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SetDirectory[NotebookDirectory[]];
\[Theta]0 = -.1 \[Pi]; \[Phi]0 = .35*\[Pi];
\[Psi]0 = {Cos[\[Theta]0] Cos[\[Phi]0], Sin[\[Theta]0] Cos[\[Phi]0],
Sin[\[Phi]0]};
Clear[BlochSphereVector];
BlochSphereVector[\[Psi]_, imSize_ : 1000, color_ : Gray,
opacity_ : 1, \[Phi]view_ : \[Pi]/4, viewdist_ : 100] := Module[{
tubeball, pointline,
blochSphereEmpty,
lineLen = 1,
mag = 4
},
tubeball[pt_, r_] :=
Sequence[Sphere[pt, 3 r],(*Opacity[.5],*)Tube[{{0, 0, 0}, pt}, r]];
pointline[pt_, r_] :=
Sequence[Point[pt],(*Opacity[.5],*)Line[{{0, 0, 0}, pt}]];
Show[
Graphics3D[{Blue, Opacity@0.02,
Specularity[Blue, 10],
Sphere[{0, 0, 0}, 1],
Lighting -> "Neutral",
Thickness@0.003, Arrowheads[.03],
Opacity[.2], Gray,
Line[lineLen*{{0, 0, 0}, {0, 0, 1}}],
Line[lineLen*{{0, 0, 0}, {1, 0, 0}}],
Line[lineLen*{{0, 0, 0}, {0, 1, 0}}],
Opacity[.03], Gray, EdgeForm[{Transparent}],
Polygon[
Table[{Cos[\[Theta]\[Prime]], Sin[\[Theta]\[Prime]],
0}, {\[Theta]\[Prime], 0, 2 \[Pi], .01}]]
},
Boxed -> False, PlotRange -> ConstantArray[1*{-1, 1}, 3]],
Graphics3D[{Opacity[1], GrayLevel[.9], PointSize@0.02,
Point[{1, 0, 0}],
Point[{0, 1, 0}],
Point[{0, 0, 1}]
}],
Graphics3D[{
Lighting -> "Neutral",
Thickness[0.005],
Arrowheads[0.025],
PointSize[0.02],
Opacity[opacity], color, tubeball[\[Psi], 0.01],
PointSize[0.02],
Opacity@1, Black, Sphere[{0, 0, 0}, 0.025]
}],
ImageSize -> imSize,
ImagePadding -> 0,
ViewVertical -> {0, 0, 1},
ViewPoint ->
viewdist*{1 Cos[\[Phi]view], 1 Cos[\[Phi]view], 1 Sin[\[Phi]view]}
]
];
BlochSphereVectorOnly[\[Psi]_, imSize_ : 1000, color_ : Gray,
opacity_ : 1] := Module[{tubeball},
tubeball[pt_, r_] :=
Sequence[Sphere[pt, 3 r],(*Opacity[.5],*)Tube[{{0, 0, 0}, pt}, r]];
Graphics3D[{Opacity[opacity], color, tubeball[\[Psi], 0.01]}]
];
BlochSphereVectorFromAngles[\[Theta]_, \[Phi]_, imSize_ : 1000,
color_ : Gray, \[Phi]view_ : \[Pi]/4, viewdist_ : 100] :=
BlochSphereVector[{Cos[\[Theta]] Cos[\[Phi]],
Sin[\[Theta]] Cos[\[Phi]], Sin[\[Phi]]}, imSize,
color, \[Phi]view, viewdist];
Clear[BlochSphereRotation];
BlochSphereRotation[\[Psi]0_, \[Theta]_, ax_, tmax_ : 1,
imSize_ : 1000, color_ : Gray, opacityScale_ : 1,
tubeOpacity_ : 1] := Module[{
\[Psi]1,
arc, arcpts,
thickness = 0.006},
If[tmax == 0, Return[BlochSphereVector[\[Psi]0, imSize]]];
\[Psi]1 = RotationMatrix[tmax*\[Theta], ax] . \[Psi]0;
arc = ParametricPlot3D[
RotationMatrix[t \[Theta], ax] . \[Psi]0, {t, 0, tmax},
PlotStyle -> Directive[Gray, Thickness[thickness]],
ColorFunction -> (Opacity[opacityScale*(#4 + .1), color] &)];
arcpts =
Table[RotationMatrix[t \[Theta], ax] . \[Psi]0, {t, 0, tmax,
0.01}];
Show[
BlochSphereVector[\[Psi]1, imSize, Gray, tubeOpacity],
arc,
Graphics3D[{
Opacity[0.1*opacityScale], color,
Thickness[0.003],
Arrowheads[0.02],
EdgeForm[{Transparent, Thickness[0.001], Dotted, color}],
Polygon[Join[
arcpts, {Normalize[ax]*Dot[Last[arcpts], Normalize[ax]]}]]
}]
]
];
BlochSphereRotationSequence[\[Psi]0_, \[Theta]List_, axList_,
animTime_ : 1, imSize_ : 1000, colorList\[Prime]_ : Null,
opacityList\[Prime]_ : Null] := Module[{
\[Psi] = \[Psi]0,
i = 0,
colorList = colorList\[Prime],
opacityList = opacityList\[Prime],
\[Theta], ax, tmax, opacity, color,
displayList = {},
arc, arcpts,
thickness = 0.006},
If[colorList == Null,
colorList = ConstantArray[Gray, Length[\[Theta]List]]];
If[opacityList == Null,
opacityList = ConstantArray[0.1, Length[\[Theta]List]]];
If[animTime == 0, Return[BlochSphereVector[\[Psi]0, imSize]]];
While[i < Length[\[Theta]List]*animTime ,
\[Theta] = \[Theta]List[[i + 1]]; (*1-indexed*)
ax = axList[[i + 1]];
color = colorList[[i + 1]];
opacity = opacityList[[i + 1]];
tmax = Clip[Length[\[Theta]List]*animTime - i, {0, 1}];
arc =
ParametricPlot3D[
RotationMatrix[t \[Theta], ax] . \[Psi], {t, 0, tmax},
PlotStyle -> Directive[Gray, Thickness[thickness]],
ColorFunction -> (Opacity[#4 + .1, color] &)];
arcpts =
Table[RotationMatrix[t \[Theta], ax] . \[Psi], {t, 0, tmax,
0.01}];
\[Psi] = RotationMatrix[tmax*\[Theta], ax] . \[Psi];
AppendTo[displayList, arc];
AppendTo[displayList,
Graphics3D[{
Opacity[opacity], color,
Thickness[0.003],
Arrowheads[0.02],
EdgeForm[{Transparent, Thickness[0.001], Dotted, color}],
Polygon[
Join[arcpts, {Normalize[ax]*Dot[Last[arcpts], Normalize[ax]]}]]
}]
];
++i;
];
Show[BlochSphereVector[\[Psi], imSize], displayList]
];
baseSwitchClosed =
Import["/Users/ben/Dropbox/Research/qpgav2/animation/switches_\
closed_2.png"];
baseSwitchOpen =
Import["/Users/ben/Dropbox/Research/qpgav2/animation/switches_open_\
2.png"];
base = baseSwitchClosed;
(*these coordinates were chosen by clicking points on the images to \
trace the photon path*)
coordsRingToBeamsplitterTop = \
{{3213.8305999348113`, 1059.3037483813007`}, {3166.0119817800314`,
1106.6882343267484`}, {3125.583593903153`,
1147.1165061254958`}, {3086.4594599043658`,
1186.67535272427`}, {3043.4227964275683`,
1229.27718752295`}, {2987.779583629292`,
1271.009597121657`}, {2905.619018309969`,
1274.9220105215356`}, {2810.8516715129053`,
1275.7914357215086`}, {2726.5174271155183`,
1276.6608609214818`}, {2650.008009517889`,
1275.7914357215086`}, {2563.934914720556`,
1275.7914357215086`}, {2471.3400862202475`,
1288.398101121118`}, {2384.3975662229414`,
1321.870971320081`}, {2303.1298738860205`,
1367.5585691098804`}, {2225.3164345665623`,
1424.505919708116`}, {2153.588739490654`,
