From 61d5a03570bac86821751a72d017d1cc9f11b7ae Mon Sep 17 00:00:00 2001
From: Simon Rochester <simon.rochester@gmail.com>
Date: Fri, 31 Aug 2012 01:15:53 -0700
Subject: Fixed problem with steady-state observables definition, and added
 population plot.

---
 mathemathica_fwm/RbXMDSSetup.nb | 221 ++++++++++++++++++++++++++++++++++------
 1 file changed, 192 insertions(+), 29 deletions(-)

(limited to 'mathemathica_fwm')

diff --git a/mathemathica_fwm/RbXMDSSetup.nb b/mathemathica_fwm/RbXMDSSetup.nb
index fc9cf40..359e36b 100755
--- a/mathemathica_fwm/RbXMDSSetup.nb
+++ b/mathemathica_fwm/RbXMDSSetup.nb
@@ -687,35 +687,78 @@ The level diagram showing resonant (co-rotating) optical couplings. \
 \>", "Text"],
 
 Cell[BoxData[
- RowBox[{"LevelDiagram", "[", 
-  RowBox[{"system", ",", 
-   RowBox[{
-    RowBox[{"Hrwa", "/.", 
+ RowBox[{"diagram", "=", 
+  RowBox[{"LevelDiagram", "[", 
+   RowBox[{"system", ",", 
+    RowBox[{
+     RowBox[{"Hrwa", "/.", 
+      RowBox[{"{", 
+       RowBox[{
+        RowBox[{
+         SubscriptBox["\[Delta]", "1"], "\[Rule]", 
+         RowBox[{"-", "\[Omega]1res"}]}], ",", 
+        RowBox[{
+         SubscriptBox["\[Delta]", "2"], "\[Rule]", 
+         RowBox[{"-", "\[Omega]2res"}]}], ",", 
+        RowBox[{
+         SubscriptBox["\[Delta]", "3"], "\[Rule]", 
+         RowBox[{"-", "\[Omega]3res"}]}]}], "}"}]}], "/.", 
      RowBox[{"{", 
       RowBox[{
        RowBox[{
-        SubscriptBox["\[Delta]", "1"], "\[Rule]", 
-        RowBox[{"-", "\[Omega]1res"}]}], ",", 
+        RowBox[{"Energy", "[", "0", "]"}], "\[Rule]", "0"}], ",", 
        RowBox[{
-        SubscriptBox["\[Delta]", "2"], "\[Rule]", 
-        RowBox[{"-", "\[Omega]2res"}]}], ",", 
+        RowBox[{"Energy", "[", "1", "]"}], "\[Rule]", "2"}], ",", 
        RowBox[{
-        SubscriptBox["\[Delta]", "3"], "\[Rule]", 
-        RowBox[{"-", "\[Omega]3res"}]}]}], "}"}]}], "/.", 
-    RowBox[{"{", 
-     RowBox[{
-      RowBox[{
-       RowBox[{"Energy", "[", "0", "]"}], "\[Rule]", "0"}], ",", 
-      RowBox[{
-       RowBox[{"Energy", "[", "1", "]"}], "\[Rule]", "2"}], ",", 
-      RowBox[{
-       RowBox[{"Energy", "[", "2", "]"}], "\[Rule]", "4"}], ",", 
+        RowBox[{"Energy", "[", "2", "]"}], "\[Rule]", "3"}], ",", 
+       RowBox[{
+        RowBox[{"HyperfineA", "[", "_", "]"}], "\[Rule]", ".2"}], ",", 
+       RowBox[{
+        RowBox[{"HyperfineB", "[", "_", "]"}], "\[Rule]", ".1"}], ",", 
+       RowBox[{"\[CapitalOmega]L", "\[Rule]", ".1"}]}], "}"}]}], ",", 
+    RowBox[{"ParityOffset", "\[Rule]", "False"}], ",", 
+    RowBox[{"Epilog", "\[Rule]", 
+     RowBox[{"{", 
       RowBox[{
