QHO-coherent3-amplitudesqueezed2dB-animation-color.gif (300 × 200 pixels, file size: 308 KB, MIME type: image/gif, looped, 120 frames, 6.0 s)
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Summary
DescriptionQHO-coherent3-amplitudesqueezed2dB-animation-color.gif |
English: Animation of the quantum wave function of a squeezed coherent state in a Quantum harmonic oscillator with α=3 and 2dB of squeezing. The probability distribution is drawn along the ordinate, while the phase is encoded by color. The gaussian wave packet oscillates in position and width such that the amplitude is defined most sharply. |
Date | |
Source |
Own work![]() This plot was created with Matplotlib. |
Author | Geek3 |
Other versions | QHO-coherent3-amplitudesqueezed2dB-animation.gif.gif |
Source Code
The plot was generated with Matplotlib.
Python Matplotlib source code |
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#!/usr/bin/python
# -*- coding: utf8 -*-
from math import *
import matplotlib.pyplot as plt
from matplotlib import animation, colors, colorbar
import numpy as np
import colorsys
from scipy.interpolate import interp1d
import os, sys
# image settings
fname = 'QHO-coherent3-amplitudesqueezed2dB-animation-color'
plt.rc('path', snap=False)
plt.rc('mathtext', default='regular')
width, height = 300, 200
ml, mr, mt, mb, mh, mc = 35, 19, 22, 45, 12, 6
x0, x1 = -7,7
y0, y1 = 0.0, 1.0
nframes = 120
fps = 20
# physics settings
omega = 2 * pi
alpha0 = 3.0
xi0 = -0.2 * log(10) # 2dB of squeezing
def color(phase):
hue = (phase / (2*pi) + 2./3.) % 1
light = interp1d([0, 1, 2, 3, 4, 5, 6], # adjust lightness
[0.64, 0.5, 0.55, 0.48, 0.70, 0.57, 0.64])(6 * hue)
hls = (hue, light, 1.0) # maximum saturation
rgb = colorsys.hls_to_rgb(*hls)
return rgb
def squeezed_coherent(alpha0, xi0, x, omega_t):
# Definition of coherent states
# https://en.wikipedia.org/wiki/Coherent_states
alpha = alpha0 * e**(-1j * omega_t)
xi = xi0 * e**(-2j * omega_t)
r = np.abs(xi)
tr = tanh(r)
kk = (r - tr * xi) / (r + tr * xi)
psi = (kk.real/pi)**0.25 * np.exp(-0.5j * omega_t # groundstate energy phase advance
- 0.5 * ((x - sqrt(2) * alpha.real))**2 * kk # spread
- 1j * alpha.imag * (alpha.real - sqrt(2) * x)) # displacement
return psi
def animate(nframe):
print str(nframe) + ' ',; sys.stdout.flush()
t = float(nframe) / nframes * 1.0 # animation repeats after t=1.0
ax.cla()
ax.grid(True)
ax.axis((x0, x1, y0, y1))
x = np.linspace(x0, x1, int(ceil(1+w_px)))
x2 = x - px_w/2.
# Let's cheat a bit: add a phase phi(t)*const(x)
# This will reduce the period from T=2*(2pi/omega) to T=1.0*(2pi/omega)
# and allow fewer frames and less file size for repetition.
# For big alpha the change is hardly visible
psi = squeezed_coherent(alpha0, xi0, x, omega*t) * np.exp(-0.5j * omega*t)
psi2 = squeezed_coherent(alpha0, xi0, x2, omega*t) * np.exp(-0.5j * omega*t)
y = np.abs(psi)**2
phase = np.angle(psi2)
# plot color filling
for x_, phase_, y_ in zip(x, phase, y):
ax.plot([x_, x_], [0, y_], color=color(phase_), lw=2*0.72)
ax.plot(x, y, lw=2, color='black')
ax.set_yticklabels([l for l in ax.get_yticks() if l < y0+0.9*(y1-y0)])
# create figure and axes
plt.close('all')
fig, ax = plt.subplots(1, figsize=(width/100., height/100.))
bounds = [float(ml)/width, float(mb)/height,
1.0 - float(mr+mc+mh)/width, 1.0 - float(mt)/height]
fig.subplots_adjust(left=bounds[0], bottom=bounds[1],
right=bounds[2], top=bounds[3], hspace=0)
w_px = width - (ml+mr+mh+mc) # plot width in pixels
px_w = float(x1 - x0) / w_px # width of one pixel in plot units
# axes labels
fig.text(0.5 + 0.5 * float(ml-mh-mc-mr)/width, 4./height,
r'$x\ \ [(\hbar/(m\omega))^{1/2}]$', ha='center')
fig.text(5./width, 1.0, '$|\psi|^2$', va='top')
# colorbar for phase
cax = fig.add_axes([1.0 - float(mr+mc)/width, float(mb)/height,
float(mc)/width, 1.0 - float(mb+mt)/height])
cax.yaxis.set_tick_params(length=2)
cmap = colors.ListedColormap([color(phase) for phase in
np.linspace(0, 2*pi, height, endpoint=False)])
norm = colors.Normalize(0, 2*pi)
cbar = colorbar.ColorbarBase(cax, cmap=cmap, norm=norm,
orientation='vertical', ticks=np.linspace(0, 2*pi, 3))
cax.set_yticklabels(['$0$', r'$\pi$', r'$2\pi$'], rotation=90)
fig.text(1.0 - 10./width, 1.0, '$arg(\psi)$', ha='right', va='top')
plt.sca(ax)
# start animation
if 0 != os.system('convert -version > ' + os.devnull):
print 'imagemagick not installed!'
# warning: imagemagick produces somewhat jagged and therefore large gifs
anim = animation.FuncAnimation(fig, animate, frames=nframes)
anim.save(fname + '.gif', writer='imagemagick', fps=fps)
else:
# unfortunately the matplotlib imagemagick backend does not support
# options which are necessary to generate high quality output without
# framewise color palettes. Therefore save all frames and convert then.
if not os.path.isdir(fname):
os.mkdir(fname)
fnames = []
for frame in range(nframes):
animate(frame)
imgname = os.path.join(fname, fname + '{:03d}'.format(frame) + '.png')
fig.savefig(imgname)
fnames.append(imgname)
# compile optimized animation with ImageMagick
cmd = 'convert -loop 0 -delay ' + str(100 / fps) + ' '
cmd += ' '.join(fnames) # now create optimized palette from all frames
cmd += r' \( -clone 0--1 \( -clone 0--1 -fill black -colorize 100% \) '
cmd += '-append +dither -colors 255 -unique-colors '
cmd += '-write mpr:colormap +delete \) +dither -map mpr:colormap '
cmd += '-alpha activate -layers OptimizeTransparency '
cmd += fname + '.gif'
os.system(cmd)
for fnamei in fnames:
os.remove(fnamei)
os.rmdir(fname)
|
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10 October 2015
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 21:29, 10 October 2015 | ![]() | 300 × 200 (308 KB) | Geek3 | {{Information |Description ={{en|1=Animation of the quantum wave function of a squeezed coherent state in a Quantum harmonic oscillator with α=3 and 2dB of sq... |
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