Highly squeezed states in ring resonators: Beyond the undepleted-pump approximation

We present a multimode theory of squeezed-state generation in resonant systems valid for arbitrary pump power and including pump depletion. The Hamiltonian is written in terms of asymptotic-in and -out fields from scattering theory, capable of describing a general interaction. As an example we consider the lossy generation of a highly squeezed state by an effective second-order interaction in a silicon nitride ring resonator point coupled to a waveguide. We calculate the photon number, the Schmidt number, and the second-order correlation function of the generated state in the waveguide. The treatment we present provides a path forward to study the deterministic generation of non-Gaussian states in resonant systems.