1485.36568370623`}, {2088.3818494926745`,
1550.137861104223`}, {2029.260935894506`,
1610.5629125023506`}, {1969.2705970963648`,
1681.8557789001418`}, {1903.4672057829514`,
1751.2574705894`}, {1783.5966424593155`,
1804.267902358066`}}; coordsRingToBeamsplitterBottom = \
{{3213.8027411834105`, 1058.23640996825`}, {3182.50343398438`,
1028.2412405691794`}, {3149.8998729072596`,
998.2460711701087`}, {3115.5574614301927`,
963.4690631711865`}, {3079.911260387559`,
928.2573425722774`}, {3040.78689423251`,
888.2637833735166`}, {2990.360232634072`,
847.8355115747693`}, {2923.414724392408`,
845.2272359748501`}, {2853.8607083945635`,
844.7925233748635`}, {2786.4801393185203`,
844.7925233748635`}, {2716.9261233206753`,
843.9230981748906`}, {2651.7190011664343`,
845.2272359748501`}, {2583.903835568535`,
844.7925233748635`}, {2514.3498195706907`,
842.1842477749444`}, {2434.7975298512865`,
828.2734445753754`}, {2355.6796044974762`,
806.537814576049`}, {2280.909037299793`,
774.3690821770456`}, {2214.397893423723`,
734.8102355782714`}, {2152.668704225636`,
689.1654125796856`}, {2102.2420426271983`,
640.9123139811809`}, {2060.944229550347`,
591.789790182703`}, {2013.9952687518016`,
538.7547369062154`}, {1951.3966543537413`,
490.50163830771044`}, {1901.8394179552768`,
433.11957510948855`}, {1850.1085024787487`,
372.6945237113607`}, {1784.032303358927`, 309.66119671331376`}};
coordsBeamsplitterToMirrorTop = {{4397.265782207965`,
1275.59}, {4341.867493152422`, 1275.59}, {4277.8731729089595`,
1275.59}, {4212.9234547059095`, 1275.59}, {4147.9737365028595`,
1275.59}, {4089.2323197232695`, 1275.59}, {4027.148030264472`,
1275.59}, {3963.63089891113`, 1275.59}, {3892.472879284618`,
1274.770400099958`}, {3819.4043187837683`,
1275.59}, {3746.8129471730385`, 1275.59}, {3683.295815819696`,
1275.59}, {3611.182653278434`, 1275.59}, {3531.428092374329`,
1275.7255430147088`}, {3443.55417908275`,
1272.382542813081`}, {3382.425032538703`,
1228.92290257983`}, {3326.0716005684094`,
1172.0918991521612`}, {3269.718168598116`,
1113.8281813523663`}, {3214.3198795425733`, 1058.907463754199`}};
coordsBeamsplitterToAtomBottom = {{4222.067322203811`,
842.69}, {4206.785035567799`, 842.69}, {4193.89098878592`,
842.69}, {4173.355288596361`, 842.69}, {4155.68527219589`,
842.69}, {4134.672128071375`, 842.69}, {4115.091315751729`,
842.69}, {4091.606022021691`,
846.1683803338327`}, {4068.6825920676724`,
842.69}, {4047.6694479431567`, 842.69}, {4006.5983026088747`,
842.69}, {3955.498284192129`, 842.69}, {3892.4588518185806`,
842.69}, {3827.5091336155306`, 842.69}, {3767.812573921191`,
842.69}, {3701.90771280339`, 842.69}, {3639.3459794096357`,
842.69}, {3575.828848056293`, 842.69}, {3511.8342727679938`,
