Two-Level: Weak Square Pulse with Decay¶
## Define and Solve
[1]:
mb_solve_json = """
{
"atom": {
"decays": [
{
"channels": [[0, 1]],
"rate": 1.0
}
],
"energies": [],
"fields": [
{
"coupled_levels": [[0, 1]],
"detuning": 0.0,
"rabi_freq": 1.0e-3,
"rabi_freq_t_args": {
"ampl": 1.0,
"on": -0.5,
"off": 0.5
},
"rabi_freq_t_func": "square"
}
],
"num_states": 2
},
"t_min": -2.0,
"t_max": 10.0,
"t_steps": 100,
"z_min": -0.2,
"z_max": 1.2,
"z_steps": 20,
"interaction_strengths": [
1.0
]
}
"""
[2]:
from maxwellbloch import mb_solve
mbs = mb_solve.MBSolve().from_json_str(mb_solve_json)
[3]:
Omegas_zt, states_zt = mbs.mbsolve()
10.0%. Run time: 0.18s. Est. time left: 00:00:00:01
20.0%. Run time: 0.55s. Est. time left: 00:00:00:02
30.0%. Run time: 0.95s. Est. time left: 00:00:00:02
40.0%. Run time: 1.34s. Est. time left: 00:00:00:02
50.0%. Run time: 1.75s. Est. time left: 00:00:00:01
60.0%. Run time: 2.17s. Est. time left: 00:00:00:01
70.0%. Run time: 2.61s. Est. time left: 00:00:00:01
80.0%. Run time: 3.05s. Est. time left: 00:00:00:00
90.0%. Run time: 3.48s. Est. time left: 00:00:00:00
Total run time: 3.91s
[4]:
import matplotlib.pyplot as plt
%matplotlib inline
import seaborn as sns
import numpy as np
sns.set_style('darkgrid')
Check the Input Pulse Profile¶
We’ll just confirm that the input pulse has the profile that we want: a Gaussian with an amplitude of \(1.0 \Gamma\) and a full-width at half maximum (FWHM) of \(1.0 \tau\).
[5]:
from scipy import interpolate
plt.plot(mbs.tlist, Omegas_zt[0,0].real/(2*np.pi))
half_max = np.max(Omegas_zt[0,0].real/(2*np.pi))/2
spline = interpolate.UnivariateSpline(mbs.tlist,
(Omegas_zt[0,0].real/(2*np.pi)-half_max), s=0)
r1, r2 = spline.roots()
# draw line at FWHM
plt.hlines(y=half_max, xmin=r1, xmax=r2, linestyle='dotted')
plt.annotate('FWHM: ' + '%0.2f'%(r2 - r1), xy=((r2+r1)/2, half_max),
xycoords='data',
xytext=(25, 0), textcoords='offset points');
Field Output¶
[6]:
fig = plt.figure(1, figsize=(16, 6))
ax = fig.add_subplot(111)
cmap_range = np.linspace(0.0, 1.0e-3, 11)
cf = ax.contourf(mbs.tlist, mbs.zlist,
np.abs(mbs.Omegas_zt[0]/(2*np.pi)),
cmap_range, cmap=plt.cm.Blues)
ax.set_title('Rabi Frequency ($\Gamma / 2\pi $)')
ax.set_xlabel('Time ($1/\Gamma$)')
ax.set_ylabel('Distance ($L$)')
for y in [0.0, 1.0]:
ax.axhline(y, c='grey', lw=1.0, ls='dotted')
plt.colorbar(cf);