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-rw-r--r--xmds2/Genas_system/Genas_system.xmds36
-rw-r--r--xmds2/Genas_system/GenerateGenasSystem.nb1521
2 files changed, 1148 insertions, 409 deletions
diff --git a/xmds2/Genas_system/Genas_system.xmds b/xmds2/Genas_system/Genas_system.xmds
index e855e4f..ed059fc 100644
--- a/xmds2/Genas_system/Genas_system.xmds
+++ b/xmds2/Genas_system/Genas_system.xmds
@@ -10,12 +10,19 @@
Solving 4 level atom in 0->1 configuration,
with field propagation along spatial axis Z
no Doppler broadening
+
+ Fields:
+ light field, default circularly polarized
+ rf field along x
+ static B-field along z
+
+ M=0 upper state sublevel can be shifted independently
We are solving
- dE/dz+(1/c)*dE/dt=i*eta*rho_ij, where j level is higher then i.
+ dE/dz+(1/c)*dE/dt=i*eta*rho_ji, 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
+ dE_dz = i*eta*rhoji - 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.
@@ -50,13 +57,14 @@
<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] -->
+ <!--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-->
+ <!--normalized rf Rabi frequency:
+ Orf = (Larmor frequency due to peak rf field)/sqrt(2)-->
<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)" />
@@ -136,16 +144,16 @@
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;
+ dr11_dt = gt - gt*r11 + (-Ey - Ex*i)*r12 + (-Ey + Ex*i)*r14 + (-Eyc + Exc*i)*r21 + g0*r22 + g0*r33 + (-Eyc - Exc*i)*r41 + g0*r44;
+ dr12_dt = (Eyc - Exc*i)*r11 + (-g0/2. - gt - delta*i + i*OL)*r12 + i*rf*r13 + (-Eyc + Exc*i)*r22 + (-Eyc - Exc*i)*r42;
+ dr13_dt = i*rf*r12 + (-g0/2. - gt - delta*i + i*delta0z(z))*r13 + i*rf*r14 + (-Eyc + Exc*i)*r23 + (-Eyc - Exc*i)*r43;
+ dr14_dt = (Eyc + Exc*i)*r11 + i*rf*r13 + (-g0/2. - gt - delta*i - i*OL)*r14 + (-Eyc + Exc*i)*r24 + (-Eyc - Exc*i)*r44;
+ dr22_dt = (Ey + Ex*i)*r12 + (Eyc - Exc*i)*r21 + (-g0 - gt)*r22 + i*rf*r23 - i*rf*r32;
+ dr23_dt = (Ey + Ex*i)*r13 + i*rf*r22 + (-g0 - gt - i*OL + i*delta0z(z))*r23 + i*rf*r24 - i*rf*r33;
+ dr24_dt = (Ey + Ex*i)*r14 + (Eyc + Exc*i)*r21 + i*rf*r23 + (-g0 - gt - 2*i*OL)*r24 - i*rf*r34;
+ dr33_dt = -(i*rf*r23) + i*rf*r32 + (-g0 - gt)*r33 + i*rf*r34 - i*rf*r43;
+ dr34_dt = -(i*rf*r24) + (Eyc + Exc*i)*r31 + i*rf*r33 + (-g0 - gt - i*OL - i*delta0z(z))*r34 - i*rf*r44;
+ dr44_dt = (Ey - Ex*i)*r14 - i*rf*r34 + (Eyc + Exc*i)*r41 + i*rf*r43 + (-g0 - gt)*r44;
]]>
</operator>
<operator kind="ex" constant="yes">
diff --git a/xmds2/Genas_system/GenerateGenasSystem.nb b/xmds2/Genas_system/GenerateGenasSystem.nb
index ab9069b..5188fd9 100644
--- a/xmds2/Genas_system/GenerateGenasSystem.nb
+++ b/xmds2/Genas_system/GenerateGenasSystem.nb
