+						dr34_dt = (Eyc + Exc*i)*r31 - i*(delta0 - (g0 + gt)*i + OL + rf)*r34;
+						dr44_dt = (Ey - Ex*i)*r14 + (Eyc + Exc*i)*r41 - (g0 + gt)*r44;
+					]]>
+				</operator>
+				<operator kind="ex" constant="yes">
+					<operator_names>Lt</operator_names>
+					<![CDATA[
+						Lt = i*1./c*kt;
+					]]>
+				</operator>
+				<integration_vectors>E_field</integration_vectors>
+				<dependencies>density_matrix</dependencies>
+				<![CDATA[
+					dEx_dz = i*eta*conj(r12-r14) - Lt[Ex] ;
+					dEy_dz = -eta*conj(r12+r14) - Lt[Ey] ;
+				]]>
+			</operators>
+		</integrate>
+	</sequence>
+
+	<!-- The output to generate -->
+	<output format="binary" filename="Genas_system.xsil">
+		<group>
+			<sampling basis="t(100)" initial_sample="yes">
+				<dependencies>E_field</dependencies>
+				<moments>Ex_re_out Ex_im_out Ey_re_out Ey_im_out</moments>
+				<![CDATA[
+					Ex_re_out = Ex.Re();
+					Ex_im_out = Ex.Im();
+					Ey_re_out = Ey.Re();
+					Ey_im_out = Ey.Im();
+				]]>
+			</sampling>
+		</group>
+
+		<group>
+			<sampling basis="t(100)" initial_sample="yes">
+				<dependencies>density_matrix</dependencies>
+				<moments>
+					r11_out r22_out r33_out r44_out 
+					r12_re_out r12_im_out r13_re_out r13_im_out r14_re_out r14_im_out
+					                      r23_re_out r23_im_out r24_re_out r24_im_out 
+					                                            r34_re_out r34_im_out
+				</moments>
+				<![CDATA[
+					// populations output 
+					r11_out = r11.Re();
+					r22_out = r22.Re();
+					r33_out = r33.Re();
+					r44_out = r44.Re();
+					// coherences output 
+					r12_re_out = r12.Re();
+					r12_im_out = r12.Im();
+					r13_re_out = r13.Re();
+					r13_im_out = r13.Im();
+					r14_re_out = r14.Re();
+					r14_im_out = r14.Im();
+					r23_re_out = r23.Re();
+					r23_im_out = r23.Im();
+					r24_re_out = r24.Re();
+					r24_im_out = r24.Im();
+					r34_re_out = r34.Re();
+					r34_im_out = r34.Im();
+				]]>
+			</sampling>
+		</group>
+	</output>
+</simulation>
+	
+<!-- 
+vim: ts=2 sw=2 foldmethod=indent: 
+-->
diff --git a/xmds2/Genas_system/GenerateGenasSystem.nb b/xmds2/Genas_system/GenerateGenasSystem.nb
new file mode 100755
index 0000000..ab9069b
--- /dev/null
+++ b/xmds2/Genas_system/GenerateGenasSystem.nb
@@ -0,0 +1,2722 @@
+(* Content-type: application/mathematica *)
+
+(*** Wolfram Notebook File ***)
+(* http://www.wolfram.com/nb *)
+
+(* CreatedBy='Mathematica 7.0' *)
+
+(*CacheID: 234*)
+(* Internal cache information:
+NotebookFileLineBreakTest
+NotebookFileLineBreakTest
+NotebookDataPosition[       145,          7]
+NotebookDataLength[     92628,       2713]
+NotebookOptionsPosition[     89973,       2618]
+NotebookOutlinePosition[     90340,       2634]
+CellTagsIndexPosition[     90297,       2631]
+WindowFrame->Normal*)
+
+(* Beginning of Notebook Content *)
+Notebook[{
+
+Cell[CellGroupData[{
+Cell["setup the system", "Section"],
+
+Cell["This loads the package.", "MathCaption",
+ CellID->836781195],
+
+Cell[BoxData[
+ RowBox[{"<<", "AtomicDensityMatrix`"}]], "Input",
+ CellID->2058623809],
+
+Cell[TextData[{
+ "We define an atomic system consisting of two even-parity lower states and \
+two odd-parity upper states. We apply a light field with components at \
+frequencies ",
+ Cell[BoxData[
+  FormBox[
+   StyleBox[
+    SubscriptBox["\[Omega]", "1"], "InlineMath"], TraditionalForm]]],
+ " (near resonant with the ",
+ Cell[BoxData[
+  StyleBox[
+   RowBox[{
+    RowBox[{
+     RowBox[{
+      RowBox[{"|", "1"}], "\[RightAngleBracket]"}], "\[Rule]", 
+     RowBox[{"|", "3"}]}], "\[RightAngleBracket]"}], "InlineMath"]]],
+ " transition), ",
+ Cell[BoxData[
+  FormBox[
+   StyleBox[
+    SubscriptBox["\[Omega]", "2"], "InlineMath"], TraditionalForm]]],
+ " (near resonant with the ",
+ Cell[BoxData[
+  StyleBox[
+   RowBox[{
+    RowBox[{
+     RowBox[{
+      RowBox[{"|", "2"}], "\[RightAngleBracket]"}], "\[Rule]", 
+     RowBox[{"|", "3"}]}], "\[RightAngleBracket]"}], "InlineMath"]]],
+ " transition), and  ",
+ Cell[BoxData[
+  FormBox[
+   StyleBox[
+    SubscriptBox["\[Omega]", "c"], "InlineMath"], TraditionalForm]]],
+ " (near resonant with the ",
+ Cell[BoxData[
+  StyleBox[
+   RowBox[{
+    RowBox[{
+     RowBox[{
+      RowBox[{"|", "2"}], "\[RightAngleBracket]"}], "\[Rule]", 
+     RowBox[{"|", "4"}]}], "\[RightAngleBracket]"}], "InlineMath"]]],
+ " transition)."
+}], "Text",
+ CellID->525777075],
+
+Cell["Define the atomic system.", "MathCaption",
+ CellID->429217524],
+
+Cell[BoxData[
+ RowBox[{
+  RowBox[{"system", "=", 
+   RowBox[{"Sublevels", "[", 
+    RowBox[{"{", "\[IndentingNewLine]", 
+     RowBox[{
+      RowBox[{"AtomicState", "[", 
+       RowBox[{"1", ",", 
+        RowBox[{"J", "\[Rule]", "0"}], ",", 
+        RowBox[{"L", "\[Rule]", "0"}], ",", 
+        RowBox[{"S", "\[Rule]", "0"}], ",", 
+        RowBox[{"NaturalWidth", "\[Rule]", "0"}], ",", 
+        RowBox[{"Energy", "\[Rule]", "0"}], ",", 
+        RowBox[{
+         RowBox[{"Polarizability", "[", "0", "]"}], "\[Rule]", "0"}]}], "]"}],
+       ",", "\[IndentingNewLine]", 
+      RowBox[{"AtomicState", "[", 
+       RowBox[{"2", ",", 
+        RowBox[{"J", "\[Rule]", "1"}], ",", 
+        RowBox[{"L", "\[Rule]", "1"}], ",", 
+        RowBox[{"S", "\[Rule]", "0"}], ",", 
+        RowBox[{"NaturalWidth", "\[Rule]", "\[CapitalGamma]"}], ",", 
+        RowBox[{"Energy", "\[Rule]", "\[Omega]0"}], ",", 
+        RowBox[{
+         RowBox[{"Polarizability", "[", "0", "]"}], "\[Rule]", 
+         RowBox[{
+          RowBox[{"-", "2"}], "/", "3"}]}], ",", 
+        RowBox[{
+         RowBox[{"Polarizability", "[", "2", "]"}], "\[Rule]", 
+         RowBox[{"2", "/", "3"}]}], ",", 
+        RowBox[{
+         RowBox[{"BranchingRatio", "[", "1", "]"}], "\[Rule]", "1"}]}], 
+       "]"}]}], "\[IndentingNewLine]", "}"}], "]"}]}], ";"}]], "Input",
+ CellID->433132487],
+
+Cell["Define the optical field ", "MathCaption",
+ CellID->133602844],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"field", "=", 
+  RowBox[{
+   FractionBox[
+    RowBox[{"2", 
+     SqrtBox["6"]}], 
+    RowBox[{"ReducedME", "[", 
+     RowBox[{"1", ",", 
+      RowBox[{"{", 
+       RowBox[{"Dipole", ",", "1"}], "}"}], ",", "2"}], "]"}]], 
+   RowBox[{"{", 
+    RowBox[{
+     RowBox[{
+      SuperscriptBox["\[ExponentialE]", 
+       RowBox[{"\[ImaginaryI]", " ", 
+        RowBox[{"(", 
+         RowBox[{"\[Phi]x", "-", 
+          RowBox[{"t", " ", "\[Omega]"}]}], ")"}]}]], " ", 
+      "\[CapitalOmega]Rx"}], " ", ",", 
+     RowBox[{
+      SuperscriptBox["\[ExponentialE]", 
+       RowBox[{"\[ImaginaryI]", " ", 
+        RowBox[{"(", 
+         RowBox[{"\[Phi]y", "-", 
+          RowBox[{"t", " ", "\[Omega]"}]}], ")"}]}]], " ", 
+      "\[CapitalOmega]Ry"}], " ", ",", "0"}], "}"}]}]}]], "Input",
+ CellID->26742303],
+
+Cell[BoxData[
+ RowBox[{"{", 
+  RowBox[{
+   FractionBox[
+    RowBox[{"2", " ", 
+     SqrtBox["6"], " ", 
+     SuperscriptBox["\[ExponentialE]", 
+      RowBox[{"\[ImaginaryI]", " ", 
+       RowBox[{"(", 
+        RowBox[{"\[Phi]x", "-", 
+         RowBox[{"t", " ", "\[Omega]"}]}], ")"}]}]], " ", 
+     "\[CapitalOmega]Rx"}], 
+    RowBox[{"ReducedME", "[", 
+     RowBox[{"1", ",", 
+      RowBox[{"{", 
+       RowBox[{"Dipole", ",", "1"}], "}"}], ",", "2"}], "]"}]], ",", 
+   FractionBox[
+    RowBox[{"2", " ", 
+     SqrtBox["6"], " ", 
+     SuperscriptBox["\[ExponentialE]", 
+      RowBox[{"\[ImaginaryI]", " ", 
+       RowBox[{"(", 
+        RowBox[{"\[Phi]y", "-", 
+         RowBox[{"t", " ", "\[Omega]"}]}], ")"}]}]], " ", 
+     "\[CapitalOmega]Ry"}], 
+    RowBox[{"ReducedME", "[", 
+     RowBox[{"1", ",", 
+      RowBox[{"{", 
+       RowBox[{"Dipole", ",", "1"}], "}"}], ",", "2"}], "]"}]], ",", "0"}], 
+  "}"}]], "Output"]
+}, Open  ]],
+
+Cell["\<\
+The Hamiltonian for the system subject to the optical field.\
+\>", "MathCaption",
+ CellID->462076121],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"MatrixForm", "[", 
+  RowBox[{"H", "=", 
+   RowBox[{
+    RowBox[{
+     RowBox[{"Expand", "@", 
+      RowBox[{"Hamiltonian", "[", 
+       RowBox[{"system", ",", 
+        RowBox[{"ElectricField", "\[Rule]", "field"}], ",", 
+        RowBox[{"MagneticField", "\[Rule]", 
