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arXiv:2605.29321 · Physical Review Letters

Quantum and classical noise characteristics of parametrically driven cavity solitons in dispersive Kerr resonators

Sophie S. Shamailov, Miro Erkintalo

physics.opticsquant-phSubmitted May 28, 2026• Announced May 29, 2026• 0 citations
arXivHTMLPDF

Abstract

Temporal cavity solitons generated in monochromatically driven dispersive Kerr resonators offer an attractive avenue for on-chip optical frequency comb generation. Key to many of their applications is to understand how noise -- both technical and quantum -- affects the soliton states, which has accordingly been extensively investigated. Here, we report on a comprehensive theoretical study that elucidates how technical and quantum fluctuations impact a new type of soliton structure that has very recently been predicted and observed in dispersive Kerr resonators under conditions of bichromatic driving: the pure-Kerr parametrically driven cavity soliton (PDCS). We examine how classical laser phase noise transfers from the two pump fields onto the soliton frequency comb, and we calculate the solitons' fundamental quantum-limited timing jitter and two-mode squeezing spectra. In each case, we find that PDCSs can out-perform conventional cavity solitons with comparable characteristics, even when driven by two uncorrelated lasers. Our results demonstrate that pure-Kerr PDCSs can offer unprecedented performance in noise-sensitive photonic applications and as a quantum resource

Comments
6 pages, 4 figures, 13 pages of Supplementary Information

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Temporal cavity solitons generated in monochromatically driven dispersive Kerr resonators offer an attractive avenue for on-chip optical frequency comb generation. Key to many of their applications is to understand how noise -- both technical and quantum -- affects the soliton states, which has accordingly been extensively investigated. Here, we report on a comprehensive theoretical study that elucidates how technical and quantum fluctuations impact a new type of soliton structure that has very recently been predicted and observed in dispersive Kerr resonators under conditions of bichromatic driving: the pure-Kerr parametrically driven cavity soliton (PDCS). We examine how classical laser phase noise transfers from the two pump fields onto the soliton frequency comb, and we calculate the solitons' fundamental quantum-limited timing jitter and two-mode squeezing spectra. In each case, we find that PDCSs can out-perform conventional cavity solitons with comparable characteristics, even when driven by two uncorrelated lasers. Our results demonstrate that pure-Kerr PDCSs can offer unprecedented performance in noise-sensitive photonic applications and as a quantum resource
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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.
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.
Abstract Quantum fluctuations disrupt the cyclic motions of dissipative Kerr solitons (DKSs) in nonlinear optical microresonators and consequently cause timing jitter of the emitted pulse trains. This problem is translated to the performance of several applications that employ DKSs as compact frequency comb sources. Recently, device manufacturing and noise reduction technologies have advanced to unveil the quantum properties of DKSs. Here we investigate the quantum decoherence of DKSs existing in normal-dispersion microresonators known as dark pulses. By virtue of the very large material nonlinearity, we directly observe the quantum decoherence of dark pulses in an AlGaAs-on-insulator microresonator, and the underlying dynamical processes are resolved by injecting stochastic photons into the microresonators. Moreover, phase correlation measurements show that the uniformity of comb spacing of quantum-limited dark pulses is better than 1.2 × 10 −16 and 2.5 × 10 −13 when normalized to the optical carrier frequencies and repetition frequencies, respectively. Comparing DKSs generated in different material platforms explicitly confirms the advantages of dark pulses over bright solitons in terms of quantum-limited coherence. Our work establishes a critical performance assessment of DKSs, providing guidelines for coherence engineering of chip-scale optical frequency combs.
Below-threshold signal-idler quantum Kerr combs are the most explored quantum Kerr state to-date, both for fundamental study and application in quantum technologies. However, after the first onset of optical parametric oscillation, the connectivity of the below-threshold modes grows in complexity as modes which were once purely populated with spontaneous photons develop comparatively strong mean fields which drive correlations themselves. In this talk, I will describe numeric and experimental study of this second class of states, with a focus on quantum correlations and quadrature squeezing as tools for understanding classical nonlinear optics.
Temporal cavity solitons in ring microresonators provide broad and controllable generation of frequency combs with applications in frequency standards and precise atomic clocks. Three-level media in the $\mathrm{\ensuremath{\Lambda}}$ configuration inside microresonators displaying electromagnetically induced transparency can be used for the generation of temporal cavity solitons and frequency combs in the presence of anomalous dispersion and two external driving fields close to resonance. Here domain walls separating regions of two dark states due to quantum interference correspond to realizations of stimulated Raman adiabatic passage without input pulses. With no need of modulational instabilities, bright temporal cavity solitons and frequency combs are formed when these domain walls lock with each other. Wide stability ranges, close to resonance operation, and the optimal shape of the cavity solitons due to three-level quantum interference can make them preferable to those in two-level media.