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buildfigures.py
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buildfigures.py
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import numpy
import json
import math
import pickle
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt
from matplotlib.ticker import NullFormatter
import matplotlib.cm as cm
import matplotlib.patches as patches
import matplotlib.path as path
from scipy.interpolate import interp1d
import copy
# Size and number of bins for spin cloud
cloud_xsize = 100.0
cloud_ysize = 250.0
cloud_zsize = 50.0
cloud_zbins = 25
cloud_levels = 20
cloud_ybins = int(float(cloud_zbins) * cloud_ysize / cloud_zsize + 0.5)
cloud_xbins = int(cloud_zbins * cloud_xsize / cloud_zsize + 0.5)
cloud_ybins = int(cloud_zbins * cloud_ysize / cloud_zsize + 0.5)
def updateParams(aspect=None):
fig_width_pt = 0.9 * 246.0
inches_per_pt = 1.0 / 72.27 # Convert pt to inches
golden_mean = (math.sqrt(5) - 1.0) / 2.4 # Aesthetic ratio
fig_width = fig_width_pt * inches_per_pt # width in inches
fig_height = fig_width * (golden_mean if aspect is None else aspect) # height in inches
fig_size = [fig_width, fig_height]
params = {
'backend': 'ps',
'axes.labelsize': 7,
'axes.linewidth': 0.35,
'font.family': 'serif',
'text.fontsize': 7,
'legend.fontsize': 7,
'xtick.labelsize': 6,
'ytick.labelsize': 6,
'text.usetex': False,
'figure.figsize': fig_size,
}
matplotlib.rcParams.update(params)
def combineNoises(data1, xarray, yarray):
data2_interp = interp1d(numpy.array(xarray), numpy.array(yarray),
kind="cubic", bounds_error=False)
data = copy.deepcopy(data1)
data['yarray'] = numpy.sqrt(numpy.array(data['yarray']) ** 2 +
data2_interp(numpy.array(data['xarray'])) ** 2).tolist()
return data
def plotXYGraph(datasets, linetypes, name, xmin=None, xmax=None, ymin=None, ymax=None):
fig = plt.figure()
a = 0.19
b = 0.23
axes = [a, b, 0.95-a, 0.96-b]
subplot = fig.add_axes(axes, xlabel=datasets[0]['xname'], ylabel=datasets[0]['yname'])
subplot.set_xlim(xmin=xmin, xmax=xmax)
subplot.set_ylim(ymin=ymin, ymax=ymax)
for dataset, linetype in zip(datasets, linetypes):
if 'yerrors' not in dataset:
kwds = dict(label=dataset['name'])
if linetype.endswith('--'):
kwds['dashes'] = (6, 3) # default value is (6, 6)
elif linetype.endswith('-.'):
kwds['dashes'] = (5, 3, 1, 3) # default value is (3, 5, 1, 5)
subplot.plot(
numpy.array(dataset['xarray']),
numpy.array(dataset['yarray']),
linetype, **kwds)
else:
subplot.scatter(
numpy.array(dataset['xarray']),
numpy.array(dataset['yarray']),
edgecolors="None", s=5, c=linetype[0]
)
subplot.errorbar(
numpy.array(dataset['xarray']),
numpy.array(dataset['yarray']),
label=dataset['name'],
yerr=numpy.array(dataset['yerrors']),
linewidth=0.75, capsize=1.0,
linestyle="None", c=linetype[0])
fig.savefig(name)
def getHeightmap(X, Y, xmin, xmax, ymin, ymax, xbins, ybins):
"""Returns heightmap, extent and levels for contour plot"""
hist, xedges, yedges = numpy.histogram2d(X, Y, bins=(xbins, ybins),
range=[[xmin, xmax], [ymin, ymax]])
