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arXiv:2512.04295

Limits of Perturbation Theory for Multimode Light Propagation in Dispersive Optical Cavities

K. S. Tikhonov, D. M. Malyshev, V. A. Averchenko

quant-phSubmitted Dec 3, 2025• Announced Dec 5, 2025• 0 citations
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Abstract

Temporal modes of quantum light pulses is a promising resource for modern quantum technologies, driving advancements in quantum computing, communication, and metrology. Precise control and manipulation of these modes remain critical challenges, particularly in systems where nonlinear multimode dynamics interact with dispersion effects. In this work, we focus on the role of group velocity dispersion (GVD) within optical cavities - a phenomenon traditionally viewed as detrimental but increasingly recognized as a versatile tool for quantum light manipulation. We present a perturbation-theory-based approach to analyze GVD effects in a synchronously pumped dispersive cavity. By comparing perturbative solutions to rigorous steady-state results, we establish the validity region of the perturbative approach and assess its limitations in multimode systems. Our study identifies key parameters governing the breakdown of perturbation theory, such as mode order, dispersion strength, and cavity decay rates.

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Temporal modes of quantum light pulses is a promising resource for modern quantum technologies, driving advancements in quantum computing, communication, and metrology. Precise control and manipulation of these modes remain critical challenges, particularly in systems where nonlinear multimode dynamics interact with dispersion effects. In this work, we focus on the role of group velocity dispersion (GVD) within optical cavities - a phenomenon traditionally viewed as detrimental but increasingly recognized as a versatile tool for quantum light manipulation. We present a perturbation-theory-based approach to analyze GVD effects in a synchronously pumped dispersive cavity. By comparing perturbative solutions to rigorous steady-state results, we establish the validity region of the perturbative approach and assess its limitations in multimode systems. Our study identifies key parameters governing the breakdown of perturbation theory, such as mode order, dispersion strength, and cavity decay rates.
Abstract Parametric down-conversion in a nonlinear crystal is a widely employed technique for generating quadrature squeezed light with multiple modes, which finds applications in quantum metrology, quantum information and communication. Here we study the generation of temporally multimode femtosecond pulsed squeezed light in a synchronously pumped optical parametric oscillator (SPOPO) operating below the oscillation threshold, while considering the presence of non-compensated intracavity group-velocity dispersion. Based on the developed time-domain model of the system, we show that the dispersion results in mode-dependent detuning of the broadband supermodes of the pulsed parametric process from the cavity resonance due to temporal Gouy phase, as well as linear coupling between these supermodes. With perturbation theory up to the second order in the coupling coefficients between modes, we obtained a solution for the amplitudes of multiple supermodes given an arbitrary sub-threshold pump level. The dispersion affects the quantum state of the supermodes by influencing their squeezing level and the rotation of the squeezing ellipse. It also affects the entanglement among the supermodes, leading to reduced suppression of shot noise level as measured in the balanced homodyne detection scheme. Furthermore, our study highlights the potential of SPOPO with group-velocity dispersion as a testbench for experimental investigations of multimode effects in linearly evanescent coupled parametric oscillators.
The propagation of light pulses through negative group velocity media is known to give rise to a number of paradoxical situations that seem to violate causality. The solution of these paradoxes has triggered the investigation of a number of interesting and unexpected features of light propagation. Here, we report a combined theoretical and experimental study of the ring-down oscillations in optical cavities filled with a medium with a sufficiently negative frequency dispersion to give a negative round-trip group delay time. We theoretically anticipate that causality imposes the existence of additional resonance peaks in the cavity transmission, resulting in a non-exponential decay of the cavity field and in a breakdown of the cavity decay rate concept. Our predictions are validated by simulations and by an experiment using a room-temperature gas of metastable helium atoms in the detuned electromagnetically induced transparency regime as the cavity medium.
