File:Wignerfunction fock 2.png

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Summary

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Description
English: Wigner function of a Fock state with photon number n=2.
Date
Source Own work
 
This diagram was created with Mathematica by n.
Author Geek3

Source code

[edit]
fock[n_, q_, p_] := (-1)^n /
   Pi Exp[-q ^2 - p^2] LaguerreL[n, 2 q^2 + 2 p^2];
rq = 4; rp = 4; t = 0.003; FontS = 20;
For[n = 0, n <= 4, n++, plot = Show[Plot3D[fock[n, 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} },
    PerformanceGoal -> "Quality",
    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 - 1/2]}],
   (*W ticks *)
   Sequence @@ 
    Table[Graphics3D[{Thickness -> t, Black, 
       Line[{ {-rq, rp, z/(2 Pi)}, {-rq - 0.2, rp, 
          z/(2 Pi)} }]}], {z, -2, 2}],
   (* box *)
   (*Graphics3D[{Thickness\[Rule]t/2,Gray,Line[{ {rq,-rp,1/Pi},{rq,rp,
   1/Pi},{-rq,rp,1/Pi} }],Line[{ {rq,rp,0},{rq,rp,1/Pi} }],
   Line[{ {rq,-rp,0},{rq,-rp,1/Pi} }]}],*)
   (* axes labels *)
   Graphics3D[Text[Style["q", FontS, Black], {0, -rp*1.15, -0.07}] ],
   Graphics3D[Text[Style["p", FontS, Black], {-rq*1.15, 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 - 0.10 Max[rq, rp], 0}, {0, 
         1}]}], {x, -Floor[rq], Floor[rq]}],
   Sequence @@ 
    Table[Graphics3D[{Text[
        Style[TextString[y], FontS, Black], {-rq - 0.10 Max[rq, rp], 
         y, 0}, {0, 1}]}], {y, -Floor[rp], Floor[rp - 1/2]}],
   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, 6}, PlotRange -> All
   ];
 trim = { {0., .25}, {.95, .91} };
 imgname = "Wignerfunction_fock_" <> TextString[n] <> ".png";
 Export[imgname, 
  ImageResize[
   ImageTrim[Image[plot, ImageResolution -> 400], trim, 
    DataRange -> { {0, 1}, {0, 1} }], 2000, Resampling -> "Linear"] ];
 ]

Licensing

[edit]
I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
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 license, 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 license as the original.

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Date/TimeThumbnailDimensionsUserComment
current16:45, 20 May 2019Thumbnail for version as of 16:45, 20 May 20192,000 × 1,250 (748 KB)Geek3 (talk | contribs)User created page with UploadWizard

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