def spinecho_single_run_population(fname):
with open(get_path(__file__, 'simulations/echo_wigner_single_run.json')) as f:
wig = json.load(f)
wig_t = numpy.array(wig['times'])
wig_N1 = numpy.array(wig['N1'])
wig_N2 = numpy.array(wig['N2'])
fig = mplh.figure(width=0.5)
s = fig.add_subplot(111,
xlabel='$t$ (s)',
ylabel='$N$')
# Pure Wigner
s.plot(wig_t, wig_N1, color=mplh.color.f.blue.main,
linestyle='-', dashes=mplh.dash['-'])
s.plot(wig_t, wig_N2, color=mplh.color.f.red.main,
linestyle='--', dashes=mplh.dash['--'])
s.set_xlim((0, 1.3))
s.set_ylim((0, 55000. / 2))
s.set_aspect((5 ** 0.5 - 1) / 2 * mplh.aspect_modifier(s))
s.text(0.1, 2500, 'spin echo sequence')
s.text(1., 4000, '$\\vert 1 \\rangle$')
s.text(1., 13000, '$\\vert 2 \\rangle$')
fig.text(0.01, 0.92, '(b)', fontweight='bold')
fig.tight_layout(pad=0.3)
fig.savefig(fname)
def spinecho_short(fname):
with open(get_path(__file__, 'experimental/echo_experimental.json')) as f:
vis_exp = json.load(f)
with open(get_path(__file__, 'simulations/echo_gpe.json')) as f:
gpe = json.load(f)
with open(get_path(__file__, 'simulations/echo_wigner.json')) as f:
wig = json.load(f)
with open(get_path(__file__, 'simulations/echo_wigner_varied_pulse.json')) as f:
wig_tech = json.load(f)
t_exp = numpy.array(vis_exp['xarray'])
v_exp = numpy.array(vis_exp['yarray'])
v_exp_err = numpy.array(vis_exp['yerrors'])
gpe_t = numpy.array(gpe['times'])
gpe_v = numpy.array(gpe['visibility'])
wig_t = numpy.array(wig['times'])
wig_v = numpy.array(wig['visibility'])
wig_tech_t = numpy.array(wig_tech['times'])
wig_tech_v = numpy.array(wig_tech['est_visibility'])
fig = mplh.figure(width=0.75)
s = fig.add_subplot(111,
xlabel='$t$ (s)',
ylabel='$\\mathcal{V}$')
s.errorbar(t_exp, v_exp, yerr=v_exp_err, color='k', linestyle='none',
capsize=1.5)
# GPE
s.plot(gpe_t, gpe_v, color=mplh.color.f.green.main,
linestyle=':', dashes=mplh.dash[':'])
# Pure Wigner
s.plot(wig_t, wig_v, color=mplh.color.f.red.main,
linestyle='--', dashes=mplh.dash['--'])
# Wigner + technical noise
s.plot(wig_tech_t, wig_tech_v, color=mplh.color.f.blue.main,
linestyle='-', dashes=mplh.dash['-'])
s.set_xlim((0, 1.8))
s.set_ylim((0, 1.))
