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IEEE Journal of Selected Topics in Quantum Electronics

Quantum-Squeezing-Engineered Third-Order Kerr Nonlinearity and Optical High-Order Sideband Comb in a Composite Resonator-Atom System

Chang Yin Gao, Feifei Liu, Z. X. Fan, Ling Fan, Ru Zhang, Cong Cao

Published Jan 1, 2024• 11 citations
Publisher

Abstract

Optical microresonators can greatly enhance light-matter interactions and reduce the power necessary to observe nonlinear optical effects. Manipulation and application of atom-resonator-coupling-induced strong nonlinearity have received much attention in recent years. Here, we present a scheme to realize quantum-squeezing-engineered third-order Kerr nonlinearity and optical high-order sideband comb in a composite system consisting of a two-level atom and two directly coupled whispering-gallery-mode optical microresonators. By quantum squeezing one of two coupled resonator modes in this system, the effective resonator-resonator and atom-resonator coupling rates as well as the frequency of the squeezed resonator mode can be effectively controlled. Based on this mechanism, we show that the Kerr nonlinearity of the composite system can be effectively engineered by using the resonator-mode squeezing when the system is monochromatically driven beyond the weak-excitation limit. On the other hand, when the composite system is bichromatically driven, the optical high-order sideband combs formed in the transmission spectra of the system can also be effectively engineered by the resonator-mode squeezing. Therefore, our scheme provides a novel mechanism to control the physical properties of composite resonator-atom systems for various applications, and demonstrates that optical nonlinear effects induced by the atom-resonator coupling can be effectively engineered via quantum squeezing.

DOI
10.1109/jstqe.2024.3492261

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The dynamical behavior of Kerr optical frequency combs is very well understood today from the perspective of the semiclassical approximation. These combs are obtained by pumping an ultrahigh-QQQ whispering-gallery mode resonator with a continuous-wave laser. The long-lifetime photons are trapped within the toruslike eigenmodes of the resonator, where they interact nonlinearly via the Kerr effect. In this article, we use quantum Langevin equations to provide a theoretical understanding of the nonclassical behavior of these combs when pumped below and above threshold. In the configuration where the system is under threshold, the pump field is the unique oscillating mode inside the resonator, and it triggers the phenomenon of spontaneous four-wave mixing, where two photons from the pump are symmetrically up- and down-converted in the Fourier domain. This phenomenon, also referred to as parametric fluorescence, can only be understood and analyzed from a fully quantum perspective as a consequence of the coupling between the field of the central (pumped) mode and the vacuum fluctuations of the various side modes. We analytically calculate the power spectra of the spontaneous emission noise, and we show that these spectra can be either single- or double-peaked depending on the value of the laser frequency, chromatic dispersion, pump power, and spectral distance between the central mode and the side mode of interest. We also calculate as well the overall spontaneous noise power per side mode and propose simplified analytical expressions for some particular cases. In the configuration where the system is pumped above threshold, we investigate the phenomena of quantum correlations and multimode squeezed states of light that can occur in the Kerr frequency combs originating from stimulated four-wave mixing. We show that for all stationary spatiotemporal patterns, the side modes that are symmetrical relative to the 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. These quantum correlations can persist regardless the dynamical state of the system (rolls or solitons), regardless of the spectral extension of the comb (number side modes) and regardless of the dispersion regime (normal or anomalous). We also explicitly determine the phase quadratures leading to photon entanglement and analytically calculate their quantum-noise spectra. For both the below- and above-threshold cases, we study with particular emphasis the two principal architectures for Kerr comb generation, namely the add-through and add-drop configurations. It is found that regardless of the configuration, an essential parameter is the ratio between out-coupling and total losses, which plays a key role as it directly determines the efficiency of the detected fluorescence or squeezing spectra. We finally discuss the relevance of Kerr combs for quantum information systems at optical telecommunication wavelengths below and above threshold.
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