extent = [xedges[0], xedges[-1], yedges[0], yedges[-1]]
hmax = hist.max()
levels = numpy.exp(numpy.arange(cloud_levels + 1) / float(cloud_levels) * numpy.log(hmax))
return hist.T, extent, levels
def plotMainView(fname, Sx, Sy, Sz):
"""Plot spin cloud and some supporting information"""
updateParams(aspect=0.3)
fig = plt.figure()
a = 0.19
b = 0.23
axes = [a, b, 0.95-a, 0.96-b]
subplot = fig.add_axes(axes, aspect=1)
# optimal squeezing angle and corresponding variance, to plot supporting info
min_angle = 9.6 / 180 * numpy.pi
min_var = numpy.sqrt(25.349280804)
# parameters for arrow pointing at the best squeezing
arrow_len = 30
arrow1_x = -(min_var + arrow_len) * numpy.sin(min_angle)
arrow1_y = (min_var + arrow_len) * numpy.cos(min_angle)
arrow1_dx = (arrow_len) * numpy.sin(min_angle)
arrow1_dy = -(arrow_len) * numpy.cos(min_angle)
arrow_kwds = dict(width=2.5, linewidth=0.3,
shape="full",
overhang=0, head_starts_at_zero=False, fill=False,
length_includes_head=True,
facecolor='blue')
# supporting lines
r = numpy.array([0, 1.0])
# axis of the ellipse
l1_x = (r * 2 - 1) * min_var * numpy.sin(min_angle)
l1_y = (-r * 2 + 1) * min_var * numpy.cos(min_angle)
# horizontal line
l2_x = r * 150
l2_y = r * 0
# projection direction line
l3_x = r * 150
l3_y = r * 150 * numpy.sin(min_angle)
# plot the cloud
hm, extent, levels = getHeightmap(Sy, Sz, -cloud_ysize, cloud_ysize, -cloud_zsize, cloud_zsize, cloud_ybins, cloud_zbins)
subplot.contourf(hm, extent=extent, cmap=cm.PuRd, levels=levels)
# plot pointing arrows
subplot.arrow(arrow1_x, arrow1_y, arrow1_dx, arrow1_dy, **arrow_kwds)
subplot.arrow(-arrow1_x, -arrow1_y, -arrow1_dx, -arrow1_dy, **arrow_kwds)
# plot supporting lines
subplot.plot(l1_x, l1_y, color='blue', linewidth=0.3)
subplot.plot(l2_x, l2_y, linestyle='--', color='black', linewidth=0.3, dashes=(6, 2))
subplot.plot(l3_x, l3_y, linestyle='--', color='black', linewidth=0.3, dashes=(6, 2))
# mark angle
arc = matplotlib.patches.Arc((0.0, 0.0), 100, 100,
theta1=0, theta2=min_angle / numpy.pi * 180, linewidth=0.3, fill=False)
subplot.add_patch(arc)
# plot labels
subplot.text(-30, 20, "$d_\\theta$", fontsize=7)
subplot.text(40, 10, "$\\theta$", fontsize=7)
subplot.set_xlabel('$S_y$')
subplot.set_ylabel('$S_z$')
subplot.set_xlim(xmin=-cloud_ysize, xmax=cloud_ysize)
subplot.set_ylim(ymin=-cloud_zsize, ymax=cloud_zsize)
fig.savefig(fname)
def plot3DView(fname, Sx, Sy, Sz):
"""Plot 3 views of the cloud"""
nullfmt = NullFormatter()
fig_width = 8
x_d = 0.12
x_dd = 0.03
x_ly = (1.0 - x_d - x_dd * 2) / (1.0 + cloud_zsize / cloud_xsize)
x_lx = (1.0 - x_d - x_dd * 2) / (1.0 + cloud_xsize / cloud_zsize)
y_d = x_d
y_dd = x_dd
y_lx = x_lx
y_lz = y_lx / cloud_xsize * cloud_zsize
aspect = (x_d + x_dd * 2 + x_ly + x_lx) / (y_d + y_dd * 2 + y_lx + y_lz)
y_d *= aspect
y_dd *= aspect
y_lx *= aspect
y_lz *= aspect
# definitions for the axes
rectYZ = [x_d, y_d, x_ly, y_lz]
rectXY = [x_d, y_d + y_dd + y_lz, x_ly, y_lx]
rectXZ = [x_d + x_dd + x_ly, y_d, x_lx, y_lz]