s.set_aspect((5 ** 0.5 - 1) / 2 * mplh.aspect_modifier(s))
s.plot([0.05, 0.16], [0.23, 0.23], color=mplh.color.f.green.main, linestyle=':', dashes=mplh.dash[':'])
s.text(0.18, 0.22, 'mean-field')
s.plot([0.05, 0.16], [0.15, 0.15], color=mplh.color.f.red.main, linestyle='--', dashes=mplh.dash['--'])
s.text(0.18, 0.14, 'Wigner')
s.plot([0.05, 0.16], [0.07, 0.07], color=mplh.color.f.blue.main, linestyle='-', dashes=mplh.dash['-'])
s.text(0.18, 0.06, 'Wigner + tech. noise')
s.errorbar([0.88], [0.07], yerr=[0.02], color='k', linestyle='none', capsize=1.5)
s.text(0.92, 0.06, 'experiment')
fig.tight_layout(pad=0.3)
fig.savefig(fname)
def illustration_noise(fname, t_ms):
with open(get_path(__file__, 'ramsey_sim_phnoise_' + str(t_ms) + 'ms.json')) as f:
meas = json.load(f)
Pz = numpy.array(meas['Pz'])
phis = numpy.array(meas['phis'])
est_phase = numpy.array(meas['est_phase'])
est_phnoise = numpy.array(meas['est_phnoise'])
est_amp = numpy.array(meas['est_amp'])
fig = mplh.figure(width=0.5)
s = fig.add_subplot(111,
xlabel='$\\phi$ (rad)',
ylabel='$P_z$')
phis_fit = numpy.linspace(0, numpy.pi * 2, 200)
Pz_fit = est_amp * numpy.cos(phis_fit + est_phase)
s.plot(phis_fit, Pz_fit, color=mplh.color.f.red.main,
linestyle='-', dashes=mplh.dash['-'])
s.scatter(phis, Pz, color='grey', s=1)
s.text(numpy.pi / 2 - est_phase - est_phnoise - 0.5, 0.05, "$\\sigma")
arrow_kwds = dict(
shape="full",
overhang=0, head_starts_at_zero=False, fill=False,
length_includes_head=True)
s.arrow(
numpy.pi / 2 - est_phase - est_phnoise - 0.5, 0.0,
0.45, 0.0,
**arrow_kwds)
s.arrow(
numpy.pi / 2 - est_phase + est_phnoise + 0.5, 0.0,
-0.45, 0.0,
**arrow_kwds)
s.set_xlim((0, 2 * numpy.pi))
s.set_ylim((-1, 1))
s.set_aspect((5 ** 0.5 - 1) / 2 * mplh.aspect_modifier(s))
s.text(0.15, -0.85, '$t=' + str(t_ms) + '\\,\\mathrm{ms}$')
fig.text(0.01, 0.92, '(a)' if t_ms == 20 else '(b)', fontweight='bold')
fig.tight_layout(pad=0.3)
fig.savefig(fname)
def _squeezing(fname, coupling, ens):
with open(get_path(__file__, 'single_well_squeezing_wigner_' + ens + '_Na200.pickle')) as f:
wigner = pickle.load(f)
suffix = '_c' if coupling else '_nc'
interaction = (100.4, 80.8, 95.5) if coupling else (100.4, 0., 100.4)
tau_exact = numpy.linspace(1e-3, 120 if coupling else 20, 200)
s_exact = get_exact_S(tau_exact, 200, *interaction)
tau_wigner = wigner['tau' + suffix]
s_wigner = wigner['s_pi2' + suffix]
s_wigner_err = wigner['s_pi2' + suffix + '_err']
s_exact = numpy.log10(s_exact) * 10
tau_wigner, s_wigner_bot, s_wigner_top = mplh.crop_bounds(
tau_wigner,
numpy.log10(s_wigner - s_wigner_err) * 10,
numpy.log10(s_wigner + s_wigner_err) * 10,
(0, (120 if coupling else 20), -15, 1))
