Deterministic Quantum State Generators and Stabilizers from Nonlinear Photonic Filter Cavities

Quantum states of light, particularly at optical frequencies, are considered necessary to realize a host of important quantum technologies and applications, spanning Heisenberg-limited metrology, continuous-variable quantum computing, and quantum communications. Nevertheless, a wide variety of important quantum light states are currently challenging to deterministically generate at optical frequencies. In part, this is due to a relatively small number of schemes that prepare target quantum states given nonlinear interactions. Here, we present an especially simple concept for deterministically generating and stabilizing important quantum states of light, using only third-order optical nonlinearities and engineered dissipation. We show how, by considering either a nonlinear cavity with frequency-dependent outcoupling or a chain of nonlinear waveguides, one can induce high loss for all but some desired light intensities. Specifically, we find that the stabilized intensities can correspond to an evenly spaced pattern of stablilized photon numbers. This is shown to produce important quantum states with coherent superpositions between various photon numbers. As examples of this phenomenon, we show cavities which can stabilize squeezed states, as well as produce "photon-number-comb" states. Moreover, in these types of filter cavities, Glauber coherent states will deterministically evolve into Schrodinger cat states of a desired order. We discuss potential realizations in quantum nonlinear optics. More broadly, we expect that combining the techniques introduced here with additional "phase-sensitive" nonlinearities (such as second-order nonlinearity) should enable passive stabilization and generation of a wider variety of states than shown here.