Wigner Function Evolution of Quantum States in Presence of Self-Kerr Interaction

A Fokker-Planck equation for the Wigner function evolution in a noisy Kerr medium ($χ^{(3)}$ non-linearity) is presented. We numerically solved this equation taking a coherent state as an initial condition. The dissipation effects are discussed. We provide examples of quantum interference, sub-Planck phase space structures, and Gaussian versus non-Gaussian dynamical evolution of the state. The results also apply to the description of a nanomechanical resonator with an intrinsic Duffing nonlinearity.

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