fig = mplh.figure(width=0.5)
s = fig.add_subplot(111,
xlabel='$\\tau$',
ylabel='$S_{\\theta + \\pi/2}$ (dB)')
s.plot(tau_exact, s_exact, color="black")
s.fill_between(
tau_wigner, s_wigner_bot, s_wigner_top,
facecolor=mplh.color.f.blue.lightest,
linewidth=0)
s.text(
18 if coupling else 3,
-1,
"interaction on" if coupling else "interaction off")
s.set_xlim((0, 120 if coupling else 20))
s.set_ylim((-15, 1))
s.set_aspect((5 ** 0.5 - 1) / 2 * mplh.aspect_modifier(s))
fig.text(0.01, 0.92, '(b)' if coupling else '(a)', fontweight='bold')
fig.tight_layout(pad=0.3)
fig.savefig(fname)
def spinecho_noise(fname):
with open(get_path(__file__, 'experimental/echo_phnoise_exp.json')) as f:
exp = json.load(f)
with open(get_path(__file__, 'simulations/echo_wigner.json')) as f:
wig = json.load(f)
with open(get_path(__file__, 'simulations/echo_wigner_varied_pulse.json')) as f:
tech_wig = json.load(f)
t_wig = numpy.array(wig['times'])
ph_wig = numpy.array(wig['est_phnoises'])
t_tech_wig = numpy.array(tech_wig['times'])
ph_tech_wig = numpy.array(tech_wig['est_phnoises'])
t_exp = numpy.array(exp['xarray'])
ph_exp = numpy.array(exp['yarray'])
ph_exp_errors = numpy.array(exp['yerrors'])
fig = mplh.figure(width=0.75)
s = fig.add_subplot(111,
xlabel='$t$ (s)',
ylabel='$\\mathcal{\\sigma}$ (rad)')
s.errorbar(t_exp, ph_exp, yerr=ph_exp_errors, color='k', linestyle='none',
capsize=1.5)
s.plot(t_wig, ph_wig, color=mplh.color.f.red.main,
linestyle='--', dashes=mplh.dash['--'])
s.plot(t_tech_wig, ph_tech_wig, color=mplh.color.f.blue.main,
linestyle='-', dashes=mplh.dash['-'])
s.set_xlim((0, 1.6))
s.set_ylim((0, 0.5))
s.set_aspect((5 ** 0.5 - 1) / 2 * mplh.aspect_modifier(s))
s.plot([0.03, 0.15], [0.43, 0.43], color=mplh.color.f.red.main, linestyle='--', dashes=mplh.dash['--'])
s.text(0.18, 0.42, 'Wigner')
s.plot([0.03, 0.15], [0.39, 0.39], color=mplh.color.f.blue.main, linestyle='-', dashes=mplh.dash['-'])
s.text(0.18, 0.38, 'Wigner + tech. noise')
s.errorbar([0.09], [0.35], yerr=[0.01], color='k', linestyle='none', capsize=1.5)
s.text(0.18, 0.34, 'experiment')
fig.tight_layout(pad=0.3)
fig.savefig(fname)
def _two_comp_gs(fname, a12):
with open(get_path(__file__, 'two_comp_gs.json'), 'rb') as f:
data = json.load(f)
zs = numpy.array(data[str(a12)]['xs']) / 1e-6 # to um
n_z = numpy.array(data[str(a12)]['n_x']) * 1e-6 # to um^-1
fig = mplh.figure()
s = fig.add_subplot(111,
xlabel='$z$ ($\\mu\\mathrm{m}$)',
ylabel='$n_z$ ($\\mu\\mathrm{m}^{-1}$)')
s.plot(zs, n_z[0], color=mplh.color.f.blue.main, linestyle='-')
s.plot(zs, n_z[1], color=mplh.color.f.red.main, linestyle='--', dashes=mplh.dash['--'])
s.text(
11,
2000. / 2500 * 1600 if a12 == 97. else 2000,