842.69}, {3437.810059262719`,
848.5562376207095`}, {3385.7548979312223`,
887.2395256681143`}, {3348.5043242559436`,
925.9228137155192`}, {3303.134908282865`,
969.859387794053`}, {3259.1983342043313`,
1014.7511047873376`}, {3214.784316190841`, 1059.1652503232467`}};
ringXY = {1125, 1060}; (* approx center of ring in pixels *)
ringRadius = 995;
(*Manipulate[Show[base,Graphics[{Magenta,Circle[{x,y}, r]}],ImageSize\
\[Rule]1500],{x,1100,1200},{y,1000,1200},{r,950,1100}]*)
\
(*Show[base,Graphics[{Magenta,Circle[ringXY, ringRadius]}],ImageSize\
\[Rule]1500]*)
coordsRing =
Table[ringXY - ringRadius*{Cos[2 \[Pi] t], Sin[2 \[Pi] t]}, {t, 0,
1, 0.01}];
(*pathRingCCW[t_]:= ringXY-ringRadius*{Cos[2\[Pi] t], Sin[2\[Pi] t]};
pathRingCW[t_] := ringXY-ringRadius*{Cos[-2\[Pi] t], Sin[-2\[Pi] \
t]};
(*Manipulate[Show[base,Graphics[{PointSize[0.05],Red,Point[pathRingCW[\
t]], Blue,Point[ pathRingCCW[t]]}],ImageSize\[Rule]1500],{t,0,1}]*)*)
ymax = 1.2*
ImageAspectRatio[
base]; (*stretch the image vertically a little to make it look \
less distorted when viewed from an angle*)
p = {{0, 0}, {1, 0}, {1, ymax}, {0, ymax}};
plane = Graphics3D[{
EdgeForm[Opacity[0.2]],
Texture[base],
Polygon[(Join[#1, {0.002}] &) /@ p,
VertexTextureCoordinates -> {{0, 0}, {1, 0}, {1, 1}, {0, 1}}]
}];
(*Show[
plane,
PlotRange\[Rule]{{0,1},{0,ymax},{-.1,.1}},
ViewPoint\[Rule] 1*{0,-1.5,2}, ViewVertical\[Rule]{0,0,1},
ImageSize\[Rule]1500,ImagePadding\[Rule]5,Boxed\[Rule]False,Lighting\
\[Rule]"Neutral"]*)
coordsRingNormalized =
Map[((#/ ImageDimensions[base])*{1, ymax}) &, coordsRing];
coordsRingToBeamsplitterTopNormalized =
Map[((#/ ImageDimensions[base])*{1, ymax}) &,
coordsRingToBeamsplitterTop];
coordsRingToBeamsplitterBottomNormalized =
Map[((#/ ImageDimensions[base])*{1, ymax}) &,
coordsRingToBeamsplitterBottom];
coordsBeamsplitterToMirrorTopNormalized =
Map[((#/ ImageDimensions[base])*{1, ymax}) &,
coordsBeamsplitterToMirrorTop];
coordsBeamsplitterToAtomBottomNormalized =
Map[((#/ ImageDimensions[base])*{1, ymax}) &,
coordsBeamsplitterToAtomBottom];
tspecTop1 =
Rescale[Prepend[
Accumulate[
Map[Norm, Differences[coordsRingToBeamsplitterTopNormalized]]],
0]];
tspecTop2 =
Rescale[Prepend[
Accumulate[
Map[Norm, Differences[coordsBeamsplitterToMirrorTopNormalized]]],
0]];
tspecBot1 =
Rescale[Prepend[
Accumulate[
Map[Norm,
Differences[coordsRingToBeamsplitterBottomNormalized]]], 0]];
(*no tspecBot2 because we want photon to seem like it's moving slower \
in chamber*)
zValueForPath = 0.0;
pathRingCCW =
Interpolation[
TimeSeries[
Join[#1, {zValueForPath}] & /@ coordsRingNormalized, {0, 1}]];
pathRingCW =
Interpolation[
TimeSeries[
Reverse[Join[#1, {zValueForPath}] & /@ coordsRingNormalized], {0,