@@ -10,10 +10,10 @@
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[ 145, 7]
-NotebookDataLength[ 92628, 2713]
-NotebookOptionsPosition[ 89973, 2618]
-NotebookOutlinePosition[ 90340, 2634]
-CellTagsIndexPosition[ 90297, 2631]
+NotebookDataLength[ 117776, 3444]
+NotebookOptionsPosition[ 115033, 3346]
+NotebookOutlinePosition[ 115398, 3362]
+CellTagsIndexPosition[ 115355, 3359]
WindowFrame->Normal*)
(* Beginning of Notebook Content *)
@@ -178,9 +178,8 @@ Cell[BoxData[
"}"}]], "Output"]
}, Open ]],
-Cell["\<\
-The Hamiltonian for the system subject to the optical field.\
-\>", "MathCaption",
+Cell["The Hamiltonian for the system subject to the optical field.", \
+"MathCaption",
CellID->462076121],
Cell[CellGroupData[{
@@ -197,12 +196,12 @@ Cell[BoxData[
RowBox[{"MagneticField", "\[Rule]",
RowBox[{
RowBox[{"{",
- RowBox[{"0", ",", "0", ",",
- RowBox[{"\[CapitalOmega]L", "+",
- RowBox[{"\[CapitalOmega]rf", " ",
- RowBox[{"Sin", "[",
- RowBox[{"\[Omega]rf", " ", "t"}], "]"}]}]}]}], "}"}], "/",
- "BohrMagneton"}]}]}], "]"}]}], "+",
+ RowBox[{
+ RowBox[{"\[CapitalOmega]rf", " ",
+ RowBox[{"Sin", "[",
+ RowBox[{"\[Omega]rf", " ", "t"}], "]"}]}], ",", "0", ",",
+ "\[CapitalOmega]L"}], "}"}], "/", "BohrMagneton"}]}]}], "]"}]}],
+ "+",
RowBox[{"Hamiltonian", "[",
RowBox[{"system", ",",
RowBox[{"ElectricField", "\[Rule]",
@@ -250,12 +249,24 @@ Cell[BoxData[
RowBox[{"Cos", "[",
RowBox[{"\[Phi]y", "-",
RowBox[{"t", " ", "\[Omega]"}]}], "]"}]}]}],
- RowBox[{"\[Omega]0", "+", "\[CapitalOmega]L", "+",
+ RowBox[{"\[Omega]0", "+", "\[CapitalOmega]L"}],
+ FractionBox[
RowBox[{"\[CapitalOmega]rf", " ",
RowBox[{"Sin", "[",
- RowBox[{"t", " ", "\[Omega]rf"}], "]"}]}]}], "0", "0"},
- {"0", "0",
- RowBox[{"\[CapitalDelta]0", "+", "\[Omega]0"}], "0"},
+ RowBox[{"t", " ", "\[Omega]rf"}], "]"}]}],
+ SqrtBox["2"]], "0"},
+ {"0",
+ FractionBox[
+ RowBox[{"\[CapitalOmega]rf", " ",
+ RowBox[{"Sin", "[",
+ RowBox[{"t", " ", "\[Omega]rf"}], "]"}]}],
+ SqrtBox["2"]],
+ RowBox[{"\[CapitalDelta]0", "+", "\[Omega]0"}],
+ FractionBox[
+ RowBox[{"\[CapitalOmega]rf", " ",
+ RowBox[{"Sin", "[",
+ RowBox[{"t", " ", "\[Omega]rf"}], "]"}]}],
+ SqrtBox["2"]]},
{
RowBox[{
RowBox[{"2", " ", "\[CapitalOmega]Rx", " ",
@@ -265,11 +276,13 @@ Cell[BoxData[
RowBox[{"2", " ", "\[ImaginaryI]", " ", "\[CapitalOmega]Ry", " ",
RowBox[{"Cos", "[",
RowBox[{"\[Phi]y", "-",
- RowBox[{"t", " ", "\[Omega]"}]}], "]"}]}]}], "0", "0",
- RowBox[{"\[Omega]0", "-", "\[CapitalOmega]L", "-",
+ RowBox[{"t", " ", "\[Omega]"}]}], "]"}]}]}], "0",
+ FractionBox[
RowBox[{"\[CapitalOmega]rf", " ",
RowBox[{"Sin", "[",
- RowBox[{"t", " ", "\[Omega]rf"}], "]"}]}]}]}
+ RowBox[{"t", " ", "\[Omega]rf"}], "]"}]}],