+         RowBox[{
+          RowBox[{"{", 
+           RowBox[{"0", ",", "0", ",", 
+            RowBox[{"\[CapitalOmega]L", "+", 
+             RowBox[{"\[CapitalOmega]rf", " ", 
+              RowBox[{"Sin", "[", 
+               RowBox[{"\[Omega]rf", " ", "t"}], "]"}]}]}]}], "}"}], "/", 
+          "BohrMagneton"}]}]}], "]"}]}], "+", 
+     RowBox[{"Hamiltonian", "[", 
+      RowBox[{"system", ",", 
+       RowBox[{"ElectricField", "\[Rule]", 
+        RowBox[{"{", 
+         RowBox[{"0", ",", "0", ",", 
+          SqrtBox["\[CapitalDelta]0"]}], "}"}]}], ",", 
+       RowBox[{"Interaction", "\[Rule]", 
+        RowBox[{"{", "Polarizability", "}"}]}]}], "]"}]}], "//", 
+    "FullSimplify"}]}], "]"}]], "Input",
+ CellID->494599775],
+
+Cell[BoxData[
+ TagBox[
+  RowBox[{"(", "\[NoBreak]", GridBox[{
+     {"0", 
+      RowBox[{
+       RowBox[{"-", "2"}], " ", 
+       RowBox[{"(", 
+        RowBox[{
+         RowBox[{"\[CapitalOmega]Rx", " ", 
+          RowBox[{"Cos", "[", 
+           RowBox[{"\[Phi]x", "-", 
+            RowBox[{"t", " ", "\[Omega]"}]}], "]"}]}], "+", 
+         RowBox[{"\[ImaginaryI]", " ", "\[CapitalOmega]Ry", " ", 
+          RowBox[{"Cos", "[", 
+           RowBox[{"\[Phi]y", "-", 
+            RowBox[{"t", " ", "\[Omega]"}]}], "]"}]}]}], ")"}]}], "0", 
+      RowBox[{
+       RowBox[{"2", " ", "\[CapitalOmega]Rx", " ", 
+        RowBox[{"Cos", "[", 
+         RowBox[{"\[Phi]x", "-", 
+          RowBox[{"t", " ", "\[Omega]"}]}], "]"}]}], "-", 
+       RowBox[{"2", " ", "\[ImaginaryI]", " ", "\[CapitalOmega]Ry", " ", 
+        RowBox[{"Cos", "[", 
+         RowBox[{"\[Phi]y", "-", 
+          RowBox[{"t", " ", "\[Omega]"}]}], "]"}]}]}]},
+     {
+      RowBox[{
+       RowBox[{
+        RowBox[{"-", "2"}], " ", "\[CapitalOmega]Rx", " ", 
+        RowBox[{"Cos", "[", 
+         RowBox[{"\[Phi]x", "-", 
+          RowBox[{"t", " ", "\[Omega]"}]}], "]"}]}], "+", 
+       RowBox[{"2", " ", "\[ImaginaryI]", " ", "\[CapitalOmega]Ry", " ", 
+        RowBox[{"Cos", "[", 
+         RowBox[{"\[Phi]y", "-", 
+          RowBox[{"t", " ", "\[Omega]"}]}], "]"}]}]}], 
+      RowBox[{"\[Omega]0", "+", "\[CapitalOmega]L", "+", 
+       RowBox[{"\[CapitalOmega]rf", " ", 
+        RowBox[{"Sin", "[", 
+         RowBox[{"t", " ", "\[Omega]rf"}], "]"}]}]}], "0", "0"},
+     {"0", "0", 
+      RowBox[{"\[CapitalDelta]0", "+", "\[Omega]0"}], "0"},
+     {
+      RowBox[{
+       RowBox[{"2", " ", "\[CapitalOmega]Rx", " ", 
+        RowBox[{"Cos", "[", 
+         RowBox[{"\[Phi]x", "-", 
+          RowBox[{"t", " ", "\[Omega]"}]}], "]"}]}], "+", 
+       RowBox[{"2", " ", "\[ImaginaryI]", " ", "\[CapitalOmega]Ry", " ", 
+        RowBox[{"Cos", "[", 
+         RowBox[{"\[Phi]y", "-", 
+          RowBox[{"t", " ", "\[Omega]"}]}], "]"}]}]}], "0", "0", 
+      RowBox[{"\[Omega]0", "-", "\[CapitalOmega]L", "-", 
+       RowBox[{"\[CapitalOmega]rf", " ", 
+        RowBox[{"Sin", "[", 
+         RowBox[{"t", " ", "\[Omega]rf"}], "]"}]}]}]}
+    },
+    GridBoxAlignment->{
+     "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
+      "RowsIndexed" -> {}},
+    GridBoxSpacings->{"Columns" -> {
+        Offset[0.27999999999999997`], {
+         Offset[0.7]}, 
+        Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
+        Offset[0.2], {
+         Offset[0.4]}, 
+        Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
+  Function[BoxForm`e$, 
+   MatrixForm[BoxForm`e$]]]], "Output"]
+}, Open  ]],
+
+Cell["The level diagram for the system.", "MathCaption",
+ CellID->358620443],
+
+Cell[BoxData[
+ RowBox[{"LevelDiagram", "[", 
+  RowBox[{"system", ",", 
+   RowBox[{"H", "/.", 
+    RowBox[{"{", 
+     RowBox[{
+      RowBox[{"\[Omega]0", "\[Rule]", "1"}], ",", 
+      RowBox[{"\[CapitalOmega]rf", "\[Rule]", "0"}], ",", 
+      RowBox[{"\[CapitalOmega]L", "\[Rule]", ".3"}], ",", 
+      RowBox[{"\[CapitalDelta]0", "\[Rule]", ".2"}]}], "}"}]}]}], 
+  "]"}]], "Input",
+ CellID->167259034],
+
+Cell["Apply the rotating-wave approximation to the Hamiltonian.", \
+"MathCaption",
+ CellID->577766068],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{
+  RowBox[{"(", 
+   RowBox[{"Hrwa", "=", 
+    RowBox[{
+     RowBox[{"RotatingWaveApproximation", "[", 
+      RowBox[{"system", ",", "H", ",", "\[Omega]"}], "]"}], "/.", 
+     RowBox[{"\[Omega]", "\[Rule]", 
+      RowBox[{"\[Omega]0", "+", "\[CapitalDelta]"}]}]}]}], ")"}], "//", 
+  "MatrixForm"}]], "Input"],
+
+Cell[BoxData[
+ TagBox[
+  RowBox[{"(", "\[NoBreak]", GridBox[{
+     {"0", 
+      RowBox[{
+       RowBox[{
+        RowBox[{"-", 
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{
+           RowBox[{"-", "\[ImaginaryI]"}], " ", "\[Phi]x"}]]}], " ", 
+        "\[CapitalOmega]Rx"}], "-", 
+       RowBox[{"\[ImaginaryI]", " ", 
+        SuperscriptBox["\[ExponentialE]", 
+         RowBox[{
+          RowBox[{"-", "\[ImaginaryI]"}], " ", "\[Phi]y"}]], " ", 
+        "\[CapitalOmega]Ry"}]}], "0", 
+      RowBox[{
+       RowBox[{
+        SuperscriptBox["\[ExponentialE]", 
+         RowBox[{
+          RowBox[{"-", "\[ImaginaryI]"}], " ", "\[Phi]x"}]], " ", 
+        "\[CapitalOmega]Rx"}], "-", 
+       RowBox[{"\[ImaginaryI]", " ", 
+        SuperscriptBox["\[ExponentialE]", 
+         RowBox[{
+          RowBox[{"-", "\[ImaginaryI]"}], " ", "\[Phi]y"}]], " ", 
+        "\[CapitalOmega]Ry"}]}]},
+     {
+      RowBox[{
+       RowBox[{
+        RowBox[{"-", 
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{"\[ImaginaryI]", " ", "\[Phi]x"}]]}], " ", 
+        "\[CapitalOmega]Rx"}], "+", 
+       RowBox[{"\[ImaginaryI]", " ", 
+        SuperscriptBox["\[ExponentialE]", 
+         RowBox[{"\[ImaginaryI]", " ", "\[Phi]y"}]], " ", 
+        "\[CapitalOmega]Ry"}]}], 
+      RowBox[{
+       RowBox[{"-", "\[CapitalDelta]"}], "+", "\[CapitalOmega]L", "+", 
+       RowBox[{
+        FractionBox["1", "2"], " ", "\[ImaginaryI]", " ", 
+        SuperscriptBox["\[ExponentialE]", 
+         RowBox[{
+          RowBox[{"-", "\[ImaginaryI]"}], " ", "t", " ", "\[Omega]rf"}]], " ",
+         "\[CapitalOmega]rf"}], "-", 
+       RowBox[{
+        FractionBox["1", "2"], " ", "\[ImaginaryI]", " ", 
+        SuperscriptBox["\[ExponentialE]", 
+         RowBox[{"\[ImaginaryI]", " ", "t", " ", "\[Omega]rf"}]], " ", 
+        "\[CapitalOmega]rf"}]}], "0", "0"},
+     {"0", "0", 
+      RowBox[{
+       RowBox[{"-", "\[CapitalDelta]"}], "+", "\[CapitalDelta]0"}], "0"},
+     {
+      RowBox[{
+       RowBox[{
+        SuperscriptBox["\[ExponentialE]", 
+         RowBox[{"\[ImaginaryI]", " ", "\[Phi]x"}]], " ", 
+        "\[CapitalOmega]Rx"}], "+", 
+       RowBox[{"\[ImaginaryI]", " ", 
+        SuperscriptBox["\[ExponentialE]", 
+         RowBox[{"\[ImaginaryI]", " ", "\[Phi]y"}]], " ", 
+        "\[CapitalOmega]Ry"}]}], "0", "0", 
+      RowBox[{
+       RowBox[{"-", "\[CapitalDelta]"}], "-", "\[CapitalOmega]L", "-", 
+       RowBox[{
+        FractionBox["1", "2"], " ", "\[ImaginaryI]", " ", 
+        SuperscriptBox["\[ExponentialE]", 
+         RowBox[{
+          RowBox[{"-", "\[ImaginaryI]"}], " ", "t", " ", "\[Omega]rf"}]], " ",
+         "\[CapitalOmega]rf"}], "+", 
+       RowBox[{
+        FractionBox["1", "2"], " ", "\[ImaginaryI]", " ", 
+        SuperscriptBox["\[ExponentialE]", 
+         RowBox[{"\[ImaginaryI]", " ", "t", " ", "\[Omega]rf"}]], " ", 
+        "\[CapitalOmega]rf"}]}]}
+    },
+    GridBoxAlignment->{
+     "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
+      "RowsIndexed" -> {}},
+    GridBoxSpacings->{"Columns" -> {
+        Offset[0.27999999999999997`], {
+         Offset[0.7]}, 
+        Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
+        Offset[0.2], {
+         Offset[0.4]}, 
+        Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
+  Function[BoxForm`e$, 
+   MatrixForm[BoxForm`e$]]]], "Output"]
+}, Open  ]],
+
+Cell[TextData[{
+ Cell[BoxData[
+  ButtonBox["IntrinsicRelaxation",
+   BaseStyle->"Link",
+   ButtonData->"paclet:AtomicDensityMatrix/ref/IntrinsicRelaxation"]]],
+ " and ",
+ Cell[BoxData[
+  ButtonBox["TransitRelaxation",
+   BaseStyle->"Link",
+   ButtonData->"paclet:AtomicDensityMatrix/ref/TransitRelaxation"]]],
+ " supply the relaxation matrices."
