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Physical Review A

High-gain squeezing in lossy resonators: An asymptotic-field approach

M. Sloan, Alice Viola, Marco Liscidini, John E. Sipe

Published Jun 2, 2025• 7 citations
Publisher

Abstract

We present a method for describing nonlinear electromagnetic interactions in integrated photonic devices utilizing an asymptotic-in (-out) field formalism. Our method expands upon previous continuous wave asymptotic treatments by describing the evolution nonperturbatively for an arbitrary pulsed input. This is presented in the context of a squeezing interaction within an integrated micro-ring resonator side coupled to an input-output waveguide, but is readily generalizable to other integrated structures, while including a variety of (nonsqueezing) third-order interactions. An example of a single-pump, nondegenerate squeezing interaction is studied, which is shown to match well with standard coupled-mode treatments for high-finesse resonators, as well as previous perturbative treatments dealing with the generation of pairs with low probability.

DOI
10.1103/physreva.111.063502

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We present a method for describing nonlinear electromagnetic interactions in integrated photonic devices utilizing an asymptotic-in (-out) field formalism. Our method expands upon previous continuous wave asymptotic treatments by describing the evolution nonperturbatively for an arbitrary pulsed input. This is presented in the context of a squeezing interaction within an integrated micro-ring resonator side coupled to an input-output waveguide, but is readily generalizable to other integrated structures, while including a variety of (nonsqueezing) third-order interactions. An example of a single-pump, nondegenerate squeezing interaction is studied, which is shown to match well with standard coupled-mode treatments for high-finesse resonators, as well as previous perturbative treatments dealing with the generation of pairs with low probability.
We present a method for describing nonlinear electromagnetic interactions in integrated photonic devices utilizing an asymptotic-in/out field formalism. Our method expands upon previous continuous wave asymptotic treatments by describing the evolution non-perturbatively for an arbitrary pulsed input. This is presented in the context of a squeezing interaction within an integrated microring resonator side coupled to an input/output waveguide, but is readily generalizable to other integrated structures, while including a variety of (non-squeezing) third-order interactions. An example of a single-pump, non-degenerate squeezing interaction is studied, which is shown to match well with standard coupled-mode treatments for high-finesse resonators, as well as previous perturbative treatments dealing with the generation of pairs with low probability.
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.
In this work, we present a quantum theory for pulsed photon pair generation in a single ring resonator. Our approach combines the Heisenberg picture input-output formalism with the Ikeda mapping from classical nonlinear optics. In doing so, we address the high-gain regime by incorporating nonperturbative effects, including self-phase modulation, cross-phase modulation, and time-ordering, which are roots for significantly different behaviors in the low-gain regime. We also account for optical losses by introducing an auxiliary waveguide, allowing for a more accurate representation of experimentally viable scenarios. Numerical simulations reveal that nonperturbative effects significantly distort transfer functions, making desirable operations challenging without careful optimization. We show that appropriate detuning of the pump frequency can mitigate these issues, leading to enhanced brightness and higher spectral purity in the high-gain regime. We further investigate the performance of a single ring resonator as a two-mode squeezer by analyzing various performance metrics under experimentally relevant optical loss conditions.
We discuss the use of asymptotic-in and -out fields in a Hamiltonian treatment of nonlinear electromagnetic problems. Our approach allows a description of nonlinear phenomena in a number of geometries and is suitable to treat integrated photonic structures, particularly cavities. We present examples in which the nonlinear phenomena are weak enough for pump depletion to be neglected, and we report some results related to the description of second-order nonlinear processes in ring resonators and layered structures.
We present a semi-analytic formalism for calculating the squeezing and antisqueezing spectrum in a channel waveguide side-coupled to a lossy ring resonator. Our approach first uses the semi-analytic evolution of the density matrix inside the ring up to the time where the squeezing is maximized. Then noting that a conservative approximate result for the squeezing can be obtained by ignoring the effect of the pump at later times, we calculate the free evolution of the field operators in the channel waveguide at all later times. We then calculate the quadrature squeezing spectrum in the waveguide, assuming that the measurement starts at the time when the squeezing in the ring is maximized. Using these results, we determine the optimum values for the pump pulse duration and amplitude and the ring-channel coupling for the pump and signal. We find that squeezing above 10 dB can be easily achieved in the channel for antisqueezing levels of less than 22 dB.
We develop a non-perturbative description of squeezed light generation in an arbitrary lossy structure consisting of multiple coupled microring resonators. This is applied to two ring photonic molecules where the interference of the fields in the coupled rings leads to a modification in the resonance spectrum near a shared resonance. Considering a dual-pump degenerate squeezing scheme under a five resonance approximation, we investigate two methods to suppress parasitic four-wave mixing contributions and compensate for group velocity dispersion within a primary resonator through hybridization effects with a second auxiliary resonator. In the former case, this comes from an effective splitting of the unwanted resonances supporting parasitic four-wave mixing interactions that add thermal noise to the desired degenerate squeezed state. For sufficiently strong coupling between the resonators, we demonstrate near complete suppression of such parasitic processes, resulting in near unit fidelities with the corresponding output state that would arise were the parasitic interactions neglected. In the latter case, the hybridization effectively shifts a pump resonance, realigning the desired dual-pump four-wave mixing process and leading to a significant enhancement of the signal generation and output squeezing.