'$a_{12}=' + str(a12) + '\\,r_B$')
s.text(
11,
1700. / 2500 * 1600 if a12 == 97. else 1700,
('(miscible)' if a12 == 97. else '(immiscible)'))
s.text(
-28 if a12 == 97. else -26,
1000. / 2500 * 1600 if a12 == 97. else 1000,
'$\\vert 1 \\rangle$')
s.text(
-15 if a12 == 97. else -13,
2000. / 2500 * 1600 if a12 == 97. else 2000,
'$\\vert 2 \\rangle$')
s.set_xlim(-40, 40)
if a12 == 97.:
s.set_ylim(0, 1600)
else:
s.set_ylim(0, 2500)
s.set_aspect((5 ** 0.5 - 1) / 2 * mplh.aspect_modifier(s))
fig.text(0.01, 0.92, '(a)' if a12 == 97. else '(b)', fontweight='bold')
fig.tight_layout(pad=0.3)
fig.savefig(fname)
def _one_comp_gs(fname, N):
with open(get_path(__file__, 'one_comp_gs.json'), 'rb') as f:
data = json.load(f)
zs = numpy.array(data[str(N)]['xs']) / 1e-6 # to um
n_z = numpy.array(data[str(N)]['n_x']) * 1e-6 # to um^-1
tf_n_z = numpy.array(data[str(N)]['tf_n_x']) * 1e-6 # to um^-1
fig = mplh.figure()
s = fig.add_subplot(111,
xlabel='$z$ ($\\mu\\mathrm{m}$)',
ylabel='$n_z$ ($\\mu\\mathrm{m}^{-1}$)')
s.plot(zs, n_z[0], color=mplh.color.f.blue.main, linestyle='-')
s.plot(zs, tf_n_z[0], color=mplh.color.f.red.main, linestyle='--', dashes=mplh.dash['--'])
s.text(
6 if N == 1000 else 15,
2400 * 0.03 if N == 1000 else 2400,
'$N=' + str(N) + '$')
s.text(
-14 if N == 1000 else -35,
500 * 0.03 if N == 1000 else 500,
'T-F')
s.text(
-7.5 if N == 1000 else -23,
500 * 0.03 if N == 1000 else 500,
'numerical')
if N == 1000:
s.set_xlim(-20, 20)
s.set_ylim(0, 90)
else:
s.set_xlim(-50, 50)
s.set_ylim(0, 3000)
s.set_aspect((5 ** 0.5 - 1) / 2 * mplh.aspect_modifier(s))
fig.text(0.01, 0.92, '(b)' if N == 1000 else '(a)', fontweight='bold')
fig.tight_layout(pad=0.3)
fig.savefig(fname)
def spinecho_long(fname):
with open(get_path(__file__, 'simulations/echo_gpe_long.json')) as f:
gpe = json.load(f)
with open(get_path(__file__, 'simulations/echo_wigner_long.json')) as f:
wig = json.load(f)
with open(get_path(__file__, 'simulations/echo_wigner_varied_pulse_long.json')) as f:
wig_tech = json.load(f)
t_gpe = numpy.array(gpe['times'])
v_gpe = numpy.array(gpe['visibility'])
t_wig = numpy.array(wig['times'])
v_wig = numpy.array(wig['visibility'])
t_tech_wig = numpy.array(wig_tech['times'])
v_tech_wig = numpy.array(wig_tech['est_visibility'])
fig = mplh.figure()
s = fig.add_subplot(111,
xlabel='$t$ (s)',
ylabel='$\\mathcal{V}$')
# GPE
s.plot(t_gpe, v_gpe, color=mplh.color.f.green.main,
linestyle=':', dashes=mplh.dash[':'])
# Pure Wigner
s.plot(t_wig, v_wig, color=mplh.color.f.red.main,
linestyle='--', dashes=mplh.dash['--'])
s.plot(t_tech_wig, v_tech_wig, color=mplh.color.f.blue.main,
linestyle='-', dashes=mplh.dash['-'])
s.set_xlim((0, 3.))
s.set_ylim((0, 1.))