+}], "MathCaption",
+ CellID->610306692],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"MatrixForm", "[", 
+  RowBox[{"relax", "=", 
+   RowBox[{
+    RowBox[{"IntrinsicRelaxation", "[", "system", "]"}], "+", 
+    RowBox[{"TransitRelaxation", "[", 
+     RowBox[{"system", ",", "\[Gamma]t"}], "]"}]}]}], "]"}]], "Input",
+ CellID->645617687],
+
+Cell[BoxData[
+ TagBox[
+  RowBox[{"(", "\[NoBreak]", GridBox[{
+     {"\[Gamma]t", "0", "0", "0"},
+     {"0", 
+      RowBox[{"\[CapitalGamma]", "+", "\[Gamma]t"}], "0", "0"},
+     {"0", "0", 
+      RowBox[{"\[CapitalGamma]", "+", "\[Gamma]t"}], "0"},
+     {"0", "0", "0", 
+      RowBox[{"\[CapitalGamma]", "+", "\[Gamma]t"}]}
+    },
+    GridBoxAlignment->{
+     "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
+      "RowsIndexed" -> {}},
+    GridBoxSpacings->{"Columns" -> {
+        Offset[0.27999999999999997`], {
+         Offset[0.7]}, 
+        Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
+        Offset[0.2], {
+         Offset[0.4]}, 
+        Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
+  Function[BoxForm`e$, 
+   MatrixForm[BoxForm`e$]]]], "Output"]
+}, Open  ]],
+
+Cell["Remove explict time dependence from the density matrix.", "MathCaption",
+ CellID->690131918],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"SetOptions", "[", 
+  RowBox[{"DensityMatrix", ",", 
+   RowBox[{"TimeDependence", "\[Rule]", "False"}], ",", 
+   RowBox[{"ComplexExpandVariables", "\[Rule]", "False"}]}], "]"}]], "Input",
+ CellID->718931880],
+
+Cell[BoxData[
+ RowBox[{"{", 
+  RowBox[{
+   RowBox[{"TimeDependence", "\[Rule]", "False"}], ",", 
+   RowBox[{"Representation", "\[Rule]", "Zeeman"}], ",", 
+   RowBox[{"DMSymbol", "\[Rule]", "\[Rho]"}], ",", 
+   RowBox[{"Label", "\[Rule]", "None"}], ",", 
+   RowBox[{"ComplexExpandVariables", "\[Rule]", "False"}], ",", 
+   RowBox[{"TimeVariable", "\[Rule]", "t"}]}], "}"}]], "Output",
+ ImageSize->{432, 33},
+ ImageMargins->{{0, 0}, {0, 0}},
+ ImageRegion->{{0, 1}, {0, 1}}]
+}, Open  ]],
+
+Cell[TextData[{
+ Cell[BoxData[
+  ButtonBox["OpticalRepopulation",
+   BaseStyle->"Link",
+   ButtonData->"paclet:AtomicDensityMatrix/ref/OpticalRepopulation"]]],
+ " and ",
+ Cell[BoxData[
+  ButtonBox["TransitRepopulation",
+   BaseStyle->"Link",
+   ButtonData->"paclet:AtomicDensityMatrix/ref/TransitRepopulation"]]],
+ " supply the repopulation matrices."
+}], "MathCaption",
+ CellID->854192725],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"MatrixForm", "[", 
+  RowBox[{"repop", "=", 
+   RowBox[{
+    RowBox[{
+     RowBox[{"OpticalRepopulation", "[", "system", "]"}], "+", 
+     RowBox[{"TransitRepopulation", "[", 
+      RowBox[{"system", ",", "\[Gamma]t"}], "]"}]}], "/.", 
+    RowBox[{
+     RowBox[{"BranchingRatio", "[", 
+      RowBox[{"a_", ",", "b_"}], "]"}], "\[Rule]", 
+     SubscriptBox["R", 
+      RowBox[{"a", ",", "b"}]]}]}]}], "]"}]], "Input",
+ CellID->465762594],
+
+Cell[BoxData[
+ TagBox[
+  RowBox[{"(", "\[NoBreak]", GridBox[{
+     {
+      RowBox[{"\[Gamma]t", "+", 
+       RowBox[{"\[CapitalGamma]", " ", 
+        SubscriptBox["\[Rho]", 
+         RowBox[{
+          RowBox[{"{", 
+           RowBox[{"2", ",", 
+            RowBox[{"-", "1"}]}], "}"}], ",", 
+          RowBox[{"{", 
+           RowBox[{"2", ",", 
+            RowBox[{"-", "1"}]}], "}"}]}]]}], "+", 
+       RowBox[{"\[CapitalGamma]", " ", 
+        SubscriptBox["\[Rho]", 
+         RowBox[{
+          RowBox[{"{", 
+           RowBox[{"2", ",", "0"}], "}"}], ",", 
+          RowBox[{"{", 
+           RowBox[{"2", ",", "0"}], "}"}]}]]}], "+", 
+       RowBox[{"\[CapitalGamma]", " ", 
+        SubscriptBox["\[Rho]", 
+         RowBox[{
+          RowBox[{"{", 
+           RowBox[{"2", ",", "1"}], "}"}], ",", 
+          RowBox[{"{", 
+           RowBox[{"2", ",", "1"}], "}"}]}]]}]}], "0", "0", "0"},
+     {"0", "0", "0", "0"},
+     {"0", "0", "0", "0"},
+     {"0", "0", "0", "0"}
+    },
+    GridBoxAlignment->{
+     "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
+      "RowsIndexed" -> {}},
+    GridBoxSpacings->{"Columns" -> {
+        Offset[0.27999999999999997`], {
+         Offset[0.7]}, 
+        Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
+        Offset[0.2], {
+         Offset[0.4]}, 
+        Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
+  Function[BoxForm`e$, 
+   MatrixForm[BoxForm`e$]]]], "Output"]
+}, Open  ]],
+
+Cell["Here are the evolution equations.", "MathCaption",
+ CellID->314466782],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"TableForm", "[", 
+  RowBox[{
+   RowBox[{"eqs", "=", 
+    RowBox[{
+     RowBox[{"LiouvilleEquation", "[", 
+      RowBox[{"system", ",", "Hrwa", ",", "relax", ",", "repop"}], "]"}], "//",
+      "Expand"}]}], ",", 
+   RowBox[{"TableHeadings", "\[Rule]", 
+    RowBox[{"{", 
+     RowBox[{
+      RowBox[{"DMVariables", "[", "system", "]"}], ",", "None"}], "}"}]}]}], 
+  "]"}]], "Input",
+ CellID->298399236],
+
+Cell[BoxData[
+ TagBox[
+  TagBox[GridBox[{
+     {
+      TagBox[
+       SubscriptBox["\[Rho]", 
+        RowBox[{
+         RowBox[{"{", 
+          RowBox[{"1", ",", "0"}], "}"}], ",", 
+         RowBox[{"{", 
+          RowBox[{"1", ",", "0"}], "}"}]}]],
+       HoldForm], 
+      RowBox[{"0", "\[Equal]", 
+       RowBox[{"\[Gamma]t", "-", 
+        RowBox[{"\[Gamma]t", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}]}]]}], "+", 
+        RowBox[{"\[ImaginaryI]", " ", 
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{"\[ImaginaryI]", " ", "\[Phi]x"}]], " ", 
+         "\[CapitalOmega]Rx", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}]}]]}], "-", 
+        RowBox[{
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{"\[ImaginaryI]", " ", "\[Phi]y"}]], " ", 
+         "\[CapitalOmega]Ry", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}]}]]}], "-", 
+        RowBox[{"\[ImaginaryI]", " ", 
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{"\[ImaginaryI]", " ", "\[Phi]x"}]], " ", 
+         "\[CapitalOmega]Rx", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}]}]]}], "-", 
+        RowBox[{
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{"\[ImaginaryI]", " ", "\[Phi]y"}]], " ", 
+         "\[CapitalOmega]Ry", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}]}]]}], "-", 
+        RowBox[{"\[ImaginaryI]", " ", 
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{
+           RowBox[{"-", "\[ImaginaryI]"}], " ", "\[Phi]x"}]], " ", 
+         "\[CapitalOmega]Rx", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}]}]]}], "-", 
+        RowBox[{
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{
+           RowBox[{"-", "\[ImaginaryI]"}], " ", "\[Phi]y"}]], " ", 
+         "\[CapitalOmega]Ry", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}]}]]}], "+", 
+        RowBox[{"\[CapitalGamma]", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}]}]]}], "+", 
+        RowBox[{"\[CapitalGamma]", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}]}]]}], "+", 
+        RowBox[{"\[ImaginaryI]", " ", 
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{
+           RowBox[{"-", "\[ImaginaryI]"}], " ", "\[Phi]x"}]], " ", 
+         "\[CapitalOmega]Rx", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}]}]]}], "-", 
+        RowBox[{
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{
+           RowBox[{"-", "\[ImaginaryI]"}], " ", "\[Phi]y"}]], " ", 
+         "\[CapitalOmega]Ry", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}]}]]}], "+", 
+        RowBox[{"\[CapitalGamma]", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}]}]]}]}]}]},
+     {
+      TagBox[
+       SubscriptBox["\[Rho]", 
+        RowBox[{
+         RowBox[{"{", 
+          RowBox[{"1", ",", "0"}], "}"}], ",", 
+         RowBox[{"{", 
+          RowBox[{"2", ",", "1"}], "}"}]}]],
+       HoldForm], 
+      RowBox[{"0", "\[Equal]", 
+       RowBox[{
+        RowBox[{
+         RowBox[{"-", "\[ImaginaryI]"}], " ", 
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{
+           RowBox[{"-", "\[ImaginaryI]"}], " ", "\[Phi]x"}]], " ", 
+         "\[CapitalOmega]Rx", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}]}]]}], "+", 
+        RowBox[{
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{
+           RowBox[{"-", "\[ImaginaryI]"}], " ", "\[Phi]y"}]], " ", 
+         "\[CapitalOmega]Ry", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}]}]]}], "-", 
+        RowBox[{
+         FractionBox["1", "2"], " ", "\[CapitalGamma]", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}]}]]}], "-", 
+        RowBox[{"\[Gamma]t", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}]}]]}], "-", 
+        RowBox[{"\[ImaginaryI]", " ", "\[CapitalDelta]", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}]}]]}], "+", 
+        RowBox[{"\[ImaginaryI]", " ", "\[CapitalOmega]L", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}]}]]}], "-", 
+        RowBox[{
+         FractionBox["1", "2"], " ", 
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{
+           RowBox[{"-", "\[ImaginaryI]"}], " ", "t", " ", "\[Omega]rf"}]], 
+         " ", "\[CapitalOmega]rf", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}]}]]}], "+", 
+        RowBox[{
+         FractionBox["1", "2"], " ", 
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{"\[ImaginaryI]", " ", "t", " ", "\[Omega]rf"}]], " ", 
+         "\[CapitalOmega]rf", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}]}]]}], "-", 
+        RowBox[{"\[ImaginaryI]", " ", 
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{
+           RowBox[{"-", "\[ImaginaryI]"}], " ", "\[Phi]x"}]], " ", 
