File:Mach-Zehnder photons animation.gif

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Mach-Zehnder_photons_animation.gif(300 × 220 pixels, file size: 110 KB, MIME type: image/gif, looped, 100 frames, 7.0 s)

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Summary

Description
English: Animation of photons in a Mach–Zehnder interferometer. In the empty interferometer each photon interferes with itself. If a detector is placed in the interferometer, the wavefunction will collapse so that the photon is either detected directly or it will move on and split at the second beam splitter without interference.
Date
Source Own work
Author user:Geek3
 
This plot was created with Matplotlib by n.

Source Code

The image is created by the following python source-code. Requirements:


Python Matplotlib source code
#!/usr/bin/python
# -*- coding: utf8 -*-

from math import *
import matplotlib.pyplot as plt
from matplotlib.patches import Polygon, Circle, Wedge
from matplotlib import animation
import numpy as np

# settings
fname = 'Mach-Zehnder_photons_animation'
width, height = 300, 220
nframes = 100
nphotons = 12
fps = 15

x0 = 100.5
x1 = 218.5
y0 = 200.5
y1 = 80.5
lx, lw, lh = 5, 46, 21 # laser
dtect = 62.5
t1, t2, tmove = 0.25, 0.9, 0.025
ymove = 24
rp = 2. # photon radius
cp1 = '#ff0000' # photon color
cp2 = '#ffaaaa' # splitphoton color

##
xstart = lx + lw / 2.
dx = x1 - x0
dy = y1 - y0
l = (x0 - xstart) + abs(dx) + abs(dy) + dtect + 2.*rp
xdet0 = (x0 + x1) / 2
fly_frac = 0.7
v = l / fly_frac
tdet0 = (xdet0 + 2.*rp - xstart) / v
tdet12 = l / v

# introduce artificial antibunching for illustration purpose
ptimes = (np.random.random() + np.sort(np.random.random(3*nphotons))[::3]) % 1

photons = [{} for i in range(nphotons)]
for i, p in enumerate(photons):
    p['t0'] = ptimes[i]
    if t1 <= (p['t0'] + tdet0) % 1 and (p['t0'] + tdet0) % 1 <= t2:
        # photon sees first detector
        if np.random.randint(2) == 0:
            # photon hits extra detector
            p['arm'] = 'none'
            p['det'] = 0
        else:
            # photon escapes first detector
            p['arm'] = 'lower'
            # => random detection at second beam splitter
            if np.random.randint(2) == 0:
                p['det'] = 1
            else:
                p['det'] = 2
    else:
        # photon sees standard Mach-Zehnder interferometer
        p['arm'] = 'both'
        p['det'] = 1
    
    if p['det'] == 0:
        p['tdet'] = (p['t0'] + tdet0) % 1
    else:
        p['tdet'] = (p['t0'] + tdet12) % 1
    p['click_frame'] = int(round(p['tdet'] * nframes)) % nframes

plt.close('all')
mpl.rc('path', snap=False)

def animate(nframe):
    # prepare a clean and image-filling canvas for each frame
    plt.clf()
    fig.gca().set_position((0, 0, 1, 1))
    plt.xlim(0, width)
    plt.ylim(0, height)
    plt.axis('off')
    
    t = float(nframe) / nframes
    
    # photons
    for p in photons:
        s0 = v * ((t - p['t0']) % 1)
        if s0 > l:
            continue
        s = s0 + start - x0
        if s <= 0:
            # from laser to first beam splitter
            x, y = x0 + s, y0
            fig.gca().add_patch(Circle((x, y), rp, color=cp1))
        elif s <= abs(dx) + abs(dy):
            # in the interferometer
            if s < abs(dx):
                xu, yu = x0 + copysign(s, dx), y0
            else:
                xu, yu = x1, y0 + copysign(s - abs(dx), dy)
            if s < abs(dy):
                xd, yd = x0, y0 + copysign(s, dy)
            else:
                xd, yd = x0 + copysign(s - abs(dy), dx), y1
                
