Several examples that make use of the built-in Simple Harmonic Oscillator tools:
from numpy import sqrt,linspace,exp
from qutip import *
import matplotlib.pyplot as plt
%matplotlib inline
N = 40 # size of the Hilbert space.
# N needs to be large enough that matrix is not truncated
a = destroy(N)
n = a.dag()*a
Define a coherent state with $\alpha = 2:$
psi = coherent(N,1)
psi
Expectation value $\langle n\rangle$:
psi.dag()*n*psi
# Convert to a density matrix:
psi_dm = ket2dm(psi)
psi*psi.dag()
# Fock state distribution of the coherent state:
plot_fock_distribution(psi_dm)
(<matplotlib.figure.Figure at 0x11a2f3358>, <matplotlib.axes._subplots.AxesSubplot at 0x11a3396d8>)
Also look at other coherent states:
# With larger N and α:
plot_fock_distribution(coherent_dm(100,6))
(<matplotlib.figure.Figure at 0x11a549ef0>, <matplotlib.axes._subplots.AxesSubplot at 0x11a8247b8>)
And some other density matrices, like a fock-state (or n eigenstate):
# With a Fock state (number state):
plot_fock_distribution(fock_dm(20,2))
(<matplotlib.figure.Figure at 0x1022aa5c0>, <matplotlib.axes._subplots.AxesSubplot at 0x1022f9940>)
fock(20,2)
And a thermal state:
# A thermal state has decaying amplitudes
plot_fock_distribution(thermal_dm(20,2))
(<matplotlib.figure.Figure at 0x124a1c2b0>, <matplotlib.axes._subplots.AxesSubplot at 0x124e6beb8>)
xvec = linspace(-10,10,200) # Create an array for the phase space coordinates.
plt.imshow(wigner(coherent(40,5j)+coherent(40,-5j),xvec,xvec), extent=[-10,10,-10,10]) # contour plot of Wigner function
<matplotlib.image.AxesImage at 0x11c80bc50>