Modern experiments in resonators are moving to ever more extreme quantum regimes, posing major challenges to established theoretical approaches, such as so-called few-mode models. While these models have driven major insights for traditional regimes, they are now hitting their limitations for highly open cavities and extended systems, as encountered in cavity experiments with molecules and solid-state systems. Here, we present a novel method that significantly extends the conceptual underpinning of these discrete-mode models, promoting them to a systematic treatment. We develop an ansatz which allows to quantize the resonator's resonances with position-resolved discrete modes, thus naturally incorporating losses in the formalism. Such a construction effectively unifies key ideas from pseudomodes and quantized quasi-normal modes theory. We further present a criterion for construction of the ansatz parameters at every point in space, and semi-analytically benchmark the resulting solution for a paradigmatic one-dimensional example resonator.
Modern experiments in resonators are moving to ever more extreme quantum regimes, posing major challenges to established theoretical approaches, such as so-called few-mode models. While these models have driven major insights for traditional regimes, they are now hitting their limitations for highly open cavities and extended systems, as encountered in cavity experiments with molecules and solid-state systems. Here, we present a novel method that significantly extends the conceptual underpinning of these discrete-mode models, promoting them to a systematic treatment. We develop an ansatz which allows to quantize the resonator's resonances with position-resolved discrete modes, thus naturally incorporating losses in the formalism. Such a construction effectively unifies key ideas from pseudomodes and quantized quasi-normal modes theory. We further present a criterion for construction of the ansatz parameters at every point in space, and semi-analytically benchmark the resulting solution for a paradigmatic one-dimensional example resonator.
In the multimode regime of cavity quantum electrodynamics (cQED), light-matter coupling can be strong enough such as to allows a quantum emitter to couple with multiple resonant field modes. This regime leaves distinctive signatures in the behavior of both the field and the emitter, which are already accessible by modern experimental techniques. To model such effects in lossy cavities, effective discrete-mode approaches have been widely employed, despite their accuracy beyond two modes remaining rarely benchmarked. In this work, we demonstrate the necessity of employing multiple modes to describe the multimode signatures by analyzing the dynamics of an atom in a one-dimensional lossy resonator. The atom's dynamics is simulated using the formalism developed in Weitzel et al. (2026) (arXiv:2512.18478), where a resonance quantization prescription is provided. We investigate its dependency with respect to two different parameters: the light-matter coupling strength and the atom's position. In the former case, we find that the minimal number of modes necessary to capture the essential features of the atom's dynamics increases with the coupling strength. In the latter, we further observe that the multimode regime leads to a strong position-dependency of the atom's dynamics. In all cases, we discuss the physical interpretation of our results and further discuss about how the employed formalism can be used to recover physically relevant quantities.
Quantum models based on few-mode master equations have been a central tool in the study of resonator quantum electrodynamics, extending the seminal single-mode Jaynes-Cummings model to include loss and multiple modes. Despite their broad application range, previous approaches within this framework have either relied on a Markov approximation or a fitting procedure. By combining ideas from pseudomode and quasinormal mode theory, we develop a certification criterion for multi-mode effects in lossy resonators. It is based on a witness observable, and neither requires a fitting procedure nor a Markov approximation. Using the resulting criterion, we demonstrate that such multi-mode effects are important for understanding previous experiments in x-ray cavity QED with Mössbauer nuclei and that they allow one to tune the nuclear ensemble properties.
In the presence of arbitrary three-dimensional linear media with material loss and amplification, we present an electromagnetic field quantization scheme for quasinormal modes (QNMs), extending previous work for lossy media [S. Franke et al., Phys. Rev. Lett. 122, 213901 (2019)]. Applying a symmetrization transformation, we show two fundamentally different ways for constructing a QNM photon Fock space, including (i) where there is a separate operator basis for both gain and loss, and (ii) where the loss and gain degrees of freedom are combined into a single basis. These QNM operator bases are subsequently used to derive the associated QNM master equations, including the interaction with a quantum emitter, modeled as a quantized two-level system (TLS). We then compare the two different quantization approaches, and also show how commonly used phenomenological methods to quantize light in gain-loss resonators are corrected by several important aspects, such as a loss-induced and gain-induced intermode coupling, which appears through the rigorous treatment of loss and amplification on a dissipative mode level. For specific resonator designs, modeled in a fully consistent way with the classical Maxwell equations with open boundary conditions, we then present numerical results for the quantum parameters and observables of a TLS weakly interacting with the medium-assisted field in a gain-loss microdisk resonator system, and discuss the validity of the different quantization approaches for several gain-loss parameter regimes.