1}]];
pathTop1 =
Interpolation[
TimeSeries[
Reverse[Join[#1, {zValueForPath}] & /@
coordsRingToBeamsplitterTopNormalized], {tspecTop1}]];
pathTop2 =
Interpolation[
TimeSeries[
Reverse[Join[#1, {zValueForPath}] & /@
coordsBeamsplitterToMirrorTopNormalized], {tspecTop2}]];
pathBot1 =
Interpolation[
TimeSeries[
Reverse[Join[#1, {zValueForPath}] & /@
coordsRingToBeamsplitterBottomNormalized], {tspecBot1}]];
pathBot2 =
Interpolation[
TimeSeries[
Reverse[Join[#1, {zValueForPath}] & /@
coordsBeamsplitterToAtomBottomNormalized], {0, 1}]];
(*define functions to show the pulses*)
dt = 0.001;(*0.0005;*)
rfunc =
Function[{x, y, z}, Abs[z] > 0.001];
opac = 0.3;
A0 = 0.05;
vg = 1.3;
\[Omega] = 70;
\[Delta]\[Omega] = 250;
Clear[pulse, ringPulse, reflectedPulse];
pulse[path_, A_, \[Tau]_, color_, op_ : opac] := ListPointPlot3D[
Table[path[t] + {0, 0,
A*A0 Cos[\[Omega] (\[Tau]/vg -
t)] Exp[-\[Delta]\[Omega] (\[Tau] - t)^2]}, {t, 0, 1,
dt}],
PlotStyle -> {color, PointSize[Small]}, Filling -> 0,
FillingStyle -> {color, Opacity[op]}, RegionFunction -> rfunc,
RegionBoundaryStyle -> None];
ringPulse[path_, A_, \[Tau]_, color_, pointOp_ : 1, op_ : opac,
numRotations_ : 1] := ListPointPlot3D[
Table[path[Mod[t/4, 1]] + {0, 0,
A*A0 Cos[\[Omega] (\[Tau]/vg -
t)] Exp[-\[Delta]\[Omega] ((\[Tau] - t)^2)]}, {t, 0,
4*numRotations, dt}],
PlotStyle -> {color, Opacity[pointOp], PointSize[Small]},
Filling -> 0, FillingStyle -> {color, Opacity[op]},
RegionFunction -> rfunc, RegionBoundaryStyle -> None];
reflectedPulse[path_, A_, \[Tau]_, color_, \[Phi]_ : -1] :=
ListPointPlot3D[
Table[path[t] + {0, 0,
A*A0 Cos[\[Omega] (\[Tau]/vg -
t)] Exp[-\[Delta]\[Omega] (\[Tau] - t)^2] + \[Phi]*A*
A0 Cos[\[Omega] ((\[Tau] - 1)/
vg + (t - 1))] Exp[-\[Delta]\[Omega] ((\[Tau] -
1) + (t - 1))^2]
}, {t, 0, 1, dt}],
PlotStyle -> {color, PointSize[Small]}, Filling -> 0,
FillingStyle -> {color, Opacity[opac]}, RegionFunction -> rfunc,
RegionBoundaryStyle -> None];
BS = 1/Sqrt[2] ({
{1, I},
{I, 1}
});
\[Phi]ringDelay = 1.465(*1.462*);
createPulses[\[Alpha]_, \[Beta]_, t_] :=
Module[{A, B, \[Alpha]\[Prime], \[Beta]\[Prime]},
{A, B} = Abs[BS . {\[Alpha], \[Beta]}];
{\[Alpha]\[Prime], \[Beta]\[Prime]} = Abs[BS . {A, -B}];
Show[
pulse[pathTop1, \[Alpha], t, Red],
pulse[pathBot1, \[Beta], t, Blue],
reflectedPulse[pathTop2, A, t - 1, Purple, 1],
reflectedPulse[pathBot2, B, t - 1, Magenta, -1],
pulse[pathTop1, \[Alpha], 3 - (t - 1), Blue],
pulse[pathBot1, \[Beta], 3 - (t - 1), Red]
]
];
createRingPulses[\[Alpha]_, \[Beta]_, t_] :=
Module[{CWpath, CCWpath},
CWpath[\[Tau]_] := pathRingCW[Mod[\[Tau] + \[Phi]ringDelay/4, 1]];
CCWpath[\[Tau]_] := pathRingCCW[Mod[\[Tau] + \[Phi]ringDelay/4, 1]];
