QuTiP Example: Parallel Steady State Jaynes-Cummings Calculation¶

J.R. Johansson and P.D. Nation

For more information about QuTiP see http://qutip.org

In [1]:

%matplotlib inline

In [2]:

import matplotlib.pyplot as plt

In [3]:

import numpy as np

In [4]:

from qutip import *

System Setup¶

In [5]:

kappa = 2
gamma = 0.2
g = 1
wc = 0
w0 = 0
N = 5
E = 0.5
nloop = 101
wlist = np.linspace(-5, 5, nloop)

Define Function to Run in Parallel¶

In [6]:

def probss(wl, E, kappa, gamma, g, wc, w0, N):
    # construct composite operators
    ida = qeye(N)
    idatom = qeye(2)
    a = tensor(destroy(N), idatom)
    sm = tensor(ida, sigmam())
    
    # Hamiltonian
    H = (w0 - wl) * sm.dag() * sm + (wc - wl) * a.dag() * a + \
        1j * g * (a.dag() * sm - sm.dag() * a) + E * (a.dag() + a)

    # Collapse operators
    C1 = np.sqrt(2 * kappa) * a
    C2 = np.sqrt(gamma) * sm
    C1dC1 = C1.dag() * C1
    C2dC2 = C2.dag() * C2

    # find steady state
    rhoss = steadystate(H, [C1, C2])

    # calculate expectation values
    count1 = expect(C1dC1, rhoss)
    count2 = expect(C2dC2, rhoss)
    infield = expect(a, rhoss)
    return count1, count2, infield

Run Simulation¶

In [7]:

count1, count2, infield = parfor(probss, wlist, E=E, kappa=kappa, gamma=gamma, g=g, wc=wc, w0=w0, N=N)

Plot Results¶

In [8]:

fig = plt.figure(1)
ax = fig.add_subplot(111)
ax.plot(wlist, count1, wlist, count2, lw=2)
ax.set_xlabel('Drive Frequency Detuning')
ax.set_ylabel('Count rates')

# plot phase shift of cavity light
fig2 = plt.figure(2)
ax2 = fig2.add_subplot(111)
ax2.plot(wlist, 180.0 * np.angle(infield) / np.pi, lw=2)
ax2.set_xlabel('Drive Frequency Detuning')
ax2.set_ylabel('Intracavity phase shift');

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In [9]:

from qutip.ipynbtools import version_table

version_table()

Out[9]:

Software	Version
QuTiP	4.3.0.dev0+6e5b1d43
Numpy	1.13.1
SciPy	0.19.1
matplotlib	2.0.2
Cython	0.25.2
Number of CPUs	2
BLAS Info	INTEL MKL
IPython	6.1.0
Python	3.6.2 \|Anaconda custom (x86_64)\| (default, Jul 20 2017, 13:14:59) [GCC 4.2.1 Compatible Apple LLVM 6.0 (clang-600.0.57)]
OS	posix [darwin]
Thu Jul 20 22:07:48 2017 MDT