The unprecedented pace of evolution in nanoscale architectures for cavity quantum electrodynamics (cQED) has posed crucial challenges for theory, where the quantum dynamics arising from the non-perturbative dressing of matter by cavity electric and magnetic fields as well as the fundamentally non-Hermitian character of the system are to be treated without significant approximation. The lossy electromagnetic resonances of photonic, plasmonic, or magnonic nanostructures are described as quasinormal modes (QNMs), whose properties and interactions with quantum emitters and spin qubits are central to the understanding of dissipative nano-optics and magnetodielectric cQED. Despite recent advancements toward a fully quantum framework for QNMs, a general and universally accepted approach to QNM quantization for arbitrary linear media remains elusive. In this work, we introduce a unified theoretical framework, based on macroscopic QED and complex coordinate transformations, which achieves QNM quantization for a wide class of spatially inhomogeneous, dissipative and dispersive, linear, magnetodielectric resonators. The complex coordinate transformations equivalently convert the radiative losses into non-radiative material dissipation, and via a suitable transformation that reflects all the losses of the resonator, we define creation and annihilation operators that allow the construction of modal Fock states for the joint excitations of field-dressed matter. By directly addressing the intricacies of modal loss in a fully quantum theory of magnetodielectric cQED, our approach enables the exploration of modern, quantum nano-optical experiments utilizing dielectric, plasmonic, magnetic, or hybrid cQED architectures and paves the way toward a rigorous assessment of room-temperature, quantum nanophotonic technologies without recourse to ad hoc quantization schemes.
Phenomenological approaches to photon loss have long been the workhorse of cavity-QED, but prove inadequate in the presence of sufficiently broadband light-matter interactions. We present a rigorous and ab initio derivation of a quantum master equation for a quantized optical cavity mode coupled to a dipole, using a quasinormal mode (QNM) quantization procedure for plasmonic and dielectric open-system cavity-QED, which is valid in broadband light-matter interaction regimes, including ultrastrong coupling (USC). The theory supports general three-dimensional resonators with arbitrary dispersion and loss, and thus can be applied to a wide range of realistic open cavities. Our ab initio and gauge-invariant approach fully recovers a recent result for the spectral density of a quantized cavity with a single dipole and reveals important departures from previous heuristic assumptions about system-reservoir coupling. We identify a new criterion for what we term the "broadband dissipative" regime of cavity-QED, where phenomenological models require corrections in accordance with the intrinsic and spatially-dependent complex phase of the QNM, and also shed light on fundamental limits to single-mode models in extreme coupling regimes. Using experimentally motivated plasmonic and dielectric cavity examples, we show validity ranges of our QNM master equation and spectral USC calculations, and discuss prospects for near-term experimental observation of the broadband dissipative effects.
We use Thomson's classical concept of mode of a leaky cavity to develop a quantum theory of cavity damping. This theory generalizes the conventional system-reservoir theory of high-Q cavity damping to arbitrary Q. The small system now consists of damped oscillators corresponding to the natural modes of the leaky cavity rather than undamped oscillators associated with the normal modes of a fictitious perfect cavity. The formalism unifies semiclassical Fox-Li modes and the normal modes traditionally used for quantization. It also lays the foundations for a full quantum description of excess noise. The connection with Siegman's semiclassical work is straightforward. In a wider context, this theory constitutes a radical departure from present models of dissipation in quantum mechanics: unlike conventional models, system and reservoir operators no longer commute with each other. This noncommutability is an unavoidable consequence of having to use natural cavity modes rather than normal modes of a fictitious perfect cavity.