Show[
ringPulse[CWpath, \[Alpha], t, Red],
ringPulse[CCWpath, \[Beta], t, Blue]
]
];
createRingPulsesReturn[\[Alpha]_, \[Beta]_, t_] :=
Module[{CWpath, CCWpath},
CWpath[\[Tau]_] := pathRingCW[Mod[\[Tau] - \[Phi]ringDelay/4, 1]];
CCWpath[\[Tau]_] := pathRingCCW[Mod[\[Tau] - \[Phi]ringDelay/4, 1]];
Show[
ringPulse[CWpath, \[Alpha], t, Red, 1, opac, 2],
ringPulse[CCWpath, \[Beta], t, Blue, 1, opac, 2]
]
];
createOtherRingPulses[t_, nPulses_ : 4 - 1] :=
Module[{t\[Prime] = t + \[Phi]ringDelay, pointOp = .1, op = .07},
Show[
ringPulse[pathRingCW, 1, Mod[t\[Prime] - 1*4/6, 4], Red, pointOp,
op],
ringPulse[pathRingCW, 1, Mod[t\[Prime] - 2*4/6, 4], Red, pointOp,
op],
ringPulse[pathRingCW, 1, Mod[t\[Prime] - 3*4/6, 4], Red, pointOp,
op],
ringPulse[pathRingCW, 1, Mod[t\[Prime] - 4*4/6, 4], Red, pointOp,
op],
ringPulse[pathRingCW, 1, Mod[t\[Prime] - 5*4/6, 4], Red, pointOp,
op],
ringPulse[pathRingCCW, 1, Mod[t\[Prime] - 1*4/6, 4], Blue, pointOp,
op],
ringPulse[pathRingCCW, 1, Mod[t\[Prime] - 2*4/6, 4], Blue, pointOp,
op],
ringPulse[pathRingCCW, 1, Mod[t\[Prime] - 3*4/6, 4], Blue, pointOp,
op],
ringPulse[pathRingCCW, 1, Mod[t\[Prime] - 4*4/6, 4], Blue, pointOp,
op],
ringPulse[pathRingCCW, 1, Mod[t\[Prime] - 5*4/6, 4], Blue, pointOp,
op]
]
]
ringSpeed = 1 + 2*(1/2 - \[Phi]ringDelay/4);
(*"retroactive" Bloch sphere rotation to show teleportation action*)
customBlochSphereRotationSequence[\[Psi]0_, \[Theta]List_, axList_,
animTime_ : 1, imSize_ : 1000, colorList\[Prime]_ : Null,
opacityList\[Prime]_ : Null, auxTime_ : 1] := Module[{
\[Psi] = \[Psi]0,
i = 0,
colorList = colorList\[Prime],
opacityList = opacityList\[Prime],
\[Theta], ax, tmax, opacity, color,
displayList = {},
arc, arcpts,
thickness = 0.006,
aux\[Theta] = 0.7 \[Pi], auxAx = {0, 1, 0}, auxInsertionPos = 1,
auxColor = Magenta, auxOp = 0.1
},
If[colorList == Null,
colorList = ConstantArray[Gray, Length[\[Theta]List]]];
If[opacityList == Null,
opacityList = ConstantArray[0.1, Length[\[Theta]List]]];
If[animTime == 0.0, Return[BlochSphereVector[\[Psi]0, imSize]]];
While[i < Length[\[Theta]List]*animTime ,
(*retroactively insert a rotation here*)
If[i == auxInsertionPos && auxTime > 0.0,
arc =
ParametricPlot3D[
RotationMatrix[t aux\[Theta], auxAx] . \[Psi], {t, 0,
auxTime},
PlotStyle -> Directive[auxColor, Thickness[thickness]],
ColorFunction -> (Opacity[#4 + .1, auxColor] &)];
arcpts =
Table[
RotationMatrix[t aux\[Theta], auxAx] . \[Psi], {t, 0, auxTime,
0.01}];
\[Psi] = RotationMatrix[auxTime*aux\[Theta], auxAx] . \[Psi];
AppendTo[displayList, arc];
AppendTo[displayList,
Graphics3D[{
Opacity[auxOp], auxColor,
Thickness[0.003],
Arrowheads[0.02],
EdgeForm[{Transparent, Thickness[0.001], Dotted, auxColor}],