# start with a rectangular Figure
fig = plt.figure(10, figsize=(fig_width, fig_width / aspect))
axYZ = plt.axes(rectYZ)
axXY = plt.axes(rectXY)
axXZ = plt.axes(rectXZ)
# no labels
axXY.xaxis.set_major_formatter(nullfmt)
axXZ.yaxis.set_major_formatter(nullfmt)
hm, extent, levels = getHeightmap(Sy, Sz, -cloud_ysize, cloud_ysize, -cloud_zsize, cloud_zsize, cloud_ybins, cloud_zbins)
axYZ.contourf(hm, extent=extent, cmap=cm.PuRd, levels=levels)
axYZ.set_xlabel('$S_y$')
axYZ.set_ylabel('$S_z$')
axYZ.set_xlim(xmin=-cloud_ysize, xmax=cloud_ysize)
axYZ.set_ylim(ymin=-cloud_zsize, ymax=cloud_zsize)
hm, extent, levels = getHeightmap(Sy, Sx, -cloud_ysize, cloud_ysize, -cloud_xsize, cloud_xsize, cloud_ybins, cloud_xbins)
axXY.contourf(hm, extent=extent, cmap=cm.PuRd, levels=levels)
axXY.set_ylabel('$S_x$')
axXY.set_xlim(xmin=-cloud_ysize, xmax=cloud_ysize)
axXY.set_ylim(ymin=-cloud_xsize, ymax=cloud_xsize)
hm, extent, levels = getHeightmap(Sx, Sz, -cloud_xsize, cloud_xsize, -cloud_zsize, cloud_zsize, cloud_xbins, cloud_zbins)
axXZ.contourf(hm, extent=extent, cmap=cm.PuRd, levels=levels)
axXZ.set_xlabel('$S_x$')
axXZ.set_xlim(xmin=-cloud_xsize, xmax=cloud_xsize)
axXZ.set_ylim(ymin=-cloud_zsize, ymax=cloud_zsize)
fig.savefig(fname)
def buildRiedelTomographyPath():
"""Process outlined blue line from Fig.3 in Riedel 2010"""
xstart = 137.35189
ystart = 90.287253
xn90 = 137.35189
x360 = 992.539
y15 = 109.64235
y0 = 398.97217
yscale = (y15 - y0) / 15
xscale = (x360 - xn90) / (360 + 90)
points = "0,0 14.50878,-1.568829 24.01256,-1.804477 9.50378,-0.235648 34.72699,2.276605 64.63501,37.401344 29.90803,35.12473 57.92996,97.02575 73.67738,186.27925 15.74742,89.2535 26.89408,328.94804 26.89408,328.94804 0,0 11.84222,-239.32902 27.17539,-324.70817 15.33317,-85.37915 37.30822,-145.80606 66.7308,-182.33072 29.42259,-36.524652 53.98301,-45.175188 75.48187,-45.648008 21.49886,-0.47282 42.77044,3.737291 73.61912,38.420108 30.84868,34.68281 51.95238,95.04074 69.15619,181.47674 17.20381,86.436 28.81508,331.37343 28.81508,331.37343 0,0 11.86912,-254.44324 30.73609,-338.09694 18.86697,-83.6537 33.03585,-128.95471 60.85126,-163.90638 27.81541,-34.95167 47.80063,-48.936916 79.15907,-49.548283 31.35845,-0.611367 50.95538,13.159523 79.60519,47.287693 28.64981,34.12817 53.63199,120.14375 61.81177,163.28546 8.17978,43.14171 12.82612,84.24291 12.82612,84.24291"
points = points.split(' ')
points = [tuple([float(x) for x in point.split(',')]) for point in points]
vertices = [[xstart, ystart]]
codes = [path.Path.MOVETO]
while len(points) > 0:
ref_x, ref_y = vertices[-1][0], vertices[-1][1]
x1, y1 = points.pop(0)
x2, y2 = points.pop(0)
x, y = points.pop(0)
codes += [path.Path.CURVE4] * 3
vertices.append([x1 + ref_x, y1 + ref_y])
vertices.append([x2 + ref_x, y2 + ref_y])
vertices.append([x + ref_x, y + ref_y])
vertices = numpy.array(vertices)
vertices[:, 0] = (vertices[:, 0] - xn90) / xscale - 90
vertices[:, 1] = (vertices[:, 1] - y0) / yscale
return vertices, codes
def calculateSqueezing(angles_radian, sy, sz):
