File:Wignerfunction catstate odd 2.5.png
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Summary
| Description |
English: Wigner function of an odd cat state with amplitude α=2.5. |
| Date | |
| Source | Own work |
| Author | Geek3 |
| PNG genesis |  This diagram was created with Mathematica |
Source code
cat[\[Alpha]_, \[Theta]_, q_, p_] :=
1/(2 Pi)*1/(1 + Cos[\[Theta]]*Exp[-2 \[Alpha]^2])*(
Exp[-p^2 - (q + Sqrt[2] \[Alpha])^2] +
Exp[-p^2 - (q - Sqrt[2] \[Alpha])^2] +
2 Cos[\[Theta] - 2 Sqrt[2] \[Alpha]*p]*Exp[-q^2 - p^2]);
rq = 6; rp = 3; t = 0.003; FontS = 20;
For[\[Theta] = 0, \[Theta] <= Pi, \[Theta] += Pi,
For[\[Alpha] = 1/2, \[Alpha] < 3, \[Alpha] += 1/2,
plot = Show[Plot3D[cat[\[Alpha], \[Theta], q, p],
{q, -rq, rq}, {p, -rp, rp}, ImageSize -> 800,
Mesh -> {Range[-Floor[rq], Floor[rq] ],
Range[-Floor[rp], Floor[rp] ], Range[-1, 1, 1/4]/Pi},
MeshFunctions -> {#1 &, #2 &, #3 &},
MeshStyle -> {Directive[Black, Thickness[t] ],
Directive[Black, Thickness[t] ],
Directive[White, Thickness[t] ]},
PlotRange -> {-1/Pi, 1/Pi}, PlotPoints -> 81, MaxRecursion -> 4,
Method -> {Refinement -> {ControlValue -> 0.02} },
PlotStyle -> Opacity[0.85], Lighting -> "Classic",
ColorFunction -> ({RGBColor[1, 1, 0.75], Glow[GrayLevel[0.06] ],
Specularity[0.5, 60]} &),
Axes -> False, Boxed -> False,
ViewPoint ->
FromSphericalCoordinates[{Sqrt[229/20], Pi/3, -0.64 Pi}] ],
Graphics3D[{Thickness -> t, Black,
Line[{ {-rq, rp, 0}, {-rq, -rp, 0}, {rq, -rp, 0} }]}],
Graphics3D[{Thickness -> t, Black,
Line[{ {-rq, rp, -1/Pi}, {-rq, rp, 1/Pi} }]}],
(* q ticks *)
Sequence @@
Table[Graphics3D[{Thickness -> t, Black,
Line[{ {x, -rp, 0}, {x, -0.2 - rp, 0} }]}], {x, -Floor[rq],
Floor[rq]}],
(* p ticks *)
Sequence @@
Table[Graphics3D[{Thickness -> t, Black,
Line[{ {-rq, y, 0}, {-rq - 0.2, y, 0} }]}], {y, -Floor[rp],
Floor[rp]}],
(*W ticks *)
Sequence @@
Table[Graphics3D[{Thickness -> t, Black,
Line[{ {-rq, rp, z/(2 Pi)}, {-rq - 0.2, rp,
z/(2 Pi)} }]}], {z, -2, 2}],
(* axes labels *)
Graphics3D[Text[Style["q", FontS, Black], {0, -rp*1.11, -0.07}] ],
Graphics3D[Text[Style["p", FontS, Black], {-rq*1.11, 0, -0.07}] ],
Graphics3D[
Text[Style["W", FontS, Black], {-rq*0.93, rp*0.93, 0.8/Pi}] ],
Sequence @@
Table[Graphics3D[{Text[
Style[TextString[x], FontS,
Black], {x, -rp - 0.07 Max[rq, rp], -0.003}, {0,
1}]}], {x, -Floor[rq], Floor[rq]}],
Sequence @@
Table[Graphics3D[{Text[
Style[TextString[y], FontS, Black], {-rq - 0.07 Max[rq, rp],
y, -0.003}, {0, 1}]}], {y, -Floor[rp], Floor[rp]}],
Sequence @@
Table[Graphics3D[{Text[
Style[If[z == 0, "0", ToString[z/(2 Pi), TraditionalForm] ],
FontS, Black], {-rq - 0.3, rp, z/2/Pi}, {1, 0}]}], {z, -2,
2}],
BoxRatios -> {Automatic, Automatic, 8}, PlotRange -> All
];
trim = { {0., .26}, {.97, .86} };
imgname =
"Wignerfunction_catstate_" <> If[\[Theta] == 0, "even_", "odd_"] <>
TextString[\[Alpha]] <> ".png";
Export[imgname,
ImageResize[
ImageTrim[Image[plot, ImageResolution -> 400], trim,
DataRange -> { {0, 1}, {0, 1} }], 2000, Resampling -> "Linear"] ];
] ]
Licensing
I, the copyright holder of this work, hereby publish it under the following licence:
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International licence.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the licence, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible licence as the original.
File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 22:15, 20 May 2019 | | 2,000 × 1,026 (728 KB) | wikimediacommons>Geek3 | User created page with UploadWizard |
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