+         "\[CapitalOmega]Rx", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}]}]]}], "-", 
+        RowBox[{
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{
+           RowBox[{"-", "\[ImaginaryI]"}], " ", "\[Phi]y"}]], " ", 
+         "\[CapitalOmega]Ry", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}]}]]}], "+", 
+        RowBox[{"\[ImaginaryI]", " ", 
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{
+           RowBox[{"-", "\[ImaginaryI]"}], " ", "\[Phi]x"}]], " ", 
+         "\[CapitalOmega]Rx", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}]}]]}], "-", 
+        RowBox[{
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{
+           RowBox[{"-", "\[ImaginaryI]"}], " ", "\[Phi]y"}]], " ", 
+         "\[CapitalOmega]Ry", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}]}]]}]}]}]},
+     {
+      TagBox[
+       SubscriptBox["\[Rho]", 
+        RowBox[{
+         RowBox[{"{", 
+          RowBox[{"1", ",", "0"}], "}"}], ",", 
+         RowBox[{"{", 
+          RowBox[{"2", ",", "0"}], "}"}]}]],
+       HoldForm], 
+      RowBox[{"0", "\[Equal]", 
+       RowBox[{
+        RowBox[{
+         RowBox[{"-", 
+          FractionBox["1", "2"]}], " ", "\[CapitalGamma]", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}]}]]}], "-", 
+        RowBox[{"\[Gamma]t", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}]}]]}], "-", 
+        RowBox[{"\[ImaginaryI]", " ", "\[CapitalDelta]", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}]}]]}], "+", 
+        RowBox[{"\[ImaginaryI]", " ", "\[CapitalDelta]0", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}]}]]}], "-", 
+        RowBox[{"\[ImaginaryI]", " ", 
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{
+           RowBox[{"-", "\[ImaginaryI]"}], " ", "\[Phi]x"}]], " ", 
+         "\[CapitalOmega]Rx", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}]}]]}], "-", 
+        RowBox[{
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{
+           RowBox[{"-", "\[ImaginaryI]"}], " ", "\[Phi]y"}]], " ", 
+         "\[CapitalOmega]Ry", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}]}]]}], "+", 
+        RowBox[{"\[ImaginaryI]", " ", 
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{
+           RowBox[{"-", "\[ImaginaryI]"}], " ", "\[Phi]x"}]], " ", 
+         "\[CapitalOmega]Rx", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}]}]]}], "-", 
+        RowBox[{
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{
+           RowBox[{"-", "\[ImaginaryI]"}], " ", "\[Phi]y"}]], " ", 
+         "\[CapitalOmega]Ry", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}]}]]}]}]}]},
+     {
+      TagBox[
+       SubscriptBox["\[Rho]", 
+        RowBox[{
+         RowBox[{"{", 
+          RowBox[{"1", ",", "0"}], "}"}], ",", 
+         RowBox[{"{", 
+          RowBox[{"2", ",", 
+           RowBox[{"-", "1"}]}], "}"}]}]],
+       HoldForm], 
+      RowBox[{"0", "\[Equal]", 
+       RowBox[{
+        RowBox[{"\[ImaginaryI]", " ", 
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{
+           RowBox[{"-", "\[ImaginaryI]"}], " ", "\[Phi]x"}]], " ", 
+         "\[CapitalOmega]Rx", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}]}]]}], "+", 
+        RowBox[{
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{
+           RowBox[{"-", "\[ImaginaryI]"}], " ", "\[Phi]y"}]], " ", 
+         "\[CapitalOmega]Ry", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}]}]]}], "-", 
+        RowBox[{
+         FractionBox["1", "2"], " ", "\[CapitalGamma]", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}]}]]}], "-", 
+        RowBox[{"\[Gamma]t", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}]}]]}], "-", 
+        RowBox[{"\[ImaginaryI]", " ", "\[CapitalDelta]", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}]}]]}], "-", 
+        RowBox[{"\[ImaginaryI]", " ", "\[CapitalOmega]L", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}]}]]}], "+", 
+        RowBox[{
+         FractionBox["1", "2"], " ", 
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{
+           RowBox[{"-", "\[ImaginaryI]"}], " ", "t", " ", "\[Omega]rf"}]], 
+         " ", "\[CapitalOmega]rf", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}]}]]}], "-", 
+        RowBox[{
+         FractionBox["1", "2"], " ", 
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{"\[ImaginaryI]", " ", "t", " ", "\[Omega]rf"}]], " ", 
+         "\[CapitalOmega]rf", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}]}]]}], "-", 
+        RowBox[{"\[ImaginaryI]", " ", 
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{
+           RowBox[{"-", "\[ImaginaryI]"}], " ", "\[Phi]x"}]], " ", 
+         "\[CapitalOmega]Rx", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}]}]]}], "-", 
+        RowBox[{
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{
+           RowBox[{"-", "\[ImaginaryI]"}], " ", "\[Phi]y"}]], " ", 
+         "\[CapitalOmega]Ry", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}]}]]}], "+", 
+        RowBox[{"\[ImaginaryI]", " ", 
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{
+           RowBox[{"-", "\[ImaginaryI]"}], " ", "\[Phi]x"}]], " ", 
+         "\[CapitalOmega]Rx", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}]}]]}], "-", 
+        RowBox[{
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{
+           RowBox[{"-", "\[ImaginaryI]"}], " ", "\[Phi]y"}]], " ", 
+         "\[CapitalOmega]Ry", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}]}]]}]}]}]},
+     {
+      TagBox[
+       SubscriptBox["\[Rho]", 
+        RowBox[{
+         RowBox[{"{", 
+          RowBox[{"2", ",", "1"}], "}"}], ",", 
+         RowBox[{"{", 
+          RowBox[{"1", ",", "0"}], "}"}]}]],
+       HoldForm], 
+      RowBox[{"0", "\[Equal]", 
+       RowBox[{
+        RowBox[{"\[ImaginaryI]", " ", 
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{"\[ImaginaryI]", " ", "\[Phi]x"}]], " ", 
+         "\[CapitalOmega]Rx", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}]}]]}], "+", 
+        RowBox[{
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{"\[ImaginaryI]", " ", "\[Phi]y"}]], " ", 
+         "\[CapitalOmega]Ry", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}]}]]}], "-", 
+        RowBox[{
+         FractionBox["1", "2"], " ", "\[CapitalGamma]", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}]}]]}], "-", 
+        RowBox[{"\[Gamma]t", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}]}]]}], "+", 
+        RowBox[{"\[ImaginaryI]", " ", "\[CapitalDelta]", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}]}]]}], "-", 
+        RowBox[{"\[ImaginaryI]", " ", "\[CapitalOmega]L", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}]}]]}], "+", 
+        RowBox[{
+         FractionBox["1", "2"], " ", 
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{
+           RowBox[{"-", "\[ImaginaryI]"}], " ", "t", " ", "\[Omega]rf"}]], 
+         " ", "\[CapitalOmega]rf", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}]}]]}], "-", 
+        RowBox[{
+         FractionBox["1", "2"], " ", 
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{"\[ImaginaryI]", " ", "t", " ", "\[Omega]rf"}]], " ", 
+         "\[CapitalOmega]rf", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}]}]]}], "+", 
+        RowBox[{"\[ImaginaryI]", " ", 
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{"\[ImaginaryI]", " ", "\[Phi]x"}]], " ", 
+         "\[CapitalOmega]Rx", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}]}]]}], "-", 
+        RowBox[{
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{"\[ImaginaryI]", " ", "\[Phi]y"}]], " ", 
+         "\[CapitalOmega]Ry", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}]}]]}], "-", 
+        RowBox[{"\[ImaginaryI]", " ", 
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{"\[ImaginaryI]", " ", "\[Phi]x"}]], " ", 
+         "\[CapitalOmega]Rx", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}]}]]}], "-", 
+        RowBox[{
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{"\[ImaginaryI]", " ", "\[Phi]y"}]], " ", 
+         "\[CapitalOmega]Ry", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}]}]]}]}]}]},
+     {
+      TagBox[
+       SubscriptBox["\[Rho]", 
+        RowBox[{
+         RowBox[{"{", 
+          RowBox[{"2", ",", "1"}], "}"}], ",", 
+         RowBox[{"{", 
+          RowBox[{"2", ",", "1"}], "}"}]}]],
+       HoldForm], 
+      RowBox[{"0", "\[Equal]", 
+       RowBox[{
+        RowBox[{"\[ImaginaryI]", " ", 
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{"\[ImaginaryI]", " ", "\[Phi]x"}]], " ", 
+         "\[CapitalOmega]Rx", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}]}]]}], "+", 
+        RowBox[{
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{"\[ImaginaryI]", " ", "\[Phi]y"}]], " ", 
+         "\[CapitalOmega]Ry", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}]}]]}], "-", 
+        RowBox[{"\[ImaginaryI]", " ", 
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{
+           RowBox[{"-", "\[ImaginaryI]"}], " ", "\[Phi]x"}]], " ", 
+         "\[CapitalOmega]Rx", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}]}]]}], "+", 
+        RowBox[{
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{
+           RowBox[{"-", "\[ImaginaryI]"}], " ", "\[Phi]y"}]], " ", 
+         "\[CapitalOmega]Ry", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}]}]]}], "-", 
+        RowBox[{"\[CapitalGamma]", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}]}]]}], "-", 
+        RowBox[{"\[Gamma]t", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}]}]]}]}]}]},
+     {
+      TagBox[
+       SubscriptBox["\[Rho]", 
+        RowBox[{
+         RowBox[{"{", 
+          RowBox[{"2", ",", "1"}], "}"}], ",", 
