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Semi-classical simulations of squeezing generation in integrated Kerr microresonators

Sara Persia, Fuchuan Lei, Vaishali Adya, Victor Torres Company

Published Jan 1, 2026• 0 citations
OpenAlex

Abstract

We demonstrate that a semi-classical approach based on the Ikeda map enables the simulation of two-mode quadrature squeezing in quantum frequency combs generated in integrated Kerr microring resonators.

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Kerr microresonators are integrated nonlinear devices widely used to generate classical optical frequency combs and nonclassical states of light. In particular, they provide a promising platform for squeezed light sources, which are important elements of emerging quantum sensing, communication, and computing technologies. Designing such sources requires numerical tools that efficiently incorporate realistic device physics and noise processes. Here, we show that established semi-classical frameworks based on the Lugiato-Lefever equation and the Ikeda map, instrumental in the development of classical light sources, can also predict the quadrature-noise properties of squeezed light when vacuum fluctuations are properly included. We consider three canonical configurations producing two-mode quadrature squeezing, single-mode quadrature squeezing, and intensity difference squeezing. In each case, the semi-classical simulations produce quadrature variances and noise spectra in close agreement with the quantum theoretical predictions. These frameworks therefore provide practical tools for designing squeezed light sources, with the capability to incorporate additional noise mechanisms, nonlinear effects, and complex resonator arrangements. More fundamentally, our results show that key experimental signatures of squeezing can be modeled as phase-sensitive amplification of properly normalized vacuum fluctuations within stochastic semi-classical field equations. This observation helps distinguish squeezing properties accessible through semi-classical field evolution from those intrinsically requiring a full quantum description.
Squeezed states, with their noise reduction below the standard quantum limit, are promising quantum states of light exploited for enhancing sensitivity in quantum sensing or as carriers of information in continuous variable quantum computing and communication. To make use of their quantum advantage, the main common challenge in generating these states is achieving high levels of squeezing in low loss setups.Over the years, several bulk optical nonlinear crystals and cavities have been employed for the generation of different types of high-quality squeezed states. However, recent progress in fabricating ultra-low loss integrated waveguides has shifted the interest of the community towards the integration of squeezing sources to gain advantages in terms of compactness, scalability, and reproducibility.The aim of this thesis is to investigate the main characteristics, limits, and requirements for the generation of vacuum and bright squeezed states by second- and third-order nonlinear devices, with more emphasis on integrated cavities. In particular, we demonstrate high on-chip intensity difference squeezing between bright mode pairs created in an engineered SiN microring resonator. In addition, we propose the use of the Ikeda map, a semi-classical simulation tool, for the investigation of two-mode quadrature squeezing generation in microresonators, discussing its competitiveness against standard quantum models. These results contribute to the optimization of engineered integrated devices with the aim of attaining high levels of squeezing sufficient to bring real advantages in classical and quantum applications.
The dynamical behavior of Kerr optical frequency combs is very well understood today from the perspective of the semi-classical approximation. In this article, we provide a theoretical understanding of the phenomena of quantum correlations, multimode entanglement and squeezed states of light that can occur in these frequency combs when quantum noise is accounted for. We prove that for all stationary spatio-temporal patterns, the side-modes that are symmetrical relatively to the central (pumped) mode in the frequency domain display quantum correlations that can lead to squeezed states of light under some optimal conditions that are analytically determined. We show that these quantum correlations can persist regardless the dynamical state of the system (rolls or solitons), regardless of the spectral extension of the comb (number sidemodes), and regardless of the dispersion regime (normal or anomalous). We study with particular emphasis the two principal architectures for Kerr comb generation, namely the add-through and add-drop configurations. We show that in both cases, the ratio between out-coupling and total losses plays a key role as it directly determines the efficiency of the squeezing. We also explicitly determine the phase quadratures leading to photon entanglement, and analytically calculate their quantum noise spectra. The relevance of Kerr combs for quantum information systems at optical telecommunication wavelengths is also discussed.
Using a general Hamiltonian treatment, we theoretically study the generation of degenerate quadrature squeezing in a dual-pumped integrated microring resonator coupled to a waveguide. Considering a dual-pump four-wave mixing configuration in an integrated Si3N4{\text{Si}}_{3}{\text{N}}_{4}Si3​N4​ platform, and following the coupled-mode theory approach, we investigate the effects of parasitic quantum nonlinear optical processes on the generation of squeezed light. Considering five resonance modes in this approach allows us to include the most important four-wave mixing processes involved in such a configuration. We theoretically explore the effects of the pump detunings on different nonlinear processes and show that the effects of some of the parasitic processes are effectively neutralized by symmetrically detuning the two pumps. This yields a significant enhancement in the output squeezing quality without physically changing the structure, but suffers from the trade-off of requiring substantially higher pump power for a fixed target level of squeezing.