QuTiP example: Wigner function animation for the dynamics of the Jaynes-Cumming model
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 mpl_toolkits.mplot3d import Axes3D
from matplotlib import cm
import time
In [5]:
from qutip import *
from qutip.ipynbtools import plot_animation
In [6]:
def jc_integrate(N, wc, wa, g, kappa, gamma, psi0, use_rwa, tlist):
# Hamiltonian
idc = qeye(N)
ida = qeye(2)
a = tensor(destroy(N), ida)
sm = tensor(idc, destroy(2))
if use_rwa:
# use the rotating wave approxiation
H = wc * a.dag() * a + wa * sm.dag() * sm + g * (a.dag() * sm + a * sm.dag())
else:
H = wc * a.dag() * a + wa * sm.dag() * sm + g * (a.dag() + a) * (sm + sm.dag())
# collapse operators
c_op_list = []
n_th_a = 0.0 # zero temperature
rate = kappa * (1 + n_th_a)
if rate > 0.0:
c_op_list.append(np.sqrt(rate) * a)
rate = kappa * n_th_a
if rate > 0.0:
c_op_list.append(np.sqrt(rate) * a.dag())
rate = gamma
if rate > 0.0:
c_op_list.append(np.sqrt(rate) * sm)
# evolve and calculate return state vectors
result = mesolve(H, psi0, tlist, c_op_list, [])
return result
In [7]:
# parameters
wc = 1.0 * 2 * np.pi # cavity frequency
wa = 1.0 * 2 * np.pi # atom frequency
g = 0.05 * 2 * np.pi # coupling strength
kappa = 0.05 # cavity dissipation rate
gamma = 0.15 # atom dissipation rate
N = 10 # number of cavity fock states
use_rwa = True
# initial state
psi0 = tensor(basis(N,0), basis(2,1)) # start with an excited atom
#psi0 = tensor(coherent(N,1.5), basis(2,0)) # or a coherent state the in cavity
#psi0 = tensor((coherent(N,2.0)+coherent(N,-2.0)).unit(), basis(2,0)) # or a superposition of coherent states
tlist = np.linspace(0, 30, 150)
In [8]:
result = jc_integrate(N, wc, wa, g, kappa, gamma, psi0, use_rwa, tlist)
In [9]:
xvec = np.linspace(-5.,5.,100)
X,Y = np.meshgrid(xvec, xvec)
In [10]:
def plot_setup(result):
fig = plt.figure(figsize=(12, 6))
ax = Axes3D(fig, azim=-107, elev=49)
return fig, ax
In [11]:
cb = None
def plot_result(result, n, fig=None, axes=None):
global cb
if fig is None or axes is None:
fig, ax = plot_setup(result)
axes.cla()
# trace out the atom
rho_cavity = ptrace(result.states[n], 0)
W = wigner(rho_cavity, xvec, xvec)
surf = axes.plot_surface(X, Y, W, rstride=1, cstride=1, cmap=cm.jet,
alpha=1.0, linewidth=0.05, vmax=0.25, vmin=-0.25)
axes.set_xlim3d(-5, 5)
axes.set_ylim3d(-5, 5)
axes.set_zlim3d(-0.25, 0.25)
if not cb:
cb = plt.colorbar(surf, shrink=0.65, aspect=20)
return fig, axes
In [12]:
plot_animation(plot_setup, plot_result, result)
Out[12]:
In [13]:
from qutip.ipynbtools import version_table
version_table()
Out[13]: