Highly Squeezed States in Ring Resonators: Beyond the Undepleted Pump Approximation

TL;DR

This paper develops a comprehensive multimode theory for generating highly squeezed states in resonant systems that accounts for pump depletion, enabling more accurate modeling of quantum state production in nonlinear optical resonators.

Contribution

It introduces a general Hamiltonian framework including pump depletion effects for resonant systems, extending beyond the undepleted pump approximation.

Findings

The theory accurately predicts photon number and squeezing levels in lossy resonators.

Application to silicon nitride ring resonators demonstrates practical generation of highly squeezed states.

Provides a foundation for deterministic non-Gaussian state generation in resonant quantum optics.

Abstract

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, 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.