s.set_aspect((5 ** 0.5 - 1) / 2 * mplh.aspect_modifier(s))
s.text(0.2, 0.1, 'spin echo sequence')
fig.text(0.01, 0.92, '(b)', fontweight='bold')
fig.tight_layout(pad=0.3)
fig.savefig(fname)
def ramsey_short(fname):
with open(get_path(__file__, 'experimental/ramsey_experimental.json')) as f:
vis_exp = json.load(f)
with open(get_path(__file__, 'simulations/ramsey_gpe_no_losses.json')) as f:
gpe_nl = json.load(f)
with open(get_path(__file__, 'simulations/ramsey_gpe.json')) as f:
gpe = json.load(f)
with open(get_path(__file__, 'simulations/ramsey_wigner.json')) as f:
wig = json.load(f)
with open(get_path(__file__, 'simulations/ramsey_wigner_varied_pulse.json')) as f:
wig_tech = json.load(f)
t_exp = numpy.array(vis_exp['xarray'])
v_exp = numpy.array(vis_exp['yarray'])
v_exp_err = numpy.array(vis_exp['yerrors'])
gpe_t = numpy.array(gpe['times'])
gpe_v = numpy.array(gpe['visibility'])
gpe_nl_t = numpy.array(gpe_nl['times'])
gpe_nl_v = numpy.array(gpe_nl['visibility'])
wig_t = numpy.array(wig['times'])
wig_v = numpy.array(wig['visibility'])
wig_tech_t = numpy.array(wig_tech['times'])
wig_tech_v = numpy.array(wig_tech['est_visibility'])
gpe_N1 = numpy.array(gpe['N1'])
gpe_N2 = numpy.array(gpe['N2'])
fig = mplh.figure(width=0.75)
s = fig.add_subplot(111,
xlabel='$t$ (s)',
ylabel='$\\mathcal{V}$')
s.errorbar(t_exp, v_exp, yerr=v_exp_err, color='k', linestyle='none',
capsize=1.5)
# Theoretical limit of visibility
s.plot(wig_t, 2 * numpy.sqrt(gpe_N1 * gpe_N2) / (gpe_N1 + gpe_N2), color='grey',
linestyle=':', dashes=mplh.dash[':'])
# GPE
s.plot(gpe_nl_t, gpe_nl_v, color=mplh.color.f.yellow.main,
linestyle='-.', dashes=mplh.dash['-.'])
s.plot(gpe_t, gpe_v, color=mplh.color.f.green.main,
linestyle=':', dashes=mplh.dash[':'])
# Pure Wigner
s.plot(wig_t, wig_v, color=mplh.color.f.red.main,
linestyle='--', dashes=mplh.dash['--'])
# Wigner + technical noise
s.plot(wig_tech_t, wig_tech_v, color=mplh.color.f.blue.main,
linestyle='-', dashes=mplh.dash['-'])
s.set_xlim((0, 1.3))
s.set_ylim((0, 1.))
s.set_aspect((5 ** 0.5 - 1) / 2 * mplh.aspect_modifier(s))
s.plot([0.04, 0.12], [0.23, 0.23], color=mplh.color.f.green.main, linestyle=':', dashes=mplh.dash[':'])
s.text(0.14, 0.22, 'mean-field')
s.plot([0.04, 0.12], [0.15, 0.15], color=mplh.color.f.red.main, linestyle='--', dashes=mplh.dash['--'])
s.text(0.14, 0.14, 'Wigner')
s.plot([0.04, 0.12], [0.07, 0.07], color=mplh.color.f.blue.main, linestyle='-', dashes=mplh.dash['-'])
s.text(0.14, 0.06, 'Wigner + tech. noise')
s.plot([0.6, 0.68], [0.23, 0.23], color=mplh.color.f.yellow.main, linestyle='-.', dashes=mplh.dash['-.'])
s.text(0.7, 0.22, 'mean-field, no losses')
s.plot([0.6, 0.68], [0.15, 0.15], color='grey', linestyle=':', dashes=mplh.dash[':'])
s.text(0.7, 0.14, 'visibility limit')
s.errorbar([0.64], [0.07], yerr=[0.02], color='k', linestyle='none', capsize=1.5)
s.text(0.7, 0.06, 'experiment')
fig.tight_layout(pad=0.3)
fig.savefig(fname)
def _squeezing_err(fname, coupling):
suffix = '_c' if coupling else '_nc'
colors = {
'10k': mplh.color.f.blue,
'1k': mplh.color.f.red,
'100': mplh.color.f.green}
dashes = {
'10k': '-',
'1k': '--'}
fig = mplh.figure(width=0.5)
s = fig.add_subplot(111,
xlabel='$\\tau$',
ylabel='Relative errors')
for tr in ('1k', '10k'):
with open(get_path(__file__, 'single_well_squeezing_wigner_' + tr + '_Na200.pickle')) as f:
wigner = pickle.load(f)
tau_wigner = wigner['tau' + suffix]
s_wigner = wigner['s_pi2' + suffix]
s_wigner_err = wigner['s_pi2' + suffix + '_err']
interaction = (100.4, 80.8, 95.5) if coupling else (100.4, 0., 100.4)
s_exact = get_exact_S(tau_wigner, 200, *interaction)
s_exact[0] = 1.