            if s < xdet0 - x0 or p['arm'] == 'both':
                fig.gca().add_patch(Circle((xu, yu), rp, color=cp2))
                fig.gca().add_patch(Circle((xd, yd), rp, color=cp2))
            elif p['arm'] == 'lower':
                fig.gca().add_patch(Circle((xd, yd), rp, color=cp1))
        else:
            # after the interferometer
            x, y = x1 + (s - abs(dx) - abs(dy)), y1
            if p['arm'] == 'both':
                fig.gca().add_patch(Circle((x, y), rp, color=cp1))
            elif p['arm'] == 'lower':
                fig.gca().add_patch(Circle((x, y), rp, color=cp2))
                x, y = x1, y1 - (s - abs(dx) - abs(dy))
                fig.gca().add_patch(Circle((x, y), rp, color=cp2))
    
    
    # laser
    fig.gca().add_patch(
        Polygon([[lx, y0-lh/2.], [lx, y0+lh/2.],
                 [lx+lw, y0+lh/2.], [lx+lw, y0-lh/2.]],
            closed=True, facecolor='#cccccc', edgecolor='black'))
    plt.text(lx+lw/2., y0-2, 'laser', fontsize=12,
        horizontalalignment='center', verticalalignment='center')
    
    # beam splitters
    b = 12
    fig.gca().add_patch(
        Polygon([[x0-b, y0+b], [x0+b, y0+b], [x0+b, y0-b],
                 [x0-b, y0-b], [x0-b, y0+b], [x0+b, y0-b]],
            closed=True, facecolor='#88aadd', edgecolor='black',
            linewidth=2, alpha=0.4))
    fig.gca().add_patch(
        Polygon([[x1-b, y1+b], [x1+b, y1+b], [x1+b, y1-b],
                 [x1-b, y1-b], [x1-b, y1+b], [x1+b, y1-b]],
            closed=True, facecolor='#88aadd', edgecolor='black',
            linewidth=2, alpha=0.4))
    
    # mirrors
    m, mw = 12, 4
    fig.gca().add_patch(
        Polygon([[x1-m+mw/2., y0+m+mw/2.], [x1+m+mw/2., y0-m+mw/2.]],
            closed=False, edgecolor='#555555', linewidth=mw))
    fig.gca().add_patch(
        Polygon([[x0-m-mw/2., y1+m-mw/2.], [x0+m-mw/2., y1-m-mw/2.]],
            closed=False, edgecolor='#555555', linewidth=mw))
    
    # detectors
    c_off = '#cccccc'
    c_on = '#cc0000'
    c0 = c1 = c2 = c_off
    for p in photons:
        if p['click_frame'] == nframe:
            if p['det'] == 0: c0 = c_on
            if p['det'] == 1: c1 = c_on
            if p['det'] == 2: c2 = c_on
    if t1 <= t and t <= t2:
        yd = y0
    else:
        yd = y0 - min((t1-t)%1, tmove, (t-t2)%1) * ymove / float(tmove)
    fig.gca().add_patch(mpl.patches.Wedge((xdet0, yd), b, 270, 90, fc=c0))
    fig.gca().add_patch(mpl.patches.Wedge((x1 + dtect, y1), b, 270, 90, fc=c1))
    fig.gca().add_patch(mpl.patches.Wedge((x1, y1 - dtect), b, 180, 0, fc=c2))

fig = plt.figure(figsize=(width/100., height/100.))
anim = animation.FuncAnimation(fig, animate, frames=nframes)
anim.save(fname + '.gif', writer='imagemagick', fps=fps)

Postprocessing with gifsicle:

gifsicle -k 64 --background="#ffffff" -O3 --careful -i < Mach-Zehnder_photons_animation.gif > Mach-Zehnder_photons_animation_.gif

Licensing

I, the copyright holder of this work, hereby publish it under the following licenses:
GNU head Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.
w:en:Creative Commons
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22 August 2015

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Date/TimeThumbnailDimensionsUserComment
current10:30, 22 August 2015Thumbnail for version as of 10:30, 22 August 2015300 × 220 (110 KB)wikimediacommons>Geek3{{Information |Description ={{en|1=Animation of photons in a en:Mach–Zehnder interferometer. In the empty interferometer each photon interferes with itself. If a detector is placed in the...

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