+         RowBox[{"{", 
+          RowBox[{"2", ",", "0"}], "}"}]}]],
+       HoldForm], 
+      RowBox[{"0", "\[Equal]", 
+       RowBox[{
+        RowBox[{"\[ImaginaryI]", " ", 
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{"\[ImaginaryI]", " ", "\[Phi]x"}]], " ", 
+         "\[CapitalOmega]Rx", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}]}]]}], "+", 
+        RowBox[{
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{"\[ImaginaryI]", " ", "\[Phi]y"}]], " ", 
+         "\[CapitalOmega]Ry", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}]}]]}], "-", 
+        RowBox[{"\[CapitalGamma]", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}]}]]}], "-", 
+        RowBox[{"\[Gamma]t", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}]}]]}], "+", 
+        RowBox[{"\[ImaginaryI]", " ", "\[CapitalDelta]0", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}]}]]}], "-", 
+        RowBox[{"\[ImaginaryI]", " ", "\[CapitalOmega]L", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}]}]]}], "+", 
+        RowBox[{
+         FractionBox["1", "2"], " ", 
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{
+           RowBox[{"-", "\[ImaginaryI]"}], " ", "t", " ", "\[Omega]rf"}]], 
+         " ", "\[CapitalOmega]rf", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}]}]]}], "-", 
+        RowBox[{
+         FractionBox["1", "2"], " ", 
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{"\[ImaginaryI]", " ", "t", " ", "\[Omega]rf"}]], " ", 
+         "\[CapitalOmega]rf", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}]}]]}]}]}]},
+     {
+      TagBox[
+       SubscriptBox["\[Rho]", 
+        RowBox[{
+         RowBox[{"{", 
+          RowBox[{"2", ",", "1"}], "}"}], ",", 
+         RowBox[{"{", 
+          RowBox[{"2", ",", 
+           RowBox[{"-", "1"}]}], "}"}]}]],
+       HoldForm], 
+      RowBox[{"0", "\[Equal]", 
+       RowBox[{
+        RowBox[{"\[ImaginaryI]", " ", 
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{"\[ImaginaryI]", " ", "\[Phi]x"}]], " ", 
+         "\[CapitalOmega]Rx", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}]}]]}], "+", 
+        RowBox[{
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{"\[ImaginaryI]", " ", "\[Phi]y"}]], " ", 
+         "\[CapitalOmega]Ry", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}]}]]}], "+", 
+        RowBox[{"\[ImaginaryI]", " ", 
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{
+           RowBox[{"-", "\[ImaginaryI]"}], " ", "\[Phi]x"}]], " ", 
+         "\[CapitalOmega]Rx", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}]}]]}], "+", 
+        RowBox[{
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{
+           RowBox[{"-", "\[ImaginaryI]"}], " ", "\[Phi]y"}]], " ", 
+         "\[CapitalOmega]Ry", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}]}]]}], "-", 
+        RowBox[{"\[CapitalGamma]", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}]}]]}], "-", 
+        RowBox[{"\[Gamma]t", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}]}]]}], "-", 
+        RowBox[{"2", " ", "\[ImaginaryI]", " ", "\[CapitalOmega]L", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}]}]]}], "+", 
+        RowBox[{
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{
+           RowBox[{"-", "\[ImaginaryI]"}], " ", "t", " ", "\[Omega]rf"}]], 
+         " ", "\[CapitalOmega]rf", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}]}]]}], "-", 
+        RowBox[{
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{"\[ImaginaryI]", " ", "t", " ", "\[Omega]rf"}]], " ", 
+         "\[CapitalOmega]rf", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}]}]]}]}]}]},
+     {
+      TagBox[
+       SubscriptBox["\[Rho]", 
+        RowBox[{
+         RowBox[{"{", 
+          RowBox[{"2", ",", "0"}], "}"}], ",", 
+         RowBox[{"{", 
+          RowBox[{"1", ",", "0"}], "}"}]}]],
+       HoldForm], 
+      RowBox[{"0", "\[Equal]", 
+       RowBox[{
+        RowBox[{
+         RowBox[{"-", 
+          FractionBox["1", "2"]}], " ", "\[CapitalGamma]", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}]}]]}], "-", 
+        RowBox[{"\[Gamma]t", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}]}]]}], "+", 
+        RowBox[{"\[ImaginaryI]", " ", "\[CapitalDelta]", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}]}]]}], "-", 
+        RowBox[{"\[ImaginaryI]", " ", "\[CapitalDelta]0", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}]}]]}], "+", 
+        RowBox[{"\[ImaginaryI]", " ", 
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{"\[ImaginaryI]", " ", "\[Phi]x"}]], " ", 
+         "\[CapitalOmega]Rx", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}]}]]}], "-", 
+        RowBox[{
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{"\[ImaginaryI]", " ", "\[Phi]y"}]], " ", 
+         "\[CapitalOmega]Ry", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}]}]]}], "-", 
+        RowBox[{"\[ImaginaryI]", " ", 
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{"\[ImaginaryI]", " ", "\[Phi]x"}]], " ", 
+         "\[CapitalOmega]Rx", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}]}]]}], "-", 
+        RowBox[{
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{"\[ImaginaryI]", " ", "\[Phi]y"}]], " ", 
+         "\[CapitalOmega]Ry", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}]}]]}]}]}]},
+     {
+      TagBox[
+       SubscriptBox["\[Rho]", 
+        RowBox[{
+         RowBox[{"{", 
+          RowBox[{"2", ",", "0"}], "}"}], ",", 
+         RowBox[{"{", 
+          RowBox[{"2", ",", "1"}], "}"}]}]],
+       HoldForm], 
+      RowBox[{"0", "\[Equal]", 
+       RowBox[{
+        RowBox[{
+         RowBox[{"-", "\[ImaginaryI]"}], " ", 
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{
+           RowBox[{"-", "\[ImaginaryI]"}], " ", "\[Phi]x"}]], " ", 
+         "\[CapitalOmega]Rx", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}]}]]}], "+", 
+        RowBox[{
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{
+           RowBox[{"-", "\[ImaginaryI]"}], " ", "\[Phi]y"}]], " ", 
+         "\[CapitalOmega]Ry", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}]}]]}], "-", 
+        RowBox[{"\[CapitalGamma]", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}]}]]}], "-", 
+        RowBox[{"\[Gamma]t", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}]}]]}], "-", 
+        RowBox[{"\[ImaginaryI]", " ", "\[CapitalDelta]0", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}]}]]}], "+", 
+        RowBox[{"\[ImaginaryI]", " ", "\[CapitalOmega]L", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}]}]]}], "-", 
+        RowBox[{
+         FractionBox["1", "2"], " ", 
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{
+           RowBox[{"-", "\[ImaginaryI]"}], " ", "t", " ", "\[Omega]rf"}]], 
+         " ", "\[CapitalOmega]rf", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}]}]]}], "+", 
+        RowBox[{
+         FractionBox["1", "2"], " ", 
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{"\[ImaginaryI]", " ", "t", " ", "\[Omega]rf"}]], " ", 
+         "\[CapitalOmega]rf", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}]}]]}]}]}]},
+     {
+      TagBox[
+       SubscriptBox["\[Rho]", 
+        RowBox[{
+         RowBox[{"{", 
+          RowBox[{"2", ",", "0"}], "}"}], ",", 
+         RowBox[{"{", 
+          RowBox[{"2", ",", "0"}], "}"}]}]],
+       HoldForm], 
+      RowBox[{"0", "\[Equal]", 
+       RowBox[{
+        RowBox[{
+         RowBox[{"-", "\[CapitalGamma]"}], " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}]}]]}], "-", 
+        RowBox[{"\[Gamma]t", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}]}]]}]}]}]},
+     {
+      TagBox[
+       SubscriptBox["\[Rho]", 
+        RowBox[{
+         RowBox[{"{", 
+          RowBox[{"2", ",", "0"}], "}"}], ",", 
+         RowBox[{"{", 
+          RowBox[{"2", ",", 
+           RowBox[{"-", "1"}]}], "}"}]}]],
+       HoldForm], 
+      RowBox[{"0", "\[Equal]", 
+       RowBox[{
+        RowBox[{"\[ImaginaryI]", " ", 
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{
+           RowBox[{"-", "\[ImaginaryI]"}], " ", "\[Phi]x"}]], " ", 
+         "\[CapitalOmega]Rx", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}]}]]}], "+", 
+        RowBox[{
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{
+           RowBox[{"-", "\[ImaginaryI]"}], " ", "\[Phi]y"}]], " ", 
+         "\[CapitalOmega]Ry", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}]}]]}], "-", 
+        RowBox[{"\[CapitalGamma]", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}]}]]}], "-", 
+        RowBox[{"\[Gamma]t", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}]}]]}], "-", 
+        RowBox[{"\[ImaginaryI]", " ", "\[CapitalDelta]0", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}]}]]}], "-", 
+        RowBox[{"\[ImaginaryI]", " ", "\[CapitalOmega]L", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}]}]]}], "+", 
+        RowBox[{
+         FractionBox["1", "2"], " ", 
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{
+           RowBox[{"-", "\[ImaginaryI]"}], " ", "t", " ", "\[Omega]rf"}]], 
+         " ", "\[CapitalOmega]rf", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}]}]]}], "-", 
+        RowBox[{
+         FractionBox["1", "2"], " ", 
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{"\[ImaginaryI]", " ", "t", " ", "\[Omega]rf"}]], " ", 
+         "\[CapitalOmega]rf", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}]}]]}]}]}]},
+     {
+      TagBox[
+       SubscriptBox["\[Rho]", 
+        RowBox[{
+         RowBox[{"{", 
+          RowBox[{"2", ",", 
+           RowBox[{"-", "1"}]}], "}"}], ",", 
+         RowBox[{"{", 