-       RowBox[{"HyperfineA", "[", "_", "]"}], "\[Rule]", ".2"}], ",", 
+       RowBox[{"Text", "[", 
+        RowBox[{
+         RowBox[{"Style", "[", 
+          RowBox[{
+          "\"\<\!\(\*SuperscriptBox[\(\[VeryThinSpace]\), \
+\(2\)]\)\!\(\*SubscriptBox[\(S\), \(1/2\)]\)\>\"", ",", 
+           RowBox[{"SingleLetterItalics", "\[Rule]", "False"}]}], "]"}], ",", 
+         RowBox[{"{", 
+          RowBox[{
+           RowBox[{"-", "2.9"}], ",", "0"}], "}"}]}], "]"}], ",", 
+       RowBox[{"Text", "[", 
+        RowBox[{
+         RowBox[{"Style", "[", 
+          RowBox[{
+          "\"\<\!\(\*SuperscriptBox[\(\[VeryThinSpace]\), \
+\(2\)]\)\!\(\*SubscriptBox[\(P\), \(1/2\)]\)\>\"", ",", 
+           RowBox[{"SingleLetterItalics", "\[Rule]", "False"}]}], "]"}], ",", 
+         RowBox[{"{", 
+          RowBox[{
+           RowBox[{"-", "2.9"}], ",", "1.6"}], "}"}]}], "]"}], ",", 
+       RowBox[{"Text", "[", 
+        RowBox[{
+         RowBox[{"Style", "[", 
+          RowBox[{
+          "\"\<\!\(\*SuperscriptBox[\(\[VeryThinSpace]\), \
+\(2\)]\)\!\(\*SubscriptBox[\(P\), \(3/2\)]\)\>\"", ",", 
+           RowBox[{"SingleLetterItalics", "\[Rule]", "False"}]}], "]"}], ",", 
+         RowBox[{"{", 
+          RowBox[{
+           RowBox[{"-", "2.9"}], ",", "2.7"}], "}"}]}], "]"}]}], "}"}]}], ",", 
+    RowBox[{"ImageSize", "\[Rule]", 
+     RowBox[{"3.5", " ", "72"}]}], ",", 
+    RowBox[{"ImagePadding", "\[Rule]", 
+     RowBox[{"{", 
       RowBox[{
-       RowBox[{"HyperfineB", "[", "_", "]"}], "\[Rule]", ".1"}], ",", 
-      RowBox[{"\[CapitalOmega]L", "\[Rule]", ".1"}]}], "}"}]}], ",", 
-   RowBox[{"ParityOffset", "\[Rule]", "False"}]}], "]"}]], "Input",
+       RowBox[{"{", 
+        RowBox[{"35", ",", "0"}], "}"}], ",", 
+       RowBox[{"{", 
+        RowBox[{"10", ",", "10"}], "}"}]}], "}"}]}]}], "]"}]}]], "Input",
  CellID->102096636],
 
 Cell[TextData[{
@@ -1081,7 +1124,9 @@ Cell[BoxData[{
       RowBox[{
        RowBox[{
         RowBox[{"DMElementPattern", "[", "]"}], "/;", 
-        RowBox[{"Label2", "\[Equal]", "2"}]}], "\[Rule]", "0"}]}], "/.", 
+        RowBox[{
+         RowBox[{"Label2", "\[Equal]", "2"}], "||", 
+         RowBox[{"F1", "\[Equal]", "2"}]}]}], "\[Rule]", "0"}]}], "/.", 
      "delreps"}], "]"}], "/.", 
    RowBox[{"\[Epsilon]", "\[Rule]", 
     RowBox[{"\[Pi]", "/", "4"}]}]}]}]}], "Input"],
@@ -1167,11 +1212,11 @@ Cell[BoxData[{
    RowBox[{"{", 
     RowBox[{
      RowBox[{
-      SubscriptBox["\[CapitalOmega]", "1"], "\[Rule]", "10."}], ",", 
+      SubscriptBox["\[CapitalOmega]", "1"], "\[Rule]", "100."}], ",", 
      RowBox[{
-      SubscriptBox["\[CapitalOmega]", "2"], "\[Rule]", ".1"}], ",", 