+ SqrtBox["2"]],
+ RowBox[{"\[Omega]0", "-", "\[CapitalOmega]L"}]}
},
GridBoxAlignment->{
"Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
@@ -288,6 +301,8 @@ Cell[BoxData[
Cell["The level diagram for the system.", "MathCaption",
CellID->358620443],
+Cell[CellGroupData[{
+
Cell[BoxData[
RowBox[{"LevelDiagram", "[",
RowBox[{"system", ",",
@@ -295,12 +310,27 @@ Cell[BoxData[
RowBox[{"{",
RowBox[{
RowBox[{"\[Omega]0", "\[Rule]", "1"}], ",",
- RowBox[{"\[CapitalOmega]rf", "\[Rule]", "0"}], ",",
+ RowBox[{"\[CapitalOmega]rf", "\[Rule]", ".5"}], ",",
RowBox[{"\[CapitalOmega]L", "\[Rule]", ".3"}], ",",
- RowBox[{"\[CapitalDelta]0", "\[Rule]", ".2"}]}], "}"}]}]}],
+ RowBox[{"\[CapitalDelta]0", "\[Rule]", ".1"}]}], "}"}]}]}],
"]"}]], "Input",
CellID->167259034],
+Cell[BoxData[
+ GraphicsBox[{{{{}, LineBox[{{-0.4, 0}, {0.4, 0}}]}, {{},
+ LineBox[{{0.6, 1.3}, {1.4, 1.3}}]}, {{},
+ LineBox[{{-0.4, 1.1}, {0.4, 1.1}}]}, {{},
+ LineBox[{{-1.4, 0.7}, {-0.6, 0.7}}]}}, {{}, {}, {}},
+ {Arrowheads[{-0.05, 0.05}],
+ ArrowBox[{{0.04000000000000001, 0}, {0.96, 1.3}}],
+ ArrowBox[{{0.04000000000000001, 1.1}, {0.96, 1.3}}],
+ ArrowBox[{{-0.04000000000000001, 0}, {-0.96, 0.7}}],
+ ArrowBox[{{-0.96, 0.7}, {-0.04000000000000001, 1.1}}]},
+ {PointSize[0.0225]}},
+ ImagePadding->{{2, 2}, {2, 2}},
+ ImageSize->144.]], "Output"]
+}, Open ]],
+
Cell["Apply the rotating-wave approximation to the Hamiltonian.", \
"MathCaption",
CellID->577766068],
@@ -357,21 +387,58 @@ Cell[BoxData[
RowBox[{"\[ImaginaryI]", " ", "\[Phi]y"}]], " ",
"\[CapitalOmega]Ry"}]}],
RowBox[{
- RowBox[{"-", "\[CapitalDelta]"}], "+", "\[CapitalOmega]L", "+",
- RowBox[{
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- SuperscriptBox["\[ExponentialE]",
- RowBox[{
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- SuperscriptBox["\[ExponentialE]",
- RowBox[{"\[ImaginaryI]", " ", "t", " ", "\[Omega]rf"}]], " ",
- "\[CapitalOmega]rf"}]}], "0", "0"},
- {"0", "0",
+ RowBox[{"-", "\[CapitalDelta]"}], "+", "\[CapitalOmega]L"}],
+ RowBox[{
+ FractionBox[
+ RowBox[{"\[ImaginaryI]", " ",
+ SuperscriptBox["\[ExponentialE]",
+ RowBox[{
+ RowBox[{"-", "\[ImaginaryI]"}], " ", "t", " ", "\[Omega]rf"}]],
+ " ", "\[CapitalOmega]rf"}],
+ RowBox[{"2", " ",
+ SqrtBox["2"]}]], "-",
+ FractionBox[
+ RowBox[{"\[ImaginaryI]", " ",
+ SuperscriptBox["\[ExponentialE]",
+ RowBox[{"\[ImaginaryI]", " ", "t", " ", "\[Omega]rf"}]], " ",
+ "\[CapitalOmega]rf"}],
+ RowBox[{"2", " ",
+ SqrtBox["2"]}]]}], "0"},
+ {"0",
RowBox[{
- RowBox[{"-", "\[CapitalDelta]"}], "+", "\[CapitalDelta]0"}], "0"},
+ FractionBox[
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+ SuperscriptBox["\[ExponentialE]",