+          RowBox[{"1", ",", "0"}], "}"}]}]],
+       HoldForm], 
+      RowBox[{"0", "\[Equal]", 
+       RowBox[{
+        RowBox[{
+         RowBox[{"-", "\[ImaginaryI]"}], " ", 
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{"\[ImaginaryI]", " ", "\[Phi]x"}]], " ", 
+         "\[CapitalOmega]Rx", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}]}]]}], "+", 
+        RowBox[{
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{"\[ImaginaryI]", " ", "\[Phi]y"}]], " ", 
+         "\[CapitalOmega]Ry", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}]}]]}], "-", 
+        RowBox[{
+         FractionBox["1", "2"], " ", "\[CapitalGamma]", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}]}]]}], "-", 
+        RowBox[{"\[Gamma]t", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}]}]]}], "+", 
+        RowBox[{"\[ImaginaryI]", " ", "\[CapitalDelta]", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}]}]]}], "+", 
+        RowBox[{"\[ImaginaryI]", " ", "\[CapitalOmega]L", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}]}]]}], "-", 
+        RowBox[{
+         FractionBox["1", "2"], " ", 
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{
+           RowBox[{"-", "\[ImaginaryI]"}], " ", "t", " ", "\[Omega]rf"}]], 
+         " ", "\[CapitalOmega]rf", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}]}]]}], "+", 
+        RowBox[{
+         FractionBox["1", "2"], " ", 
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{"\[ImaginaryI]", " ", "t", " ", "\[Omega]rf"}]], " ", 
+         "\[CapitalOmega]rf", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}]}]]}], "+", 
+        RowBox[{"\[ImaginaryI]", " ", 
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{"\[ImaginaryI]", " ", "\[Phi]x"}]], " ", 
+         "\[CapitalOmega]Rx", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}]}]]}], "-", 
+        RowBox[{
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{"\[ImaginaryI]", " ", "\[Phi]y"}]], " ", 
+         "\[CapitalOmega]Ry", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}]}]]}], "-", 
+        RowBox[{"\[ImaginaryI]", " ", 
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{"\[ImaginaryI]", " ", "\[Phi]x"}]], " ", 
+         "\[CapitalOmega]Rx", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}]}]]}], "-", 
+        RowBox[{
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{"\[ImaginaryI]", " ", "\[Phi]y"}]], " ", 
+         "\[CapitalOmega]Ry", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}]}]]}]}]}]},
+     {
+      TagBox[
+       SubscriptBox["\[Rho]", 
+        RowBox[{
+         RowBox[{"{", 
+          RowBox[{"2", ",", 
+           RowBox[{"-", "1"}]}], "}"}], ",", 
+         RowBox[{"{", 
+          RowBox[{"2", ",", "1"}], "}"}]}]],
+       HoldForm], 
+      RowBox[{"0", "\[Equal]", 
+       RowBox[{
+        RowBox[{
+         RowBox[{"-", "\[ImaginaryI]"}], " ", 
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{"\[ImaginaryI]", " ", "\[Phi]x"}]], " ", 
+         "\[CapitalOmega]Rx", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}]}]]}], "+", 
+        RowBox[{
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{"\[ImaginaryI]", " ", "\[Phi]y"}]], " ", 
+         "\[CapitalOmega]Ry", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}]}]]}], "-", 
+        RowBox[{"\[ImaginaryI]", " ", 
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{
+           RowBox[{"-", "\[ImaginaryI]"}], " ", "\[Phi]x"}]], " ", 
+         "\[CapitalOmega]Rx", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}]}]]}], "+", 
+        RowBox[{
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{
+           RowBox[{"-", "\[ImaginaryI]"}], " ", "\[Phi]y"}]], " ", 
+         "\[CapitalOmega]Ry", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}]}]]}], "-", 
+        RowBox[{"\[CapitalGamma]", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}]}]]}], "-", 
+        RowBox[{"\[Gamma]t", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}]}]]}], "+", 
+        RowBox[{"2", " ", "\[ImaginaryI]", " ", "\[CapitalOmega]L", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}]}]]}], "-", 
+        RowBox[{
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{
+           RowBox[{"-", "\[ImaginaryI]"}], " ", "t", " ", "\[Omega]rf"}]], 
+         " ", "\[CapitalOmega]rf", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}]}]]}], "+", 
+        RowBox[{
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{"\[ImaginaryI]", " ", "t", " ", "\[Omega]rf"}]], " ", 
+         "\[CapitalOmega]rf", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "1"}], "}"}]}]]}]}]}]},
+     {
+      TagBox[
+       SubscriptBox["\[Rho]", 
+        RowBox[{
+         RowBox[{"{", 
+          RowBox[{"2", ",", 
+           RowBox[{"-", "1"}]}], "}"}], ",", 
+         RowBox[{"{", 
+          RowBox[{"2", ",", "0"}], "}"}]}]],
+       HoldForm], 
+      RowBox[{"0", "\[Equal]", 
+       RowBox[{
+        RowBox[{
+         RowBox[{"-", "\[ImaginaryI]"}], " ", 
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{"\[ImaginaryI]", " ", "\[Phi]x"}]], " ", 
+         "\[CapitalOmega]Rx", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}]}]]}], "+", 
+        RowBox[{
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{"\[ImaginaryI]", " ", "\[Phi]y"}]], " ", 
+         "\[CapitalOmega]Ry", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}]}]]}], "-", 
+        RowBox[{"\[CapitalGamma]", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}]}]]}], "-", 
+        RowBox[{"\[Gamma]t", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}]}]]}], "+", 
+        RowBox[{"\[ImaginaryI]", " ", "\[CapitalDelta]0", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}]}]]}], "+", 
+        RowBox[{"\[ImaginaryI]", " ", "\[CapitalOmega]L", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}]}]]}], "-", 
+        RowBox[{
+         FractionBox["1", "2"], " ", 
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{
+           RowBox[{"-", "\[ImaginaryI]"}], " ", "t", " ", "\[Omega]rf"}]], 
+         " ", "\[CapitalOmega]rf", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}]}]]}], "+", 
+        RowBox[{
+         FractionBox["1", "2"], " ", 
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{"\[ImaginaryI]", " ", "t", " ", "\[Omega]rf"}]], " ", 
+         "\[CapitalOmega]rf", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", "0"}], "}"}]}]]}]}]}]},
+     {
+      TagBox[
+       SubscriptBox["\[Rho]", 
+        RowBox[{
+         RowBox[{"{", 
+          RowBox[{"2", ",", 
+           RowBox[{"-", "1"}]}], "}"}], ",", 
+         RowBox[{"{", 
+          RowBox[{"2", ",", 
+           RowBox[{"-", "1"}]}], "}"}]}]],
+       HoldForm], 
+      RowBox[{"0", "\[Equal]", 
+       RowBox[{
+        RowBox[{
+         RowBox[{"-", "\[ImaginaryI]"}], " ", 
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{"\[ImaginaryI]", " ", "\[Phi]x"}]], " ", 
+         "\[CapitalOmega]Rx", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}]}]]}], "+", 
+        RowBox[{
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{"\[ImaginaryI]", " ", "\[Phi]y"}]], " ", 
+         "\[CapitalOmega]Ry", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}]}]]}], "+", 
+        RowBox[{"\[ImaginaryI]", " ", 
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{
+           RowBox[{"-", "\[ImaginaryI]"}], " ", "\[Phi]x"}]], " ", 
+         "\[CapitalOmega]Rx", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}]}]]}], "+", 
+        RowBox[{
+         SuperscriptBox["\[ExponentialE]", 
+          RowBox[{
+           RowBox[{"-", "\[ImaginaryI]"}], " ", "\[Phi]y"}]], " ", 
+         "\[CapitalOmega]Ry", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"1", ",", "0"}], "}"}]}]]}], "-", 
+        RowBox[{"\[CapitalGamma]", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}]}]]}], "-", 
+        RowBox[{"\[Gamma]t", " ", 
+         SubscriptBox["\[Rho]", 
+          RowBox[{
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}], ",", 
+           RowBox[{"{", 
+            RowBox[{"2", ",", 
+             RowBox[{"-", "1"}]}], "}"}]}]]}]}]}]}
+    },
+    GridBoxAlignment->{
+     "Columns" -> {{Left}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}}, 
+      "RowsIndexed" -> {}},
+    GridBoxDividers->{
+     "Columns" -> {False, {True}, False}, "ColumnsIndexed" -> {}, 
+      "Rows" -> {{False}}, "RowsIndexed" -> {}},
+    GridBoxSpacings->{"Columns" -> {
+        Offset[0.27999999999999997`], {
+         Offset[0.5599999999999999]}, 
+        Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
+        Offset[0.2], {
+         Offset[0.4]}, 
+        Offset[0.2]}, "RowsIndexed" -> {}}],
+   OutputFormsDump`HeadedColumn],
+  Function[BoxForm`e$, 
+   TableForm[BoxForm`e$, TableHeadings -> {{
+       Subscript[AtomicDensityMatrix`DensityMatrix`\[Rho], {1, 0}, {1, 0}], 
+       Subscript[AtomicDensityMatrix`DensityMatrix`\[Rho], {1, 0}, {2, 1}], 
+       Subscript[AtomicDensityMatrix`DensityMatrix`\[Rho], {1, 0}, {2, 0}], 
+       Subscript[AtomicDensityMatrix`DensityMatrix`\[Rho], {1, 0}, {2, -1}], 
+       Subscript[AtomicDensityMatrix`DensityMatrix`\[Rho], {2, 1}, {1, 0}], 
+       Subscript[AtomicDensityMatrix`DensityMatrix`\[Rho], {2, 1}, {2, 1}], 
+       Subscript[AtomicDensityMatrix`DensityMatrix`\[Rho], {2, 1}, {2, 0}], 
+       Subscript[AtomicDensityMatrix`DensityMatrix`\[Rho], {2, 1}, {2, -1}], 
+       Subscript[AtomicDensityMatrix`DensityMatrix`\[Rho], {2, 0}, {1, 0}], 
+       Subscript[AtomicDensityMatrix`DensityMatrix`\[Rho], {2, 0}, {2, 1}], 
+       Subscript[AtomicDensityMatrix`DensityMatrix`\[Rho], {2, 0}, {2, 0}], 
