V-Type Three-Level: Solitons form Simulton¶
In this example, a soliton is put in on both the probe and the coupling fields.
[1]:
import numpy as np
sech_fwhm_conv = 1./2.6339157938
t_width = 1.0*sech_fwhm_conv # [τ]
print('t_width', t_width)
n_1 = np.sqrt(8) # For a pulse area of nπ
ampl_1 = n_1/t_width/(2*np.pi) # Pulse amplitude [2π Γ]
print('ampl_1', ampl_1)
n_2 = np.sqrt(8) # For a pulse area of nπ
ampl_2 = n_2/t_width/(2*np.pi) # Pulse amplitude [2π Γ]
print('ampl_2', ampl_2)
t_width 0.3796628587572578
ampl_1 1.1856786822710181
ampl_2 1.1856786822710181
[2]:
np.sqrt(n_1**2 + n_2**2)
[2]:
4.0
[3]:
mb_solve_json = """
{{
"atom": {{
"fields": [
{{
"coupled_levels": [[0, 1]],
"label": "probe",
"rabi_freq": 1.0,
"rabi_freq_t_args":
{{
"ampl": {ampl_1},
"centre": 0.0,
"width": {t_width}
}},
"rabi_freq_t_func": "sech"
}},
{{
"coupled_levels": [[0, 2]],
"label": "coupling",
"rabi_freq": 1.0,
"rabi_freq_t_args":
{{
"ampl": {ampl_2},
"centre": 3.0,
"width": {t_width}
}},
"rabi_freq_t_func": "sech"
}}
],
"num_states": 3
}},
"t_min": -2.0,
"t_max": 14.0,
"t_steps": 200,
"z_min": -0.5,
"z_max": 1.5,
"z_steps": 500,
"z_steps_inner": 1,
"interaction_strengths": [50.0, 10.0],
"savefile": "mbs-vee-sech-sqrt8pi-sqrt8pi-collision"
}}
""".format(ampl_1=ampl_1, t_width=t_width, ampl_2=ampl_2)
[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=False, pbar_chunk_size=2)
Loaded tuple object.
CPU times: user 1.03 ms, sys: 16.1 ms, total: 17.2 ms
Wall time: 17.4 ms
[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, 0.8, 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, 0.8, 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 ($\pi$)');
[7]:
fields_area_abs = np.trapz(np.abs(mb_solve_00.Omegas_zt), mb_solve_00.tlist, axis=2)
Animation¶
[8]:
C = 0.1 # speed of light
Y_MIN = 0.0 # Y-axis min
Y_MAX = 3.0 # y-axis max
ZOOM = 2 # level of linear interpolation
FPS = 60 # frames per second
ATOMS_ALPHA = 0.2 # Atom indicator transparency
[9]:
FNAME = "mbs-vee-sech-sqrt8pi-sqrt8pi-collision"
FNAME_JSON = FNAME + '.json'
with open(FNAME_JSON, "w") as f:
f.write(mb_solve_json)