Heralded dissipative preparation of nonclassical states in a Kerr oscillator

We present a heralded state preparation scheme for driven nonlinear open quantum systems. The protocol is based on a continuous photon counting measurement of the system's decay channel. When no photons are detected for a period of time, the system has relaxed to a measurement-induced pseudosteady state. We illustrate the protocol by the creation of states with a negative Wigner function in a Kerr oscillator, a system whose unconditional steady state is strictly positive.