+       Subscript[AtomicDensityMatrix`DensityMatrix`\[Rho], {2, 0}, {2, -1}], 
+       Subscript[AtomicDensityMatrix`DensityMatrix`\[Rho], {2, -1}, {1, 0}], 
+       Subscript[AtomicDensityMatrix`DensityMatrix`\[Rho], {2, -1}, {2, 1}], 
+       Subscript[AtomicDensityMatrix`DensityMatrix`\[Rho], {2, -1}, {2, 0}], 
+       Subscript[AtomicDensityMatrix`DensityMatrix`\[Rho], {2, -1}, {2, -1}]},
+       None}]]]], "Output"]
+}, Open  ]],
+
+Cell["Convert to c form.", "Text"],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[{
+ RowBox[{
+  RowBox[{"MapThread", "[", 
+   RowBox[{"Equal", ",", 
+    RowBox[{"{", 
+     RowBox[{
+      RowBox[{
+       RowBox[{"DMVariables", "[", "system", "]"}], "/.", 
+       RowBox[{"\[Rho]", "\[Rule]", "dr"}]}], ",", 
+      RowBox[{"Collect", "[", 
+       RowBox[{
+        RowBox[{
+         RowBox[{
+          RowBox[{"eqs", "[", 
+           RowBox[{"[", 
+            RowBox[{"All", ",", "2"}], "]"}], "]"}], "/.", 
+          RowBox[{"{", 
+           RowBox[{
+            RowBox[{
+             SuperscriptBox["\[ExponentialE]", 
+              RowBox[{"\[ImaginaryI]", " ", "\[Phi]x"}]], " ", "\[Rule]", 
+             RowBox[{"Ex", "/", "\[CapitalOmega]Rx"}]}], ",", 
+            RowBox[{
+             SuperscriptBox["\[ExponentialE]", 
+              RowBox[{
+               RowBox[{"-", "\[ImaginaryI]"}], " ", "\[Phi]x"}]], " ", 
+             "\[Rule]", 
+             RowBox[{"Exc", "/", "\[CapitalOmega]Rx"}]}], ",", 
+            RowBox[{
+             SuperscriptBox["\[ExponentialE]", 
+              RowBox[{"\[ImaginaryI]", " ", "\[Phi]y"}]], " ", "\[Rule]", 
+             RowBox[{"Ey", "/", "\[CapitalOmega]Ry"}]}], ",", 
+            RowBox[{
+             SuperscriptBox["\[ExponentialE]", 
+              RowBox[{
+               RowBox[{"-", "\[ImaginaryI]"}], " ", "\[Phi]y"}]], " ", 
+             "\[Rule]", 
+             RowBox[{"Eyc", "/", "\[CapitalOmega]Ry"}]}], ",", " ", 
+            RowBox[{"\[Gamma]t", "\[Rule]", "gt"}], ",", 
+            RowBox[{"\[CapitalGamma]", "\[Rule]", "g0"}], ",", 
+            RowBox[{"\[CapitalDelta]0", "\[Rule]", "delta0"}], ",", 
+            RowBox[{"\[CapitalDelta]", "\[Rule]", "delta"}], ",", 
+            RowBox[{"\[CapitalOmega]L", "\[Rule]", "OL"}], ",", 
+            RowBox[{"\[CapitalOmega]rf", "\[Rule]", "Orf"}], ",", 
+            RowBox[{"\[Omega]rf", "\[Rule]", "orf"}]}], "}"}]}], "/.", 
+         RowBox[{"\[Rho]", "\[Rule]", "r"}]}], ",", 
+        RowBox[{"DMElementPattern", "[", "]"}], ",", "FullSimplify"}], 
+       "]"}]}], "}"}]}], "]"}], ";"}], "\[IndentingNewLine]", 
+ RowBox[{
+  RowBox[{
+   RowBox[{
+    RowBox[{"%", "/.", " ", 
+     RowBox[{
+      RowBox[{"Orf", " ", 
+       RowBox[{"Sin", "[", 
+        RowBox[{"orf", " ", "t"}], "]"}]}], "\[Rule]", "rf"}]}], "/.", 
+    RowBox[{
+     RowBox[{"Complex", "[", 
+      RowBox[{"0", ",", "a_"}], "]"}], "\[Rule]", 
+     RowBox[{"a", " ", "i"}]}]}], "/.", 
+   RowBox[{"Table", "[", 
+    RowBox[{
+     RowBox[{
+      RowBox[{"{", 
+       RowBox[{
+        RowBox[{"Label", "[", 
+         RowBox[{"system", "[", 
+          RowBox[{"[", "i", "]"}], "]"}], "]"}], ",", 
+        RowBox[{"M", "[", 
+         RowBox[{"system", "[", 
+          RowBox[{"[", "i", "]"}], "]"}], "]"}]}], "}"}], "\[Rule]", "i"}], 
+     ",", 
+     RowBox[{"{", 
+      RowBox[{"i", ",", 
+       RowBox[{"Length", "[", "system", "]"}]}], "}"}]}], "]"}]}], 
+  ";"}], "\[IndentingNewLine]", 
+ RowBox[{
+  RowBox[{"DeleteCases", "[", 
+   RowBox[{"%", ",", 
+    RowBox[{
+     RowBox[{
+      SubscriptBox["dr", 
+       RowBox[{"a_", ",", "b_"}]], "\[Equal]", "_"}], "/;", 
+     RowBox[{"b", "<", "a"}]}]}], "]"}], ";"}], "\[IndentingNewLine]", 
+ RowBox[{"StringJoin", "[", 
+  RowBox[{
+   RowBox[{
+    RowBox[{"StringReplace", "[", 
+     RowBox[{
+      RowBox[{
+       RowBox[{"ToString", "@", 
+        RowBox[{"CForm", "[", "#", "]"}]}], "<>", "\"\<;\\n\>\""}], ",", 
+      RowBox[{"{", 
+       RowBox[{
+        RowBox[{"\"\<==\>\"", "\[Rule]", "\"\<=\>\""}], ",", 
+        RowBox[{
+         RowBox[{
+         "\"\<Subscript(dr,\>\"", "~~", "a_", "~~", "\"\<,\>\"", "~~", "b_", 
+          "~~", "\"\<)\>\""}], ":>", 
+         RowBox[{"\"\<dr\>\"", "<>", "a", "<>", "b", "<>", "\"\<_dt\>\""}]}], 
+        ",", 
+        RowBox[{
+         RowBox[{
+         "\"\<Subscript(\>\"", "~~", "r_", "~~", "\"\<,\>\"", "~~", "a_", 
+          "~~", "\"\<,\>\"", "~~", "b_", "~~", "\"\<)\>\""}], 
+         "\[RuleDelayed]", 
+         RowBox[{"r", "<>", "a", "<>", "b"}]}]}], "}"}]}], "]"}], "&"}], "/@",
+    "%"}], "]"}], "\[IndentingNewLine]", 
+ RowBox[{"Export", "[", 
+  RowBox[{
+   RowBox[{"ToFileName", "[", 
+    RowBox[{
+     RowBox[{"NotebookDirectory", "[", "]"}], ",", "\"\<code.txt\>\""}], 
+    "]"}], ",", "%"}], "]"}]}], "Input"],
+
+Cell[BoxData["\<\"dr11_dt = gt - gt*r11 + (-Ey - Ex*i)*r12 + i*(Ex + \
+Ey*i)*r14 + i*(Exc + Eyc*i)*r21 + (-Eyc - Exc*i)*r41 + g0*(r22 + r33 + \
+r44);\\ndr12_dt = (2*(Eyc - Exc*i)*r11 - i*((2*delta - (g0 + 2*gt)*i - 2*OL - \
+2*rf)*r12 - 2*(Exc + Eyc*i)*r22 + 2*(Exc - Eyc*i)*r42))/2.;\\ndr13_dt = \
+(-g0/2. - gt - delta*i + delta0*i)*r13 + i*(Exc + Eyc*i)*r23 + (-Eyc - \
+Exc*i)*r43;\\ndr14_dt = -(i*((2*delta - (g0 + 2*gt)*i + 2*OL + 2*rf)*r14 - \
+2*(Exc + Eyc*i)*r24 - 2*(Exc - Eyc*i)*(r11 - r44)))/2.;\\ndr22_dt = (Ey + \
+Ex*i)*r12 + (Eyc - Exc*i)*r21 - (g0 + gt)*r22;\\ndr23_dt = (Ey + Ex*i)*r13 + \
+i*(delta0 + i*(g0 + gt + i*OL) - rf)*r23;\\ndr24_dt = (Ey + Ex*i)*r14 + (Eyc \
++ Exc*i)*r21 - (g0 + gt + 2*i*OL + 2*i*rf)*r24;\\ndr33_dt = -((g0 + gt)*r33);\
+\\ndr34_dt = (Eyc + Exc*i)*r31 - i*(delta0 - (g0 + gt)*i + OL + \
+rf)*r34;\\ndr44_dt = (Ey - Ex*i)*r14 + (Eyc + Exc*i)*r41 - (g0 + \
+gt)*r44;\\n\"\>"], "Output"],
+
+Cell[BoxData["\<\"C:\\\\cygwin\\\\home\\\\Simon\\\\Nresonances\\\\xmds2\\\\\
+Gena_system\\\\code.txt\"\>"], "Output"]
+}, Open  ]],
+
+Cell["Find medium polarization", "Text"],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"TensorForm", "[", 
+  RowBox[{"dcart", "=", 
+   RowBox[{"Most", "@", 
+    RowBox[{"ToCartesian", "@", 
+     RowBox[{"WignerEckart", "[", 
+      RowBox[{"system", ",", 
+       RowBox[{"{", 
+        RowBox[{"Dipole", ",", "1"}], "}"}]}], "]"}]}]}]}], "]"}]], "Input"],
+
+Cell[BoxData[
+ RowBox[{"{", 
+  RowBox[{
+   TagBox[
+    RowBox[{"(", "\[NoBreak]", GridBox[{
+       {"0", 
+        FractionBox[
+         RowBox[{"ReducedME", "[", 
+          RowBox[{"1", ",", 
+           RowBox[{"{", 
+            RowBox[{"Dipole", ",", "1"}], "}"}], ",", "2"}], "]"}], 
+         SqrtBox["6"]], "0", 
+        RowBox[{"-", 
+         FractionBox[
+          RowBox[{"ReducedME", "[", 
+           RowBox[{"1", ",", 
+            RowBox[{"{", 
+             RowBox[{"Dipole", ",", "1"}], "}"}], ",", "2"}], "]"}], 
+          SqrtBox["6"]]}]},
+       {
+        FractionBox[
+         RowBox[{"ReducedME", "[", 
+          RowBox[{"1", ",", 
+           RowBox[{"{", 
+            RowBox[{"Dipole", ",", "1"}], "}"}], ",", "2"}], "]"}], 
+         SqrtBox["6"]], "0", "0", "0"},
+       {"0", "0", "0", "0"},
+       {
+        RowBox[{"-", 
+         FractionBox[
+          RowBox[{"ReducedME", "[", 
+           RowBox[{"1", ",", 
+            RowBox[{"{", 
+             RowBox[{"Dipole", ",", "1"}], "}"}], ",", "2"}], "]"}], 
+          SqrtBox["6"]]}], "0", "0", "0"}
+      },
+      GridBoxAlignment->{
+       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
+        "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
+      GridBoxSpacings->{"Columns" -> {
+          Offset[0.27999999999999997`], {
+           Offset[0.7]}, 
+          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
+          Offset[0.2], {
+           Offset[0.4]}, 
+          Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
+    Function[BoxForm`e$, 
+     MatrixForm[BoxForm`e$]]], ",", 
+   TagBox[
+    RowBox[{"(", "\[NoBreak]", GridBox[{
+       {"0", 
+        FractionBox[
+         RowBox[{"\[ImaginaryI]", " ", 
+          RowBox[{"ReducedME", "[", 
+           RowBox[{"1", ",", 
+            RowBox[{"{", 
+             RowBox[{"Dipole", ",", "1"}], "}"}], ",", "2"}], "]"}]}], 
+         SqrtBox["6"]], "0", 
+        FractionBox[
+         RowBox[{"\[ImaginaryI]", " ", 
+          RowBox[{"ReducedME", "[", 
+           RowBox[{"1", ",", 
+            RowBox[{"{", 
+             RowBox[{"Dipole", ",", "1"}], "}"}], ",", "2"}], "]"}]}], 
+         SqrtBox["6"]]},
+       {
+        RowBox[{"-", 
+         FractionBox[
+          RowBox[{"\[ImaginaryI]", " ", 
+           RowBox[{"ReducedME", "[", 
+            RowBox[{"1", ",", 
+             RowBox[{"{", 
+              RowBox[{"Dipole", ",", "1"}], "}"}], ",", "2"}], "]"}]}], 
+          SqrtBox["6"]]}], "0", "0", "0"},
+       {"0", "0", "0", "0"},
+       {
+        RowBox[{"-", 
+         FractionBox[
+          RowBox[{"\[ImaginaryI]", " ", 
+           RowBox[{"ReducedME", "[", 
+            RowBox[{"1", ",", 
+             RowBox[{"{", 
+              RowBox[{"Dipole", ",", "1"}], "}"}], ",", "2"}], "]"}]}], 
+          SqrtBox["6"]]}], "0", "0", "0"}
+      },
+      GridBoxAlignment->{
+       "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
+        "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
+      GridBoxSpacings->{"Columns" -> {
+          Offset[0.27999999999999997`], {
+           Offset[0.7]}, 
+          Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
+          Offset[0.2], {
+           Offset[0.4]}, 
+          Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}],
+    Function[BoxForm`e$, 
+     MatrixForm[BoxForm`e$]]]}], "}"}]], "Output"]