Polygon[Join[
arcpts, {Normalize[auxAx]*
Dot[Last[arcpts], Normalize[auxAx]]}]]
}]
];
];
\[Theta] = \[Theta]List[[i + 1]]; (*1-indexed*)
ax = axList[[i + 1]];
color = colorList[[i + 1]];
opacity = opacityList[[i + 1]];
tmax = Clip[Length[\[Theta]List]*animTime - i, {0, 1}];
arc =
ParametricPlot3D[
RotationMatrix[t \[Theta], ax] . \[Psi], {t, 0, tmax},
PlotStyle -> Directive[Gray, Thickness[thickness]],
ColorFunction -> (Opacity[#4 + .1, color] &)];
arcpts =
Table[RotationMatrix[t \[Theta], ax] . \[Psi], {t, 0, tmax,
0.01}];
\[Psi] = RotationMatrix[tmax*\[Theta], ax] . \[Psi];
AppendTo[displayList, arc];
AppendTo[displayList,
Graphics3D[{
Opacity[opacity], color,
Thickness[0.003],
Arrowheads[0.02],
EdgeForm[{Transparent, Thickness[0.001], Dotted, color}],
Polygon[Join[
arcpts, {Normalize[ax]*Dot[Last[arcpts], Normalize[ax]]}]]
}]
];
++i;
];
Show[BlochSphereVector[\[Psi], imSize], displayList]
];
(*
Timings:
t~0-0.1:red photon enters scattering unit
t~0.1-0.2:blue photon enters scattering unit
t~0.4-0.6 photon passes phase shifter
t=1:photon passes beamsplitter
t=2:photon hits atom/mirror
t=3:photon passes beamsplitter (return)
t~3.4:photon passes phase shifter
t=4:photon re-injected into ring
t=4-4.75:atom state rotated
t=5.25-5.75:atom measured,teleportation animation shown
*)
\[Theta]0atom = \[Pi]/2; \[Phi]0atom = 0;
\[Psi]0atom = {Cos[\[Theta]0atom] Cos[\[Phi]0atom],
Sin[\[Theta]0atom] Cos[\[Phi]0atom], Sin[\[Phi]0atom]};
\[Psi]1atom = {0, 0, -1};
scaleTime01[t_, min_,
max_] := (Clip[t, {min, max}] - min)/(max -
min); (*scales a time range between min and max to run from 0 to \
1*)
laserImg =
Import["/Users/ben/Dropbox/Research/qpgav2/animation/laser_pulse.\
png"];
baseSwitchClosedLaserOn =
Import["/Users/ben/Dropbox/Research/qpgav2/animation/switches_\
closed_laser_on.png"];
baseSwitchClosedMeterOn =
Import["/Users/ben/Dropbox/Research/qpgav2/animation/switches_\
closed_meter_on_laser_on_labeled.png"];
laserPlane = Graphics3D[{
EdgeForm[Opacity[0.0]], Texture[laserImg],
Polygon[(Join[#1, {0.003}] &) /@ p,
VertexTextureCoordinates -> {{0, 0}, {1, 0}, {1, 1}, {0, 1}}]
}];
Clear[showBase];
showBase[t_, imSize_ : 1500, debug_ : False] :=
Module[{texture, blochPhoton, blochAtom, tAtomRotate, tPhotonZ,
tMeas, ballSize, imScale, meterAngle, meterPivot, meterEnd, meter},
ballSize = imSize/5;
imScale = imSize/1500;
(* set up progress of different events of animation *)
tPhotonZ = 0;
tPhotonZ += 1/2*scaleTime01[t, 0.4, 0.6];
tPhotonZ += 1/2*2/3*scaleTime01[t, 1.9, 2.1];
tPhotonZ += 1/2*1/3*scaleTime01[t, 3.4, 3.6];
tAtomRotate = scaleTime01[t, 4, 4.75];
tMeas = scaleTime01[t, 5.25, 5.65];
If[debug,
Print[tPhotonZ];
