Pseudo-probability functions¶

J.R. Johansson and P.D. Nation

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

In [1]:

import matplotlib as mpl
import matplotlib.pylab as plt
import numpy as np
from matplotlib import cm
from mpl_toolkits.mplot3d import Axes3D
from qutip import about, basis, dag, destroy, qfunc, wigner, wigner_cmap

%matplotlib inline

Wigner function for superposition of fock states¶

In [2]:

x = 1.0 / np.sqrt(2) * (basis(10, 4) + basis(10, 2))
xvec = np.arange(-5, 5, 10.0 / 100)
yvec = xvec
W = wigner(x, xvec, yvec)
cmap = wigner_cmap(W)
X, Y = np.meshgrid(xvec, yvec)

In [3]:

fig = plt.figure(figsize=(8, 6))
plt.contourf(X, Y, W, 50, cmap=cmap)
plt.colorbar();

In [4]:

fig = plt.figure(figsize=(10, 8))
ax = Axes3D(fig, azim=-30, elev=73)
ax.plot_surface(X, Y, W, cmap=cmap, rstride=1, cstride=1, alpha=1, linewidth=0)
ax.set_zlim3d(-0.25, 0.25)
for a in ax.w_zaxis.get_ticklines() + ax.w_zaxis.get_ticklabels():
    a.set_visible(False)
nrm = mpl.colors.Normalize(W.min(), W.max())
cax, kw = mpl.colorbar.make_axes(ax, shrink=0.66, pad=0.02)
cb1 = mpl.colorbar.ColorbarBase(cax, cmap=cmap, norm=nrm)
cb1.set_label("Pseudoprobability")

/tmp/ipykernel_9059/1375824337.py:2: MatplotlibDeprecationWarning: Axes3D(fig) adding itself to the figure is deprecated since 3.4. Pass the keyword argument auto_add_to_figure=False and use fig.add_axes(ax) to suppress this warning. The default value of auto_add_to_figure will change to False in mpl3.5 and True values will no longer work in 3.6.  This is consistent with other Axes classes.
  ax = Axes3D(fig, azim=-30, elev=73)

Winger and Q-function for squeezed states¶

In [5]:

N = 20
alpha = -1.0  # Coherent amplitude of field
epsilon = 0.5j  # Squeezing parameter
a = destroy(N)

D = (alpha * a.dag() - np.conj(alpha) * a).expm()  # Displacement
S = (
    0.5 * np.conj(epsilon) * a * a - 0.5 * epsilon * a.dag() * a.dag()
).expm()  # Squeezing
psi = D * S * basis(N, 0)  # Apply to vacuum state
g = 2

Wigner function¶

In [6]:

xvec = np.arange(-40.0, 40.0) * 5.0 / 40
X, Y = np.meshgrid(xvec, xvec)

W = wigner(psi, xvec, xvec)

fig1 = plt.figure(figsize=(8, 6))
ax = Axes3D(fig1)
ax.plot_surface(X, Y, W, rstride=2, cstride=2, cmap=cm.jet, alpha=0.7)
ax.contour(X, Y, W, 15, zdir="x", offset=-6)
ax.contour(X, Y, W, 15, zdir="y", offset=6)
ax.contour(X, Y, W, 15, zdir="z", offset=-0.3)
ax.set_xlim3d(-6, 6)
ax.set_xlim3d(-6, 6)
ax.set_zlim3d(-0.3, 0.4)
plt.title("Wigner function of squeezed state");

/tmp/ipykernel_9059/1340448683.py:7: MatplotlibDeprecationWarning: Axes3D(fig) adding itself to the figure is deprecated since 3.4. Pass the keyword argument auto_add_to_figure=False and use fig.add_axes(ax) to suppress this warning. The default value of auto_add_to_figure will change to False in mpl3.5 and True values will no longer work in 3.6.  This is consistent with other Axes classes.
  ax = Axes3D(fig1)