Two-Level: Gaussian Pulse 1.8π

[1]:

mb_solve_json = """
{
  "atom": {
    "fields": [
      {
        "coupled_levels": [[0, 1]],
        "rabi_freq_t_args": {
          "n_pi": 1.8,
          "centre": 0.0,
          "fwhm": 1.0
        },
        "rabi_freq_t_func": "gaussian"
      }
    ],
    "num_states": 2
  },
  "t_min": -2.0,
  "t_max": 10.0,
  "t_steps": 120,
  "z_min": -0.5,
  "z_max": 1.5,
  "z_steps": 100,
  "interaction_strengths": [
    10.0
  ],
  "savefile": "mbs-two-gaussian-1.8pi"
}
"""

[2]:

from maxwellbloch import mb_solve

mbs = mb_solve.MBSolve().from_json_str(mb_solve_json)

[3]:

import numpy as np

[4]:

# Check the input pulse area is correct
print(
    "The input pulse area is {0:.3f}".format(
        np.trapezoid(mbs.Omegas_zt[0, 0, :].real, mbs.tlist) / np.pi
    )
)

The input pulse area is 1.800

Solve the Problem

[5]:

Omegas_zt, states_zt = mbs.mbsolve(recalc=False)

/home/docs/checkouts/readthedocs.org/user_builds/maxwellbloch/envs/v0.8.1/lib/python3.11/site-packages/qutip/fileio.py:253: VisibleDeprecationWarning: dtype(): align should be passed as Python or NumPy boolean but got `align=0`. Did you mean to pass a tuple to create a subarray type? (Deprecated NumPy 2.4)
  out = pickle.load(fileObject, encoding='latin1')

Plot Output

[6]:

import matplotlib.pyplot as plt

%matplotlib inline
import seaborn as sns

sns.set_style("darkgrid")

fig = plt.figure(1, figsize=(16, 6))
ax = fig.add_subplot(111)
cmap_range = np.linspace(0.0, 1.0, 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(r"Rabi Frequency ($\Gamma / 2\pi $)")
ax.set_xlabel(r"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);

../_images/examples_mbs-two-gaussian-1.8pi_8_0.png

[7]:

fig, ax = plt.subplots(figsize=(16, 4))
ax.plot(mbs.zlist, mbs.fields_area()[0] / np.pi, clip_on=False)
ax.set_ylim([0.0, 8.0])
ax.set_xlabel("Distance ($L$)")
ax.set_ylabel(r"Pulse Area ($\pi$)");

../_images/examples_mbs-two-gaussian-1.8pi_9_0.png

Movie

[8]:

# FNAME = "mb-solve-two-gaussian-0.8pi"

[9]:

# z_steps was 200 for movie

[10]:

# C = 0.1 # speed of light
# Y_MIN = 0.0 # Y-axis min
# Y_MAX = 4.0 # y-axis max
# ZOOM = 2 # level of linear interpolation
# FPS = 30 # frames per second
# ATOMS_ALPHA = 0.2 # Atom indicator transparency

[11]:

# FNAME_IMG = "images/" + FNAME
# FNAME_JSON = FNAME_IMG + '.json'
# with open(FNAME_JSON, "w") as f:
#     f.write(mb_solve_json)

[12]:

# !make-mp4-fixed-frame.py -f $FNAME_JSON -c $C --fps $FPS --y-min $Y_MIN --y-max $Y_MAX \
#     --zoom $ZOOM --atoms-alpha $ATOMS_ALPHA #--peak-line --c-line

[13]:

# FNAME_MP4 = FNAME_IMG + '.mp4'
# !make-gif-ffmpeg.sh -f $FNAME_MP4 --in-fps $FPS

[14]:

# from IPython.display import Image
# Image(url=FNAME_MP4+'.gif', format='gif')