diff = numpy.abs(s_wigner - s_exact) / s_exact
err = s_wigner_err / s_exact
tau_diff, min_diff, max_diff = mplh.crop_bounds(
tau_wigner, diff-err, diff+err, (0, (120 if coupling else 20), 0, 0.1))
s.fill_between(tau_diff, min_diff, max_diff,
facecolor=colors[tr].light,
linewidth=0,
alpha=0.5)
s.plot(tau_wigner, diff, color=colors[tr].dark, dashes=mplh.dash[dashes[tr]])
s.text(
72 if coupling else 12,
0.085,
"interaction on" if coupling else "interaction off")
if coupling:
s.text(55, 0.06, '$20,000$')
s.text(55, 0.052, 'trajectories')
s.text(19, 0.02, '$200,000$')
s.text(19, 0.012, 'trajectories')
else:
s.text(13, 0.06, '$20,000$')
s.text(13, 0.052, 'trajectories')
s.text(4, 0.02, '$200,000$')
s.text(4, 0.012, 'trajectories')
s.set_xlim((0, 120 if coupling else 20))
s.set_ylim((0, 0.1))
s.set_aspect((5 ** 0.5 - 1) / 2 * mplh.aspect_modifier(s))
fig.text(0.01, 0.92, '(b)' if coupling else '(a)', fontweight='bold')
fig.tight_layout(pad=0.3)
fig.savefig(fname)
def _squeezing_N_err(fname, coupling):
suffix = '_c' if coupling else '_nc'
fig = mplh.figure(width=0.5)
s = fig.add_subplot(111,
xlabel='$\\tau / \\tau_c(N)$',
ylabel='Relative errors')
colors = {
20: mplh.color.f.blue,
200: mplh.color.f.red,
2000: mplh.color.f.green}
dashes = {
20: '-',
200: '--',
2000: ':'}
for Na in (20, 200, 2000):
with open(get_path(__file__, 'single_well_squeezing_wigner_10k_Na' + str(Na) + '.pickle')) as f:
wigner = pickle.load(f)
tau_wigner = wigner['tau' + suffix]
s_wigner = wigner['s_pi2' + suffix]
s_wigner_err = wigner['s_pi2' + suffix + '_err']
interaction = (100.4, 80.8, 95.5) if coupling else (100.4, 0., 100.4)
s_exact = get_exact_S(tau_wigner, Na, *interaction)
s_exact[0] = 1.
tau = tau_wigner / tau_wigner[-1]
diff = numpy.abs(s_wigner - s_exact) / s_exact
err = s_wigner_err / s_exact
tau_diff, min_diff, max_diff = mplh.crop_bounds(tau, diff-err, diff+err, (0, 1., 0, 0.16))
s.fill_between(tau_diff, min_diff, max_diff,
facecolor=colors[Na].light,
linewidth=0,
alpha=0.5)
s.plot(tau, diff, color=colors[Na].dark, dashes=mplh.dash[dashes[Na]])
s.text(
0.6,
0.135,
"interaction on" if coupling else "interaction off")
if coupling:
s.text(0.12, 0.12, '$N=20$')
s.text(0.25, 0.062, '$N=200$')
s.text(0.17, 0.03, '$N=2000$')
else:
s.text(0.1, 0.12, '$N=20$')
s.text(0.27, 0.082, '$N=200$')
s.text(0.16, 0.01, '$N=2000$')
s.set_xlim((0, 1.))
s.set_ylim((0, 0.16))
s.set_aspect((5 ** 0.5 - 1) / 2 * mplh.aspect_modifier(s))
fig.text(0.01, 0.92, '(b)' if coupling else '(a)', fontweight='bold')
fig.tight_layout(pad=0.3)
fig.savefig(fname)