Λ-Type Three-Level: Weak Pulse, No Coupling¶
Define and Solve¶
[1]:
mb_solve_json = """
{
"atom": {
"fields": [
{
"coupled_levels": [[0, 1]],
"detuning": 0.0,
"detuning_positive": true,
"label": "probe",
"rabi_freq": 1.0e-3,
"rabi_freq_t_args":
{
"ampl": 1.0,
"centre": 0.0,
"fwhm": 1.0
},
"rabi_freq_t_func": "gaussian"
},
{
"coupled_levels": [[1, 2]],
"detuning": 0.0,
"detuning_positive": false,
"label": "coupling",
"rabi_freq": 0.0,
"rabi_freq_t_args":
{
"ampl": 1.0,
"fwhm": 0.2,
"on": -1.0,
"off": 9.0
},
"rabi_freq_t_func": "ramp_onoff"
}
],
"num_states": 3
},
"t_min": -2.0,
"t_max": 10.0,
"t_steps": 120,
"z_min": -0.2,
"z_max": 1.2,
"z_steps": 100,
"z_steps_inner": 2,
"interaction_strengths": [10.0, 10.0],
"savefile": "mbs-lambda-weak-pulse-more-atoms-no-coupling"
}
"""
[2]:
from maxwellbloch import mb_solve
mbs = mb_solve.MBSolve().from_json_str(mb_solve_json)
[3]:
%time Omegas_zt, states_zt = mbs.mbsolve(recalc=False)
Loaded tuple object.
CPU times: user 4.43 ms, sys: 0 ns, total: 4.43 ms
Wall time: 4.44 ms
## Field Output
[4]:
import matplotlib.pyplot as plt
%matplotlib inline
import seaborn as sns
import numpy as np
sns.set_style('darkgrid')
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);
[5]:
import matplotlib.pyplot as plt
%matplotlib inline
import seaborn as sns
import numpy as np
sns.set_style('darkgrid')
fig = plt.figure(1, figsize=(16, 6))
ax = fig.add_subplot(111)
cmap_range = np.linspace(0.0, 10.0, 11)
cf = ax.contourf(mbs.tlist, mbs.zlist,
np.abs(mbs.Omegas_zt[1]/(2*np.pi)),
cmap_range, cmap=plt.cm.Greens)
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);
## Analysis
With no coupling, the weak probe pulse is absorbed just like in the two-level atom case.