# Calculate \Delta^2 \hat{S}_\theta.
# sy, sz and the result have shape (subsets, points)
N = 1200.0
ss = sy.shape[0]
tp = angles_radian.size
ca = numpy.tile(numpy.cos(angles_radian), (ss, 1))
sa = numpy.tile(numpy.sin(angles_radian), (ss, 1))
# calculate mean inside subset and tile it to match cosine and sine data
mean = lambda x: numpy.tile(x.mean(1).reshape(ss, 1), (1, tp))
d2S = mean(sz ** 2) * ca ** 2 + mean(sy ** 2) * sa ** 2 - \
2 * mean(sz * sy) * sa * ca - mean(sy) ** 2 * sa ** 2 - mean(sz) ** 2 * ca ** 2 + \
2 * mean(sz) * mean(sy) * sa * ca
return d2S / N * 4
def getAngles(amin, amax, n=300):
# angles for tomography
angles = numpy.arange(n + 1) / float(n) * (amax - amin) + amin
angles_radian = angles * 2 * numpy.pi / 360
return angles, angles_radian
def plotRotationErrors(fname, Sy, Sz):
amin = -90
amax = 90
angles, angles_radian = getAngles(amin, amax)
ens = Sy.size # total number of ensembles
subsets = 128 # number of subsets used to estimate error
ens_half = ens / 2
Sy_half = Sy[:ens_half]
Sz_half = Sz[:ens_half]
res_full = calculateSqueezing(angles_radian, Sy.reshape(1, ens), Sz.reshape(1, ens)) # average result using all data
res_subsets = calculateSqueezing(angles_radian,
Sy.reshape(subsets, ens / subsets),
Sz.reshape(subsets, ens / subsets))
res_subsets_half = calculateSqueezing(angles_radian,
Sy_half.reshape(subsets, ens_half / subsets),
Sz_half.reshape(subsets, ens_half / subsets))
res_errors = res_subsets.std(0) / numpy.sqrt(subsets)
res_errors_half = res_subsets_half.std(0) / numpy.sqrt(subsets)
min_i = res_full[0].argmin()
max_i = res_full[0].argmax()
print "{ens} ensembles:".format(ens=ens_half)
print "Maximum squeezing: avg={avg}, avg-err={lb}, avg+err={ub}".format(
avg=numpy.log10(res_full[0,min_i]) * 10,
lb=numpy.log10(res_full[0,min_i] - res_errors_half[min_i]) * 10,
ub=numpy.log10(res_full[0,min_i] + res_errors_half[min_i]) * 10)
print "Maximum unsqueezing: avg={avg}, avg-err={lb}, avg+err={ub}".format(
avg=numpy.log10(res_full[0,max_i]) * 10,
lb=numpy.log10(res_full[0,max_i] - res_errors_half[max_i]) * 10,
ub=numpy.log10(res_full[0,max_i] + res_errors_half[max_i]) * 10)
print "{ens} ensembles:".format(ens=ens)
print "Maximum squeezing: avg={avg}, avg-err={lb}, avg+err={ub}".format(
avg=numpy.log10(res_full[0,min_i]) * 10,
lb=numpy.log10(res_full[0,min_i] - res_errors[min_i]) * 10,
ub=numpy.log10(res_full[0,min_i] + res_errors[min_i]) * 10)
print "Maximum unsqueezing: avg={avg}, avg-err={lb}, avg+err={ub}".format(
avg=numpy.log10(res_full[0,max_i]) * 10,
lb=numpy.log10(res_full[0,max_i] - res_errors[max_i]) * 10,
ub=numpy.log10(res_full[0,max_i] + res_errors[max_i]) * 10)
fig = plt.figure()
subplot = fig.add_subplot(111)
subplot.plot(angles, numpy.log10(res_full[0]) * 10, 'r', label="$\\log_{10}(squeezing)$")
subplot.plot(angles, numpy.log10(res_full[0] - res_errors) * 10, 'r--',
label="$\\log_{{10}}(squeezing - error)$, {ens} ensembles".format(ens=ens))
subplot.plot(angles, numpy.log10(res_full[0] + res_errors) * 10, 'r--',
label="$\\log_{{10}}(squeezing + error)$, {ens} ensembles".format(ens=ens))