Quantum states of light can be used to encode quantum information, and it can be transmitted over free-space or optical fibers for long-distance quantum communication. Since quantum signals or qubits cannot be amplified, long-distance quantum communication often requires pre-conditioning or preparation of the quantum states for a specific group velocity dispersion (GVD) of the desired fiber-optic channel, which is often difficult experimentally. Moreover, in entanglement-based quantum communication, GVD can be used as another degree of freedom to certify an entanglement signature. However, introducing and controlling large GVD with minimal loss is a challenging problem. In this work, we demonstrate a fiber-optic module capable of introducing a desired amount of GVD to the quantum signal and verify its operation using an entangled photon pair at the telecom wavelength. Our GVD module is based on dense wavelength-division multiplexing (DWDM) technology, and it can be easily designed and operated for various quantum communication scenarios, making it a valuable tool in implementing long-distance quantum communication in varying real-world conditions.
Over the past 15 years, several groups have engineered media that are both strongly dispersive and roughly transparent for some finite bandwidth. Relationships and intuitive models that are satisfactory when it is reasonable to neglect dispersion may then fail. We analyze three such cases of failure. First, a simple generalization of the Abraham and Minkowski momenta to dispersive media entails multiplying each per-photon momentum by n/ngn/n_gn/ng​, where nnn is the refractive index and ngn_gng​ is the group index. The resulting forms are experimentally relevant for the case of the Abraham momentum, but not for the Minkowski momentum. We show how dispersion modulates the displacement of a sphere embedded in a dispersive medium by a pulse. Second, pulse transformation in a nonstationary medium is modulated by the presence of dispersion. Using an explicit description of the kinetics of dispersive nonstationary inhomogeneous media, we show how the group velocity can modulate pulse response to a change in the refractive index and how Doppler shifts may become large in a dispersive medium as the velocity of the Doppler shifting surface approaches the group velocity. We explain a simple way to use existing technology to either compress or decompress a given pulse, changing its bandwidth and spatial extent by several orders of magnitude while otherwise preserving its envelope shape. Finally, we note that the nature of a single optical cavity quasimode depends on intracavity dispersion. We show that the quantum field noise associated with a single cavity mode may be modulated by dispersion. For a well-chosen mode in a high-Q cavity, this can amount to either an increase or a decrease in total vacuum field energy by several orders of magnitude. We focus on the "white light cavity," showing that the quantum noise of an ideal white light cavity diverges as the cavity finesse improves.
Abstract Nonlinear sources of quantum light are foundational to a majority of optical quantum technologies and are actively advancing toward real-world deployment. Achieving this goal requires fabrication capabilities to be scaled to industrial standards, necessitating precise modeling tools that can both guide device design within realistic fabrication constraints and enable accurate post-fabrication characterization. In this paper, building on existing work, we introduce a modeling framework that explicitly integrates the engineering tools used for designing classical properties of integrated waveguides with quantum mechanical theory describing the underlying nonlinear interactions. We analyze the validity and limitations of approximations relevant to this framework and apply it to comprehensively study how typical fabrication errors and deviations from nominal design—common in practical waveguide manufacturing—affect the nonlinear optical response. Our findings highlight, in particular, a critical sensitivity of the framework to group-velocity dispersion, the potentially highly disruptive role of geometric inhomogeneities in the waveguide, and an upper bound on uncorrelated squeezed-state generation arising from asymmetric group-velocity matching conditions.
Parametrically driven cavity solitons (PDCS), unlike single-pumped cavity solitons, are localized optical pulses arising from parametric processes. These cavity solitons, recently discovered in pure-Kerr media, offer great promise for nonlinear dynamics studies and metrology. Here, we present the first multimode quantum description of pure-Kerr PDCS. In the below threshold regime, we verify single- and two-mode squeezing, while above threshold we uncover novel "quantum" dispersive waves - the quantum analog of soliton Cherenkov radiation. Besides revealing these unexplored quantum properties, we show that PDCS generates up to 20 dB of squeezing, only limited by overcoupling and intrinsic losses for experimentally routine parameters. We therefore provide a pathway to observe strong multimode quantum noise reduction in these systems.