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Quantum states of light, particularly at optical frequencies, are considerednecessary 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 quantumlight states are currently challenging to deterministically generate at opticalfrequencies. In part, this is due to a relatively small number of schemes thatprepare target quantum states given nonlinear interactions. Here, we present anespecially simple concept for deterministically generating and stabilizingimportant quantum states of light, using only simple third-order opticalnonlinearities and engineered dissipation. We show how by considering either anonlinear cavity with frequency-dependent outcoupling, or a chain of nonlinearwaveguides, one can "filter" out all but a periodic ladder of photon numbercomponents of a density matrix. As examples of this phenomenon, we showcavities 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 catstates of a desired order. We discuss potential realizations in quantumnonlinear optics. More broadly, we expect that combining the techniquesintroduced here with additional "phase-sensitive" nonlinearities (such assecond-order nonlinearity) should enable passive stabilization and generationof a wider variety of states than shown here.

Deterministic quantum state generators and stabilizers from nonlinear photonic filter cavities