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Classifying and harnessing multi-mode light-matter interaction in lossy resonators

Dominik Lentrodt, Oliver Diekmann, Christoph H. Keitel, Stefan Rotter, Jörg Evers

Published Jul 25, 2021• 1 citation
OpenAlex

Abstract

A practical framework is developed to characterize multi-mode effects on quantum systems coupled to lossy resonators. By relating a generic quantum optical few-mode model to the Mittag-Leffler pole expansion of the cavity's classical Green's function, we identify three distinct classes of multi-mode effects in the loss-dominated regime. We show that these effects are crucial for understanding spectroscopic signatures in leaky and absorptive resonators, and that they further provide a tuning knob to design artificial quantum systems through such environments. Both aspects are illustrated using examples in X-ray cavity QED with Mossbauer nuclei.

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Quantum simulation of weak-field light-matter interactions

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Simulation of the interaction of light with matter, including at the few-photon level, is important for understanding the optical and optoelectronic properties of materials and for modeling next-generation nonlinear spectroscopies that use entangled light. At the few-photon level the quantum properties of the electromagnetic field must be accounted for with a quantized treatment of the field, and then such simulations quickly become intractable, especially if the matter subsystem must be modeled with a large number of degrees of freedom, as can be required to accurately capture many-body effects and quantum noise sources. Motivated by this we develop a quantum simulation framework for simulating such light-matter interactions on platforms with controllable bosonic degrees of freedom, such as vibrational modes in the trapped ion platform. The key innovation in our work is a scheme for simulating interactions with a continuum field using only a few discrete bosonic modes, which is enabled by a Green's function (response function) formalism. We develop the simulation approach, sketch how the simulation can be performed using trapped ions, and then illustrate the method with numerical examples. Our work expands the reach of quantum simulation to important light-matter interaction models and illustrates the advantages of extracting dynamical quantities such as response functions from quantum simulations.

arXiv:2112.07177•Physical Review Research•Jan 20, 2023•3 citations
A practical framework is developed to characterize multi-mode effects on quantum systems coupled to lossy resonators. By relating a generic quantum optical few-mode model to the Mittag-Leffler pole expansion of the cavity's classical Green's function, we identify three distinct classes of multi-mode effects in the loss-dominated regime. We show that these effects are crucial for understanding spectroscopic signatures in leaky and absorptive resonators, and that they further provide a tuning knob to design artificial quantum systems through such environments. Both aspects are illustrated using examples in X-ray cavity QED with Mossbauer nuclei.
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 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.
Multimode cavity-QED systems can be leveraged to explore a wide range of physical phenomena; however, a complex multimode environment makes systematic characterization of light-matter interactions challenging. Here we present a general measurement protocol, applicable to both atomic and synthetic cavity-QED systems, that enables the determination of coupling to individual photonic modes. The method leverages measurements of the AC-Stark and Kerr effects, along with known detuning dependencies, to eliminate the need for single-photon resolution, independent photon-number calibration, or insertion-loss calibration. We demonstrate the method using a superconducting transmon qubit coupled to a one-dimensional microwave resonator lattice. We validate the consistency of the extracted light-matter couplings ggg determined at multiple qubit detunings, and from the self-Kerr and cross-Kerr shifts for three photon modes, which provide separate measurements of ggg for each of the three modes.
We study a generic cavity-QED system where a set of (artificial) two-level dipoles is coupled to the electric field of a single-mode LCLCLC resonator. This setup is used to derive a minimal quantum mechanical model for cavity QED, which accounts for both dipole-field and direct dipole-dipole interactions. The model is applicable for arbitrary coupling strengths and allows us to extend the usual Dicke model into the nonperturbative regime of QED, where the dipole-field interaction can be associated with an effective fine-structure constant of order unity. In this regime, we identify three distinct classes of normal, superradiant, and subradiant vacuum states and discuss their characteristic properties and the transitions between them. Our findings reconcile many of the previous, often contradictory predictions in this field and establish a common theoretical framework to describe ultrastrong-coupling phenomena in a diverse range of cavity-QED platforms.
We present a systematic study of the properties of systems composed of NNN two-level quantum emitters coupled to a single cavity mode, for light-matter interaction strengths ranging from the weak to the ultrastrong and deep-strong coupling regimes. Beginning with an analysis of the energy spectrum as a function of the light-matter coupling strength, we examine systems with varying numbers of emitters, from a pair to large collections, approaching the thermodynamic limit $(N\ensuremath{\rightarrow}\ensuremath{\infty})$. Additionally, we explore the emission properties of these systems under incoherent excitation of the emitters, employing a general theoretical framework for open cavity-QED systems, which is valid across all light-matter interaction regimes and preserves gauge invariance within truncated Hilbert spaces. Furthermore, we study the influence of the emitter-environment interaction on the spectral properties of the system. Specifically, when each emitter interacts independently with its own reservoir, we observe the emergence of an emission peak at the cavity's resonant frequency for even values of NNN. Our analysis also clarifies the evolution of the system as the number of emitters increases, ultimately converging toward an equivalent system composed of two interacting single-mode bosonic fields.
Simulation of the interaction of light with matter, including at the few-photon level, is important for understanding the optical and optoelectronic properties of materials and for modeling next-generation nonlinear spectroscopies that use entangled light. At the few-photon level the quantum properties of the electromagnetic field must be accounted for with a quantized treatment of the field, and then such simulations quickly become intractable, especially if the matter subsystem must be modeled with a large number of degrees of freedom, as can be required to accurately capture many-body effects and quantum noise sources. Motivated by this we develop a quantum simulation framework for simulating such light-matter interactions on platforms with controllable bosonic degrees of freedom, such as vibrational modes in the trapped ion platform. The key innovation in our work is a scheme for simulating interactions with a continuum field using only a few discrete bosonic modes, which is enabled by a Green's function (response function) formalism. We develop the simulation approach, sketch how the simulation can be performed using trapped ions, and then illustrate the method with numerical examples. Our work expands the reach of quantum simulation to important light-matter interaction models and illustrates the advantages of extracting dynamical quantities such as response functions from quantum simulations.