subplot.plot(angles, numpy.log10(res_full[0] - res_errors_half) * 10, 'b--',
label="$\\log_{{10}}(squeezing - error)$, {ens} ensembles".format(ens=ens_half))
subplot.plot(angles, numpy.log10(res_full[0] + res_errors_half) * 10, 'b--',
label="$\\log_{{10}}(squeezing + error)$, {ens} ensembles".format(ens=ens_half))
subplot.set_ylim(ymin=-15, ymax=20)
subplot.set_xlim(xmin=0, xmax=12)
subplot.legend()
fig.savefig(fname)
def plotRotation(fname, Sx, Sy, Sz):
"""Plot spin tomography figure"""
amin = -90
amax = 90
angles, angles_radian = getAngles(amin, amax)
ens = Sy.size # total number of ensembles
res_full = calculateSqueezing(angles_radian, Sy.reshape(1, ens), Sz.reshape(1, ens)) # average result using all data
vertices, codes = buildRiedelTomographyPath()
riedel_path = path.Path(vertices, codes)
patch = patches.PathPatch(riedel_path, edgecolor='blue', facecolor='none', linestyle='dashed')
updateParams()
fig = plt.figure()
a = 0.19
b = 0.23
axes = [a, b, 0.95-a, 0.96-b]
subplot = fig.add_axes(axes)
subplot.plot(angles, numpy.log10(res_full[0]) * 10, 'r')
subplot.add_patch(patch)
subplot.set_xlim(xmin=amin, xmax=amax)
subplot.set_ylim(ymin=-13, ymax=20)
subplot.xaxis.set_ticks((-90, -45, 0, 45, 90))
subplot.xaxis.set_ticklabels(('-90', '-45', '0', '45', '90'))
subplot.set_xlabel('Turning angle, $\\theta$ (degrees)')
subplot.set_ylabel('$\\Delta \\hat{S}_\\theta^2 / (N / 4)$ (dB)')
fig.savefig(fname)
if __name__ == '__main__':
updateParams()
ramsey_visibility_gpe = json.load(open('data/long_time_ramsey/ramsey_gpe_vis.json'))
ramsey_visibility_qn = json.load(open('data/long_time_ramsey/ramsey_wigner_vis.json'))
plotXYGraph(
[ramsey_visibility_gpe, ramsey_visibility_qn],
['r--', 'b-'],
'long_ramsey_visibility.eps',
xmin=0, xmax=5.0, ymin=0, ymax=1.05)
ramsey_visibility_gpe = json.load(open('data/long_time_rephasing/rephasing_gpe_vis.json'))
ramsey_visibility_qn = json.load(open('data/long_time_rephasing/rephasing_wigner_vis.json'))
plotXYGraph(
[ramsey_visibility_gpe, ramsey_visibility_qn],
['r--', 'b-'],
'long_rephasing_visibility.eps',
xmin=0, xmax=5.0, ymin=0, ymax=1.05)
ramsey_squeezing_qn_80 = json.load(open('data/squeezing/squeezing_ramsey_80.0.json'))
ramsey_squeezing_qn_85 = json.load(open('data/squeezing/squeezing_ramsey_85.0.json'))
ramsey_squeezing_qn_90 = json.load(open('data/squeezing/squeezing_ramsey_90.0.json'))
ramsey_squeezing_qn_95 = json.load(open('data/squeezing/squeezing_ramsey_95.0.json'))
plotXYGraph(
[ramsey_squeezing_qn_80, ramsey_squeezing_qn_85, ramsey_squeezing_qn_90, ramsey_squeezing_qn_95],
['b-', 'r--', 'g-.', 'k:'],
'ramsey_squeezing.eps',
xmin=0, xmax=100.0, ymin=-7.0, ymax=1.0)
spins = pickle.load(open('data/riedel_comparison/split_potentials_spins_last.pickle'))
Sx = spins['Sx']
Sy = -spins['Sy'] # for some reason Y direction in Riedel is swapped (is it the sign of detuning?)
Sz = spins['Sz']
plotRotationErrors('riedel_rotation_errors.pdf', Sy, Sz)
plotRotation('riedel_rotation.eps', Sx, Sy, Sz)
Sx -= Sx.mean()
Sy -= Sy.mean()
Sz -= Sz.mean()
# plot3DView('riedel_cloud_3d.eps', Sx, Sy, Sz)
plotMainView('riedel_cloud_yz.eps', Sx, Sy, Sz)