+}, Open  ]],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[{
+ RowBox[{
+  RowBox[{
+   RowBox[{
+    RowBox[{
+    "4", "\[Pi]", " ", "\[ImaginaryI]", " ", "\[Omega]0", " ", "n", " ", 
+     FractionBox[
+      RowBox[{"ReducedME", "[", 
+       RowBox[{"1", ",", 
+        RowBox[{"{", 
+         RowBox[{"Dipole", ",", "1"}], "}"}], ",", "2"}], "]"}], 
+      RowBox[{"2", 
+       SqrtBox["6"]}]], " ", 
+     RowBox[{"Sum", "[", 
+      RowBox[{
+       RowBox[{
+        RowBox[{
+         RowBox[{"DensityMatrix", "[", "system", "]"}], "[", 
+         RowBox[{"[", 
+          RowBox[{"i", ",", "j"}], "]"}], "]"}], 
+        RowBox[{"#", "[", 
+         RowBox[{"[", 
+          RowBox[{"j", ",", "i"}], "]"}], "]"}]}], ",", 
+       RowBox[{"{", 
+        RowBox[{"i", ",", 
+         RowBox[{"Length", "[", "system", "]"}]}], "}"}], ",", 
+       RowBox[{"{", 
+        RowBox[{"j", ",", "i"}], "}"}]}], "]"}]}], "&"}], "/@", "dcart"}], "//",
+   "Simplify"}], "\[IndentingNewLine]", 
+ RowBox[{
+  RowBox[{
+   RowBox[{"ExpandDipoleRME", "[", 
+    RowBox[{"system", ",", "%"}], " ", "]"}], "/.", 
+   RowBox[{"\[Omega]0", "\[Rule]", 
+    RowBox[{"2", 
+     RowBox[{"\[Pi]", "/", "\[Lambda]"}]}]}]}], "//", 
+  "Simplify"}], "\[IndentingNewLine]", 
+ RowBox[{
+  RowBox[{
+   RowBox[{"%", " ", 
+    RowBox[{"eta", "/", 
+     RowBox[{"(", 
+      FractionBox[
+       RowBox[{"3", " ", "n", " ", "\[CapitalGamma]", " ", 
+        SuperscriptBox["\[Lambda]", "2"], " "}], 
+       RowBox[{"16", " ", "\[Pi]"}]], ")"}]}]}], "/.", 
+   RowBox[{"Table", "[", 
+    RowBox[{
+     RowBox[{
+      RowBox[{"{", 
+       RowBox[{
+        RowBox[{"Label", "[", 
+         RowBox[{"system", "[", 
+          RowBox[{"[", "i", "]"}], "]"}], "]"}], ",", 
+        RowBox[{"M", "[", 
+         RowBox[{"system", "[", 
+          RowBox[{"[", "i", "]"}], "]"}], "]"}]}], "}"}], "\[Rule]", "i"}], 
+     ",", 
+     RowBox[{"{", 
+      RowBox[{"i", ",", 
+       RowBox[{"Length", "[", "system", "]"}]}], "}"}]}], "]"}]}], "/.", 
+  RowBox[{"\[Rho]", "\[Rule]", "r"}]}]}], "Input"],
+
+Cell[BoxData[
+ RowBox[{"{", 
+  RowBox[{
+   RowBox[{
+    RowBox[{"-", 
+     FractionBox["1", "3"]}], " ", "\[ImaginaryI]", " ", "n", " ", "\[Pi]", 
+    " ", "\[Omega]0", " ", 
+    SuperscriptBox[
+     RowBox[{"ReducedME", "[", 
+      RowBox[{"1", ",", 
+       RowBox[{"{", 
+        RowBox[{"Dipole", ",", "1"}], "}"}], ",", "2"}], "]"}], "2"], " ", 
+    RowBox[{"(", 
+     RowBox[{
+      SubscriptBox["\[Rho]", 
+       RowBox[{
+        RowBox[{"{", 
+         RowBox[{"2", ",", 
+          RowBox[{"-", "1"}]}], "}"}], ",", 
+        RowBox[{"{", 
+         RowBox[{"1", ",", "0"}], "}"}]}]], "-", 
+      SubscriptBox["\[Rho]", 
+       RowBox[{
+        RowBox[{"{", 
+         RowBox[{"2", ",", "1"}], "}"}], ",", 
+        RowBox[{"{", 
+         RowBox[{"1", ",", "0"}], "}"}]}]]}], ")"}]}], ",", 
+   RowBox[{
+    RowBox[{"-", 
+     FractionBox["1", "3"]}], " ", "n", " ", "\[Pi]", " ", "\[Omega]0", " ", 
+    SuperscriptBox[
+     RowBox[{"ReducedME", "[", 
+      RowBox[{"1", ",", 
+       RowBox[{"{", 
+        RowBox[{"Dipole", ",", "1"}], "}"}], ",", "2"}], "]"}], "2"], " ", 
+    RowBox[{"(", 
+     RowBox[{
+      SubscriptBox["\[Rho]", 
+       RowBox[{
+        RowBox[{"{", 
+         RowBox[{"2", ",", 
+          RowBox[{"-", "1"}]}], "}"}], ",", 
+        RowBox[{"{", 
+         RowBox[{"1", ",", "0"}], "}"}]}]], "+", 
+      SubscriptBox["\[Rho]", 
+       RowBox[{
+        RowBox[{"{", 
+         RowBox[{"2", ",", "1"}], "}"}], ",", 
+        RowBox[{"{", 
+         RowBox[{"1", ",", "0"}], "}"}]}]]}], ")"}]}]}], "}"}]], "Output"],
+
+Cell[BoxData[
+ RowBox[{"{", 
+  RowBox[{
+   RowBox[{"-", 
+    FractionBox[
+     RowBox[{"3", " ", "\[ImaginaryI]", " ", "n", " ", "\[CapitalGamma]", " ", 
+      SuperscriptBox["\[Lambda]", "2"], " ", 
+      RowBox[{"(", 
+       RowBox[{
+        SubscriptBox["\[Rho]", 
+         RowBox[{
+          RowBox[{"{", 
+           RowBox[{"2", ",", 
+            RowBox[{"-", "1"}]}], "}"}], ",", 
+          RowBox[{"{", 
+           RowBox[{"1", ",", "0"}], "}"}]}]], "-", 
+        SubscriptBox["\[Rho]", 
+         RowBox[{
+          RowBox[{"{", 
+           RowBox[{"2", ",", "1"}], "}"}], ",", 
+          RowBox[{"{", 
+           RowBox[{"1", ",", "0"}], "}"}]}]]}], ")"}]}], 
+     RowBox[{"16", " ", "\[Pi]"}]]}], ",", 
+   RowBox[{"-", 
+    FractionBox[
+     RowBox[{"3", " ", "n", " ", "\[CapitalGamma]", " ", 
+      SuperscriptBox["\[Lambda]", "2"], " ", 
+      RowBox[{"(", 
+       RowBox[{
+        SubscriptBox["\[Rho]", 
+         RowBox[{
+          RowBox[{"{", 
+           RowBox[{"2", ",", 
+            RowBox[{"-", "1"}]}], "}"}], ",", 
+          RowBox[{"{", 
+           RowBox[{"1", ",", "0"}], "}"}]}]], "+", 
+        SubscriptBox["\[Rho]", 
+         RowBox[{
+          RowBox[{"{", 
+           RowBox[{"2", ",", "1"}], "}"}], ",", 
+          RowBox[{"{", 
+           RowBox[{"1", ",", "0"}], "}"}]}]]}], ")"}]}], 
+     RowBox[{"16", " ", "\[Pi]"}]]}]}], "}"}]], "Output"],
+
+Cell[BoxData[
+ RowBox[{"{", 
+  RowBox[{
+   RowBox[{
+    RowBox[{"-", "\[ImaginaryI]"}], " ", "eta", " ", 
+    RowBox[{"(", 
+     RowBox[{
+      RowBox[{"-", 
+       SubscriptBox["r", 
+        RowBox[{"2", ",", "1"}]]}], "+", 
+      SubscriptBox["r", 
+       RowBox[{"4", ",", "1"}]]}], ")"}]}], ",", 
+   RowBox[{
+    RowBox[{"-", "eta"}], " ", 
+    RowBox[{"(", 
+     RowBox[{
+      SubscriptBox["r", 
+       RowBox[{"2", ",", "1"}]], "+", 
+      SubscriptBox["r", 
+       RowBox[{"4", ",", "1"}]]}], ")"}]}]}], "}"}]], "Output"]
+}, Open  ]]
+}, Open  ]]
+},
+WindowSize->{871, 917},
+WindowMargins->{{67, Automatic}, {Automatic, -11}},
+ShowSelection->True,
+FrontEndVersion->"7.0 for Microsoft Windows (64-bit) (February 18, 2009)",
+StyleDefinitions->"Default.nb"
+]
+(* End of Notebook Content *)
+
+(* Internal cache information *)
+(*CellTagsOutline
+CellTagsIndex->{}
+*)
+(*CellTagsIndex
+CellTagsIndex->{}
+*)
+(*NotebookFileOutline
+Notebook[{
+Cell[CellGroupData[{
+Cell[567, 22, 35, 0, 71, "Section"],
+Cell[605, 24, 66, 1, 43, "MathCaption",
+ CellID->836781195],
+Cell[674, 27, 85, 2, 31, "Input",
+ CellID->2058623809],
+Cell[762, 31, 1290, 44, 65, "Text",
+ CellID->525777075],
+Cell[2055, 77, 68, 1, 43, "MathCaption",
+ CellID->429217524],
+Cell[2126, 80, 1346, 33, 112, "Input",
+ CellID->433132487],
+Cell[3475, 115, 68, 1, 43, "MathCaption",
+ CellID->133602844],
+Cell[CellGroupData[{
+Cell[3568, 120, 818, 26, 53, "Input",
+ CellID->26742303],
+Cell[4389, 148, 922, 29, 52, "Output"]
+}, Open  ]],
+Cell[5326, 180, 111, 3, 43, "MathCaption",
+ CellID->462076121],
+Cell[CellGroupData[{
+Cell[5462, 187, 1015, 27, 126, "Input",
+ CellID->494599775],
+Cell[6480, 216, 2675, 68, 72, "Output"]
+}, Open  ]],
+Cell[9170, 287, 76, 1, 43, "MathCaption",
+ CellID->358620443],
+Cell[9249, 290, 400, 11, 31, "Input",
+ CellID->167259034],
+Cell[9652, 303, 102, 2, 43, "MathCaption",
+ CellID->577766068],
+Cell[CellGroupData[{
+Cell[9779, 309, 330, 9, 31, "Input"],
+Cell[10112, 320, 3369, 89, 96, "Output"]
+}, Open  ]],
+Cell[13496, 412, 384, 12, 43, "MathCaption",
+ CellID->610306692],
+Cell[CellGroupData[{
+Cell[13905, 428, 272, 7, 31, "Input",
+ CellID->645617687],
+Cell[14180, 437, 814, 22, 72, "Output"]
+}, Open  ]],
+Cell[15009, 462, 98, 1, 43, "MathCaption",
+ CellID->690131918],
+Cell[CellGroupData[{
+Cell[15132, 467, 230, 5, 31, "Input",
+ CellID->718931880],
+Cell[15365, 474, 471, 11, 50, "Output"]
+}, Open  ]],
+Cell[15851, 488, 390, 12, 43, "MathCaption",
+ CellID->854192725],
+Cell[CellGroupData[{
+Cell[16266, 504, 459, 13, 52, "Input",
+ CellID->465762594],
+Cell[16728, 519, 1463, 43, 74, "Output"]
+}, Open  ]],
+Cell[18206, 565, 76, 1, 43, "MathCaption",
+ CellID->314466782],
+Cell[CellGroupData[{
+Cell[18307, 570, 424, 13, 52, "Input",
+ CellID->298399236],
+Cell[18734, 585, 56724, 1597, 384, "Output"]
+}, Open  ]],
+Cell[75473, 2185, 34, 0, 29, "Text"],
+Cell[CellGroupData[{
+Cell[75532, 2189, 4224, 113, 310, "Input"],
+Cell[79759, 2304, 922, 12, 278, "Output"],
+Cell[80684, 2318, 117, 1, 30, "Output"]
+}, Open  ]],
+Cell[80816, 2322, 40, 0, 29, "Text"],
+Cell[CellGroupData[{
+Cell[80881, 2326, 288, 8, 31, "Input"],
+Cell[81172, 2336, 3317, 96, 260, "Output"]
+}, Open  ]],
+Cell[CellGroupData[{
+Cell[84526, 2437, 1976, 61, 161, "Input"],
+Cell[86505, 2500, 1530, 49, 83, "Output"],
+Cell[88038, 2551, 1375, 42, 51, "Output"],
+Cell[89416, 2595, 529, 19, 30, "Output"]
+}, Open  ]]
+}, Open  ]]
+}
+]
+*)
+
+(* End of internal cache information *)
diff --git a/xmds2/Genas_system/Makefile b/xmds2/Genas_system/Makefile
new file mode 100755
index 0000000..0e82991
--- /dev/null
+++ b/xmds2/Genas_system/Makefile
@@ -0,0 +1,37 @@
+###  -*- make -*-
+### This file is part of the Debian xmds package
+### Copyright (C) 2006 Rafael Laboissiere
+### This file is relased under the GNU General Public License
+### NO WARRANTIES!
+
+### This makefile can be used to build and run the XMDS examples
+
+XMDS_FILES = $(shell ls *.xmds)
+RUN_FILES = $(patsubst %.xmds,%.run,$(XMDS_FILES))
+CC_FILES = $(patsubst %.xmds,%.cc,$(XMDS_FILES))
+XSIL_FILES = $(patsubst %.xmds,%.xsil,$(XMDS_FILES))
+M_FILES = $(patsubst %.xmds,%.m,$(XMDS_FILES))
+
+XMDS = xmds2
+XSIL2GRAPHICS = xsil2graphics2
+
+all: $(M_FILES) 
+
+%.run: %.xmds
+	$(XMDS) $<
+	mv $(patsubst %.xmds,%,$<) $@
+
+%.xsil: %.run
+	./$<
+
+%.m: %.xsil
+	$(XSIL2GRAPHICS) -e $<
+
+plot: $(M_FILES)
+	octave pp.m
+
+clean:
+	rm -f $(CC_FILES) $(RUN_FILES) $(M_FILES) $(XSIL_FILES) *.wisdom.fftw3 *.dat octave-core *.wisdom *.pdf
+
+.PRECIOUS: %.run %.xsil %.m
+.PHONY: all clean
-- 
cgit v1.2.3