+      SubscriptBox["\[CapitalOmega]", "2"], "\[Rule]", ".01"}], ",", 
      RowBox[{
-      SubscriptBox["\[CapitalOmega]", "3"], "\[Rule]", "100."}], ",", 
+      SubscriptBox["\[CapitalOmega]", "3"], "\[Rule]", "10."}], ",", 
      RowBox[{
       SubscriptBox["\[CapitalOmega]", "4"], "\[Rule]", "0."}], ",", 
      RowBox[{
@@ -1224,7 +1269,124 @@ Cell[BoxData[{
      RowBox[{"table", "[", 
       RowBox[{"[", 
        RowBox[{"All", ",", "2", ",", "2"}], "]"}], "]"}]}], "}"}], "]"}], 
-  "]"}]}], "Input"]
+  "]"}]}], "Input"],
+
+Cell["\<\
+Plot atomic populations for a given set of parameters.\
+\>", "Text"],
+
+Cell[BoxData[{
+ RowBox[{
+  RowBox[{"params", "=", 
+   RowBox[{"{", 
+    RowBox[{
+     RowBox[{
+      SubscriptBox["\[CapitalOmega]", "1"], "\[Rule]", "10"}], ",", 
+     RowBox[{
+      SubscriptBox["\[CapitalOmega]", "2"], "\[Rule]", ".01"}], ",", 
+     RowBox[{
+      SubscriptBox["\[CapitalOmega]", "3"], "\[Rule]", "1."}], ",", 
+     RowBox[{
+      SubscriptBox["\[CapitalOmega]", "4"], "\[Rule]", "0."}], ",", 
+     RowBox[{
+      SubscriptBox["\[Delta]", "2"], "\[Rule]", "0"}], ",", 
+     RowBox[{
+      SubscriptBox["\[Delta]", "1"], "\[Rule]", "0"}], ",", 
+     RowBox[{
+      SubscriptBox["\[Delta]", "3"], "\[Rule]", "0"}], ",", 
+     RowBox[{"\[Gamma]t", "\[Rule]", ".1"}], ",", 
+     RowBox[{"\[CapitalOmega]L", "\[Rule]", "0."}]}], "}"}]}], 
+  ";"}], "\[IndentingNewLine]", 
+ RowBox[{
+  RowBox[{"steadyeqs1", "=", 
+   RowBox[{"steadyeqs", "/.", "params"}]}], ";"}], "\[IndentingNewLine]", 
+ RowBox[{
+  RowBox[{"sol", "=", 
+   RowBox[{
+    RowBox[{"Chop", "@", 
+     RowBox[{
+      RowBox[{"NSolve", "[", 
+       RowBox[{"steadyeqs1", ",", "vars"}], "]"}], "\[LeftDoubleBracket]", 
+      "1", "\[RightDoubleBracket]"}]}], "/.", "params"}]}], ";"}], "\n", 
+ RowBox[{"LevelDiagram", "[", 
+  RowBox[{"system", ",", 
+   RowBox[{
+    RowBox[{
+     RowBox[{"Hrwa", "/.", 
+      RowBox[{"{", 
+       RowBox[{
+        RowBox[{
+         SubscriptBox["\[Delta]", "1"], "\[Rule]", 
+         RowBox[{"-", "\[Omega]1res"}]}], ",", 
+        RowBox[{
+         SubscriptBox["\[Delta]", "2"], "\[Rule]", 
+         RowBox[{"-", "\[Omega]2res"}]}], ",", 
+        RowBox[{
+         SubscriptBox["\[Delta]", "3"], "\[Rule]", 
+         RowBox[{"-", "\[Omega]3res"}]}]}], "}"}]}], "/.", "params"}], "/.", 
+    RowBox[{"{", 
+     RowBox[{
+      RowBox[{
+       RowBox[{"Energy", "[", "0", "]"}], "\[Rule]", "0"}], ",", 
+      RowBox[{
+       RowBox[{"Energy", "[", "1", "]"}], "\[Rule]", "2"}], ",", 
+      RowBox[{
+       RowBox[{"Energy", "[", "2", "]"}], "\[Rule]", "3"}], ",", 
+      RowBox[{
