Cubic phase state definition and Wigner function

cubic.py

import numpy as np

from qutip.wigner import wigner
from qutip import coherent, squeeze, destroy, displace

import matplotlib.pyplot as plt
from matplotlib import colors


def cubic(initial_state, squeezing, gamma):
    """
    Generates the cubic phase state ket.
    
    Args:
        initial_state (qutip.Qobj): Ket representing the initial state
                                    Default: vacuum, i.e., coherent(N, 0)
        squeezing (float): Squeezing parameter.
        gamma (float): Cubicity.

    Returns:
        state (qutip.Qobj): ket representing the initial state
    """
    hilbert_size = initial_state.shape[0]
    a = destroy(hilbert_size)

    op = (1j) * gamma * ((a + a.dag()) / np.sqrt(2)) ** 3

    cubic_op = op.expm()
    squeezing_op = squeeze(hilbert_size, -squeezing)

    state = cubic_op * (squeezing_op * initial_state)
    state = state.unit()  # Trace normalization

    return state


N = 128  # Hilbert space cutoff

squeezing = 0.5
cubicity = -0.3

# initial vacuum state
initial_state = coherent(N, 0)
target_state = cubic(initial_state, squeezing, cubicity)

# Marina displaces the state up to see more of the fringes
target_state = displace(N, 1.5j) * target_state

xvec = np.linspace(-4, 4, 200)
yvec = np.linspace(-4, 4, 200)

# g = 2 sets the convention for hbar that Marina used
w_target = wigner(target_state, xvec, yvec, g=2)

norm = colors.TwoSlopeNorm(vmin=-2 / np.pi, vcenter=0, vmax=2 / np.pi)
im = plt.pcolor(xvec, yvec, w_target, cmap="RdBu_r", norm=norm, shading="auto")

plt.colorbar(im)
plt.xlabel("x")
plt.xlabel("p")
plt.title(
    "Cubic phase state \n Squeezing = {} cubicity = {}".format(squeezing, cubicity)
)
plt.show()