V-Type Three-Level: √8π Sech Pulse, √8π Coupling¶
[1]:
import numpy as np
sech_fwhm_conv = 1./2.6339157938
t_width = 1.0*sech_fwhm_conv # [τ]
print(np.sqrt(8))
print('t_width', t_width)
n = np.sqrt(8) # For a pulse area of nπ
ampl = n/t_width/(2*np.pi) # Pulse amplitude [2π Γ]
print('ampl', ampl)
n = np.sqrt(8) # For a pulse area of nπ
ampl_2 = n/t_width/(2*np.pi) # Pulse amplitude [2π Γ]
print('ampl_2', ampl_2)
2.8284271247461903
t_width 0.3796628587572578
ampl 1.1856786822710181
ampl_2 1.1856786822710181
[2]:
a = np.sqrt(8)
b = np.sqrt(8)
np.sqrt(a**2 + b**2)
[2]:
4.0
[3]:
mb_solve_json = """
{
"atom": {
"decays": [
{ "channels": [[0,1], [0,2]],
"rate": 0.0
}
],
"energies": [],
"fields": [
{
"coupled_levels": [[0, 1]],
"detuning": 0.0,
"detuning_positive": true,
"label": "probe",
"rabi_freq": 1.18567868227,
"rabi_freq_t_args":
{
"ampl": 1.0,
"centre": 0.0,
"width": 0.3796628587572578
},
"rabi_freq_t_func": "sech"
},
{
"coupled_levels": [[0, 2]],
"detuning": 0.0,
"detuning_positive": true,
"label": "coupling",
"rabi_freq": 1.18567868227,
"rabi_freq_t_args":
{
"ampl": 1.0,
"centre": 0.0,
"width": 0.3796628587572578
},
"rabi_freq_t_func": "sech"
}
],
"num_states": 3
},
"t_min": -2.0,
"t_max": 10.0,
"t_steps": 60,
"z_min": -0.2,
"z_max": 1.2,
"z_steps": 70,
"z_steps_inner": 1,
"interaction_strengths": [10.0, 10.0],
"savefile": "mbs-vee-sech-sqrt8pi-sqrt8pi"
}
"""
[4]:
from maxwellbloch import mb_solve
mb_solve_00 = mb_solve.MBSolve().from_json_str(mb_solve_json)
%time Omegas_zt, states_zt = mb_solve_00.mbsolve(recalc=True)
10.0%. Run time: 1.86s. Est. time left: 00:00:00:16
20.0%. Run time: 4.12s. Est. time left: 00:00:00:16
30.0%. Run time: 7.40s. Est. time left: 00:00:00:17
40.0%. Run time: 10.83s. Est. time left: 00:00:00:16
50.0%. Run time: 14.29s. Est. time left: 00:00:00:14
60.0%. Run time: 17.91s. Est. time left: 00:00:00:11
70.0%. Run time: 21.61s. Est. time left: 00:00:00:09
80.0%. Run time: 25.38s. Est. time left: 00:00:00:06
90.0%. Run time: 29.17s. Est. time left: 00:00:00:03
Total run time: 32.89s
Saving MBSolve to mbs-vee-sech-sqrt8pi-sqrt8pi.qu
CPU times: user 32.8 s, sys: 91.5 ms, total: 32.8 s
Wall time: 32.9 s
[5]:
import matplotlib.pyplot as plt
%matplotlib inline
import seaborn as sns
sns.set_style('darkgrid')
fig = plt.figure(1, figsize=(16, 12))
# Probe
ax = fig.add_subplot(211)
cmap_range = np.linspace(0.0, 2.0, 11)
cf = ax.contourf(mb_solve_00.tlist, mb_solve_00.zlist,
np.abs(mb_solve_00.Omegas_zt[0]/(2*np.pi)),
cmap_range, cmap=plt.cm.Blues)
ax.set_title('Rabi Frequency ($\Gamma / 2\pi $)')
ax.set_ylabel('Distance ($L$)')
ax.text(0.02, 0.95, 'Probe',
verticalalignment='top', horizontalalignment='left',
transform=ax.transAxes, color='grey', fontsize=16)
plt.colorbar(cf)
# Coupling
ax = fig.add_subplot(212)
cmap_range = np.linspace(0.0, 2.0, 11)
cf = ax.contourf(mb_solve_00.tlist, mb_solve_00.zlist,
np.abs(mb_solve_00.Omegas_zt[1]/(2*np.pi)),
cmap_range, cmap=plt.cm.Greens)
ax.set_xlabel('Time ($1/\Gamma$)')
ax.set_ylabel('Distance ($L$)')
ax.text(0.02, 0.95, 'Coupling',
verticalalignment='top', horizontalalignment='left',
transform=ax.transAxes, color='grey', fontsize=16)
plt.colorbar(cf)
# Both
for ax in fig.axes:
for y in [0.0, 1.0]:
ax.axhline(y, c='grey', lw=1.0, ls='dotted')
plt.tight_layout()
[6]:
total_area = np.sqrt(mb_solve_00.fields_area()[0]**2 + mb_solve_00.fields_area()[1]**2)
fig, ax = plt.subplots(figsize=(16, 4))
ax.plot(mb_solve_00.zlist, mb_solve_00.fields_area()[0]/np.pi, label='Probe', clip_on=False)
ax.plot(mb_solve_00.zlist, mb_solve_00.fields_area()[1]/np.pi, label='Coupling', clip_on=False)
ax.plot(mb_solve_00.zlist, total_area/np.pi, label='Total', ls='dashed', clip_on=False)
ax.legend()
ax.set_ylim([0.0, 4.0])
ax.set_xlabel('Distance ($L$)')
ax.set_ylabel('Pulse Area ($\pi$)');