+       RowBox[{"HyperfineA", "[", "_", "]"}], "\[Rule]", ".2"}], ",", 
+      RowBox[{
+       RowBox[{"HyperfineB", "[", "_", "]"}], "\[Rule]", ".1"}], ",", 
+      RowBox[{"\[CapitalOmega]L", "\[Rule]", "0"}]}], "}"}]}], ",", 
+   RowBox[{
+    RowBox[{
+     RowBox[{"DensityMatrix", "[", "system", "]"}], "/.", "sol"}], "/.", 
+    RowBox[{
+     RowBox[{"DMElementPattern", "[", "]"}], "\[Rule]", "0"}]}], ",", 
+   RowBox[{"ParityOffset", "\[Rule]", "False"}], ",", 
+   RowBox[{"Epilog", "\[Rule]", 
+    RowBox[{"{", 
+     RowBox[{
+      RowBox[{"Text", "[", 
+       RowBox[{
+        RowBox[{"Style", "[", 
+         RowBox[{
+         "\"\<\!\(\*SuperscriptBox[\(\[VeryThinSpace]\), \
+\(2\)]\)\!\(\*SubscriptBox[\(S\), \(1/2\)]\)\>\"", ",", 
+          RowBox[{"SingleLetterItalics", "\[Rule]", "False"}]}], "]"}], ",", 
+        RowBox[{"{", 
+         RowBox[{
+          RowBox[{"-", "2.9"}], ",", "0"}], "}"}]}], "]"}], ",", 
+      RowBox[{"Text", "[", 
+       RowBox[{
+        RowBox[{"Style", "[", 
+         RowBox[{
+         "\"\<\!\(\*SuperscriptBox[\(\[VeryThinSpace]\), \
+\(2\)]\)\!\(\*SubscriptBox[\(P\), \(1/2\)]\)\>\"", ",", 
+          RowBox[{"SingleLetterItalics", "\[Rule]", "False"}]}], "]"}], ",", 
+        RowBox[{"{", 
+         RowBox[{
+          RowBox[{"-", "2.9"}], ",", "1.6"}], "}"}]}], "]"}], ",", 
+      RowBox[{"Text", "[", 
+       RowBox[{
+        RowBox[{"Style", "[", 
+         RowBox[{
+         "\"\<\!\(\*SuperscriptBox[\(\[VeryThinSpace]\), \
+\(2\)]\)\!\(\*SubscriptBox[\(P\), \(3/2\)]\)\>\"", ",", 
+          RowBox[{"SingleLetterItalics", "\[Rule]", "False"}]}], "]"}], ",", 
+        RowBox[{"{", 
+         RowBox[{
+          RowBox[{"-", "2.9"}], ",", "2.7"}], "}"}]}], "]"}]}], "}"}]}], ",", 
+   RowBox[{"ImageSize", "\[Rule]", 
+    RowBox[{"3.5", " ", "72"}]}], ",", 
+   RowBox[{"ImagePadding", "\[Rule]", 
+    RowBox[{"{", 
+     RowBox[{
+      RowBox[{"{", 
+       RowBox[{"35", ",", "0"}], "}"}], ",", 
+      RowBox[{"{", 
+       RowBox[{"10", ",", "10"}], "}"}]}], "}"}]}], ",", 
+   RowBox[{"PopulationStyle", "\[Rule]", 
+    RowBox[{"PointSize", "[", ".018", "]"}]}]}], "]"}]}], "Input"]
 }, Open  ]],
 
 Cell[CellGroupData[{
@@ -2058,10 +2220,11 @@ Cell[BoxData[{
      "\"\<RbPropEquations.txt\>\""}], "]"}], ",", "%"}], "]"}]}], "Input"]
 }, Open  ]]
 },
-WindowSize->{837, 825},
-WindowMargins->{{1, Automatic}, {Automatic, 6}},
+WindowSize->{1032, 898},
+WindowMargins->{{0, Automatic}, {Automatic, 3}},
 PrivateNotebookOptions->{"FileOutlineCache"->False},
 ShowSelection->True,
 FrontEndVersion->"8.0 for Microsoft Windows (64-bit) (October 6, 2011)",
 StyleDefinitions->"Default.nb"
 ]
+
-- 
cgit v1.2.3