+ RowBox[{
+ RowBox[{"-", "\[ImaginaryI]"}], " ", "t", " ", "\[Omega]rf"}]],
+ " ", "\[CapitalOmega]rf"}],
+ RowBox[{"2", " ",
+ SqrtBox["2"]}]], "-",
+ FractionBox[
+ RowBox[{"\[ImaginaryI]", " ",
+ SuperscriptBox["\[ExponentialE]",
+ RowBox[{"\[ImaginaryI]", " ", "t", " ", "\[Omega]rf"}]], " ",
+ "\[CapitalOmega]rf"}],
+ RowBox[{"2", " ",
+ SqrtBox["2"]}]]}],
+ RowBox[{
+ RowBox[{"-", "\[CapitalDelta]"}], "+", "\[CapitalDelta]0"}],
+ RowBox[{
+ FractionBox[
+ RowBox[{"\[ImaginaryI]", " ",
+ SuperscriptBox["\[ExponentialE]",
+ RowBox[{
+ RowBox[{"-", "\[ImaginaryI]"}], " ", "t", " ", "\[Omega]rf"}]],
+ " ", "\[CapitalOmega]rf"}],
+ RowBox[{"2", " ",
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+ FractionBox[
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+ SuperscriptBox["\[ExponentialE]",
+ RowBox[{"\[ImaginaryI]", " ", "t", " ", "\[Omega]rf"}]], " ",
+ "\[CapitalOmega]rf"}],
+ RowBox[{"2", " ",
+ SqrtBox["2"]}]]}]},
{
RowBox[{
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@@ -381,20 +448,25 @@ Cell[BoxData[
RowBox[{"\[ImaginaryI]", " ",
SuperscriptBox["\[ExponentialE]",
RowBox[{"\[ImaginaryI]", " ", "\[Phi]y"}]], " ",
- "\[CapitalOmega]Ry"}]}], "0", "0",
+ "\[CapitalOmega]Ry"}]}], "0",
RowBox[{
- RowBox[{"-", "\[CapitalDelta]"}], "-", "\[CapitalOmega]L", "-",
- RowBox[{
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- SuperscriptBox["\[ExponentialE]",
- RowBox[{
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- SuperscriptBox["\[ExponentialE]",
- RowBox[{"\[ImaginaryI]", " ", "t", " ", "\[Omega]rf"}]], " ",
- "\[CapitalOmega]rf"}]}]}
+ FractionBox[
+ RowBox[{"\[ImaginaryI]", " ",
+ SuperscriptBox["\[ExponentialE]",
+ RowBox[{
+ RowBox[{"-", "\[ImaginaryI]"}], " ", "t", " ", "\[Omega]rf"}]],
+ " ", "\[CapitalOmega]rf"}],
+ RowBox[{"2", " ",
+ SqrtBox["2"]}]], "-",
+ FractionBox[
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+ SuperscriptBox["\[ExponentialE]",
+ RowBox[{"\[ImaginaryI]", " ", "t", " ", "\[Omega]rf"}]], " ",
+ "\[CapitalOmega]rf"}],
+ RowBox[{"2", " ",
+ SqrtBox["2"]}]]}],
+ RowBox[{
+ RowBox[{"-", "\[CapitalDelta]"}], "-", "\[CapitalOmega]L"}]}
},
GridBoxAlignment->{
"Columns" -> {{Center}}, "ColumnsIndexed" -> {}, "Rows" -> {{Baseline}},
@@ -749,6 +821,33 @@ Cell[BoxData[
RowBox[{"1", ",", "0"}], "}"}], ",",
RowBox[{"{",
RowBox[{"1", ",", "0"}], "}"}]}]]}], "-",
+ FractionBox[
+ RowBox[{
+ SuperscriptBox["\[ExponentialE]",
+ RowBox[{
+ RowBox[{"-", "\[ImaginaryI]"}], " ", "t", " ", "\[Omega]rf"}]],
+ " ", "\[CapitalOmega]rf", " ",
+ SubscriptBox["\[Rho]",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"1", ",", "0"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"2", ",", "0"}], "}"}]}]]}],