Print[tAtomRotate];
Print[tMeas];
];
meterAngle = 80 Degree *(Sin[\[Pi] tMeas] - .5);
meterPivot = {0.9235, ymax*.5, 0};
meterEnd =
meterPivot +
RotationMatrix[meterAngle, {0, 0, -1}] . {0, .03, 0};
meter = Line[{meterPivot, meterEnd}];
blochPhoton =
customBlochSphereRotationSequence[\[Psi]0, {\[Pi]/
4, \[Pi]/2 + \[Pi]/4}, {{0, 0, 1}, {0, 0, 1}}, tPhotonZ,
ballSize, {Gray, Gray}, Null, tMeas];
blochAtom = Show[
BlochSphereRotation[\[Psi]0atom, 0.7 \[Pi], {1, 0, 0},
tAtomRotate, ballSize, Magenta, 1 - tMeas, 1 - tMeas],
BlochSphereVectorOnly[\[Psi]1atom, ballSize, Magenta, tMeas]
];
texture = If[0 <= t <= 0.2 || 3.8 <= t <= 4.0, baseSwitchOpen,
If[0 < tAtomRotate < 1, baseSwitchClosedLaserOn,
If[0 < tMeas < 1, baseSwitchClosedMeterOn,
baseSwitchClosed]
]
];
Show[
Graphics3D[{
Inset[blochPhoton, {.58, 1.07*ymax, -.12}],
Inset[blochAtom, {.88, 1.07*ymax, -.12}],
EdgeForm[Opacity[0.0]],
Texture[texture],
Polygon[(Join[#1, {0.002}] &) /@ p,
VertexTextureCoordinates -> {{0, 0}, {1, 0}, {1, 1}, {0, 1}}],
Text[
Style["|photon\[RightAngleBracket]", 25*imScale,
Gray], {0.58 - .12, 1.07*ymax + .02, -.00}],
Text[
Style["|atom\[RightAngleBracket]", 25*imScale,
Gray], {0.88 - .12, 1.07*ymax + .02, -.00}],
If[tAtomRotate > 0, Text[Style["Subscript[R, x](\[Theta])", 18*imScale, Magenta,
Opacity[tAtomRotate - tMeas]], {0.89, .90*ymax, -.00}]],
If[tMeas > 0, Text[Style["Subscript[R, y](-\[Theta])", 18*imScale, Magenta, Opacity[tMeas]], {0.55, .86*ymax, -.00}]],
Thick, Black, meter,
If[debug,
Text[Style["t=" <> ToString[N[t, 3]], 25*imScale, Gray], {0.1,
1.07*ymax + .02, -.00}]]
}],
PlotRange -> {{0, 1}, {0, ymax}, {-.1, .1}},
ViewPoint -> 1*{0, -1.5, 2}, ViewVertical -> {0, 0, 1},
ImageSize -> imSize, ImagePadding -> 5, Boxed -> False,
Lighting -> "Neutral"]
];
Clear[renderFrame];
renderFrame[t_, imSize_ : 1000, debug_ : False] := Quiet@Show[
showBase[t, imSize, debug],
createRingPulses[1, 1 , ringSpeed (t) + 4],
createRingPulsesReturn[-1, -1, ringSpeed (t - 4)],
createOtherRingPulses[t ringSpeed],
createPulses[-1, -1, t],
PlotRange -> {{0, 1}, {0, ymax}, {-.1, .1}},
ViewPoint -> 1*{0, -1.5, 2}, ViewVertical -> {0, 0, 1},
ImageSize -> imSize, ImagePadding -> 5, Boxed -> False,
Lighting -> "Neutral"]
saveFrame[t_] := Module[{frame, title},
frame = Quiet[renderFrame[t, 2000]];
title = IntegerString[Floor[10^4 * (t + 2)], 10, 6] <> ".png";
Export["frames/" <> title, frame];
Print["rendered frame: " <> title]
]
start = -1; stop = 8.5;
simTimescale = (stop - start);
animationTime = 15;
framesPerSec = 60;
frameStep = simTimescale /(animationTime*framesPerSec);
ParallelDo[saveFrame[t], {t, start, stop, frameStep}]
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