Wigner negativity in the steady-state output of a Kerr parametric oscillator

A quantum mechanical state can be fully characterized in phase space by its Wigner function. Unlike a proper probability distribution which is always positive, the Wigner function can take negative values in some regions of phase space. This is indicative of nonclassicality, and quantum states with a negative Wigner functions can be useful resources for quantum computing.

In this work, we study the Wigner negativity of the steady-state output field from a parametrically driven Kerr oscillator, where the output states are defined in terms of wave packet modes. Remarkably, we find that even though the steady-state cavity field is always characterized by a positive Wigner function, the output may exhibit Wigner negativity depending on the properties of the selected mode.