+ RowBox[{"2", " ",
+ SqrtBox["2"]}]], "+",
+ FractionBox[
+ RowBox[{
+ SuperscriptBox["\[ExponentialE]",
+ RowBox[{"\[ImaginaryI]", " ", "t", " ", "\[Omega]rf"}]], " ",
+ "\[CapitalOmega]rf", " ",
+ SubscriptBox["\[Rho]",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"1", ",", "0"}], "}"}], ",",
+ RowBox[{"{",
+ RowBox[{"2", ",", "0"}], "}"}]}]]}],
+ RowBox[{"2", " ",
+ SqrtBox["2"]}]], "-",
RowBox[{
FractionBox["1", "2"], " ", "\[CapitalGamma]", " ",
SubscriptBox["\[Rho]",
@@ -778,29 +877,6 @@ Cell[BoxData[
RowBox[{"1", ",", "0"}], "}"}], ",",
RowBox[{"{",
RowBox[{"2", ",", "1"}], "}"}]}]]}], "-",
- RowBox[{
- FractionBox["1", "2"], " ",
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- SubscriptBox["\[Rho]",
- RowBox[{
- RowBox[{"{",
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- RowBox[{"{",
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- SubscriptBox["\[Rho]",
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RowBox[{"\[ImaginaryI]", " ",
SuperscriptBox["\[ExponentialE]",
RowBox[{
@@ -858,9 +934,38 @@ Cell[BoxData[
HoldForm],
RowBox[{"0", "\[Equal]",
RowBox[{
+ RowBox[{"-",
+ FractionBox[
+ RowBox[{
+ SuperscriptBox["\[ExponentialE]",
+ RowBox[{
+ RowBox[{"-", "\[ImaginaryI]"}], " ", "t", " ", "\[Omega]rf"}]],
+ " ", "\[CapitalOmega]rf", " ",
+ SubscriptBox["\[Rho]",
+ RowBox[{
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+ RowBox[{"1", ",", "0"}], "}"}], ",",
+ RowBox[{"{",
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+ FractionBox[
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+ SubscriptBox["\[Rho]",
+ RowBox[{
+ RowBox[{"{",
+ RowBox[{"1", ",", "0"}], "}"}], ",",
+ RowBox[{"{",
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RowBox[{
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SubscriptBox["\[Rho]",
RowBox[{
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@@ -888,6 +993,33 @@ Cell[BoxData[
RowBox[{"1", ",", "0"}], "}"}], ",",
RowBox[{"{",
RowBox[{"2", ",", "0"}], "}"}]}]]}], "-",
+ FractionBox[
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+ SuperscriptBox["\[ExponentialE]",
+ RowBox[{
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+ RowBox[{
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+ RowBox[{
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@@ -1000,32 +1132,34 @@ Cell[BoxData[
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+ RowBox[{
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+ FractionBox[
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generated by cgit v1.2.3 (git 2.39.1) at 2024-11-16 13:02:06 +0000