Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2308.12957

Semi-analytical Framework for Modeling Strong Coupling of Quantum Emitters in Electromagnetic Resonators

Mohammad Abutoama, George Kountouris, Jesper Mørk, Philip Trøst Kristensen

Published Aug 24, 2023• 0 citations
arXivHTMLPDF

Abstract

We present a semi-analytical framework for studying interactions between quantum emitters and general electromagnetic resonators. The method relies on the Lippmann-Schwinger equation to calculate the complex resonance frequencies of the coupled system based only on a single calculation for the electromagnetic resonator without the quantum emitter and with no fitting parameters. This is in stark contrast to standard approaches in the literature, in which the properties of the coupled system are fitted from calculated spectra. As an application example, we consider a recent dielectric cavity design featuring deep subwavelength confinement of light. We find the expected anti-crossing of the emitter and cavity resonance frequencies, and comparing to independent reference calculations, we find an extraordinary quantitative agreement with a relative error below one part in ten thousand. In order to unambiguously connect with the Jaynes-Cummings model, we derive an explicit expression relating the classical description of the emitter, as modeled by a spherical inclusion with a Lorentzian material response, to the dipole moment of the corresponding quantum optical model. The combined framework therefore enables classical calculations to be used for evaluating the coupling strength entering quantum optical theories in a transparent way.

DOI
10.48550/arxiv.2308.12957

Related papers

Modal approach to the coupling strength of quantum emitters in electromagnetic resonators

Mohammad Abutoama, George Kountouris, Jesper Mørk +1 more

We present a modal analysis of a popular modeling framework for studying light-matter interaction between quantum emitters and general electromagnetic resonators, in which the active materials are modeled via Lorentzian material responses. The method relies on the Lippmann-Schwinger equation to calculate the complex resonance frequencies of the coupled system based only on a single calculation for the electromagnetic resonator without the active material and without fitting to calculated spectra. As an application example, we consider a recent dielectric cavity design featuring deep subwavelength confinement of light. We find the expected anticrossing of the emitter and cavity resonance frequencies, and comparing with independent reference calculations, we find an extraordinary quantitative agreement with a relative error below one part in ten thousand. To connect with the Jaynes-Cummings model, we relate the classical description of the emitter to the dipole moment in the corresponding quantum optical model. The combined framework therefore enables classical calculations to be used for evaluating the coupling strength entering quantum optical theories in a transparent way. The methodology is expected to be useful in the design and interpretation of ongoing and future experiments and devices involving single-photon sources for quantum information and quantum communication technology.

Physical review. B./Physical review. B•Nov 21, 2024•2 citations

Semi-analytical Approach for Modeling Strong Coupling of Quantum Emitters in Electromagnetic Resonators

Mohammad Abutoama, George Kountouris, Jesper Mørk +1 more

We theoretically examine the interaction between a single quantum emitter (QE) and a general electromagnetic resonator and provide a semi-analytical approach to calculate the coupling strength in the combined system. The model relies on the Lippmann-Schwinger equation to calculate the quasi-normal modes of the coupled system with no fitting parameters. This is in stark contrast to standard approaches in the literature, in which the properties of the coupled system are typically fitted from scattering spectra.

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Jun 26, 2023•0 citations

Beyond the Tavis-Cummings model: Revisiting cavity QED with ensembles of quantum emitters

Martin Blaha, Aisling Johnson, Arno Rauschenbeutel +1 more

The interaction of an ensemble of $N$ two-level quantum emitters with a single-mode electromagnetic field is described by the Tavis-Cummings model. There, the collectively enhanced light-matter coupling strength is given by ${g}_{N}=\sqrt{N}{\overline{g}}_{1}$, where ${\overline{g}}_{1}$ is the ensemble-averaged single-emitter coupling strength. This model has been employed to describe and to analyze numerous cavity-based experiments. Here, we show that this is only justified if the effective scattering rate into noncavity modes is negligible compared to the cavity's free-spectral range. In terms of experimental parameters, this requires that the optical depth of the ensemble is low, a condition that is violated in several state-of-the-art experiments. We give quantitative conditions for the validity of the Tavis-Cummings model and derive a more general Hamiltonian description that takes into account the cascaded interaction of the photons with all consecutive emitters. We show that the predictions of our cascaded model can differ quantitatively and even qualitatively from those obtained with the Tavis-Cummings model. Finally, we present experimental data, for which the deviation from the predictions of the Tavis-Cummings model is apparent. Our findings are relevant for all experiments in which optically dense ensembles of quantum emitters are coupled to an optical resonator.

arXiv:2107.04583•Physical Review A•Jan 28, 2022•28 citations

The Jaynes-Cummings model breaks down when the cavity significantly reduces the emitter's free-space emission rate

Blaha, Martin, Arno Rauschenbeutel, Jürgen Volz

Strong coupling between a single resonator mode and a single quantum emitter is key to a plethora of experiments and applications in quantum science and technology and is commonly described by means of the Jaynes-Cummings model. Here, we show that the Jaynes-Cummings model only applies when the cavity does not significantly change the emitter's emission rate into free-space. Most notably, the predictions made by the Jaynes-Cummings model become increasingly wrong when approaching the ideal emitter-resonator systems with no free-space decay channels. We present a Hamiltonian that provides, within the validity range of the rotating wave approximation, a correct theoretical description that applies to all regimes. As minimizing the coupling to free-space modes is paramount for many cavity-based applications, a correct description of strong light-matter interaction is therefore crucial for developing and optimizing quantum protocols.

arXiv:2301.07674•Jan 18, 2023•1 citation

Jaynes–Cummings model breaks down when the cavity geometry significantly reduces free-space emission

Martin Blaha, Arno Rauschenbeutel, Jürgen Volz

Strong coupling between a single resonator mode and a single quantum emitter is key to a plethora of experiments and applications in quantum science and technology and is commonly described by means of the Jaynes–Cummings model. Here, we show that the Jaynes–Cummings model only applies when the cavity does not significantly change the emitter’s decay rate into free-space. Most notably, the predictions made by the Jaynes–Cummings model become increasingly wrong when approaching the ideal emitter-resonator systems with no free-space decay channels. We present a Hamiltonian that provides, within the validity range of the rotating wave approximation, a correct theoretical description that applies to all regimes. As minimizing the coupling to free-space modes is paramount for many cavity-based applications, a correct description of strong light-matter interaction is therefore crucial for developing and optimizing quantum protocols.

Journal of the Optical Society of America B•Jun 17, 2024•2 citations

Cavity QED from few to many emitters: Energy levels and emission spectra from weak to deep-strong coupling

Andrea Zappalà, Alberto Mercurio, Daniele Lamberto +3 more

We present a systematic study of the properties of systems composed of $N$ 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 $N$. 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.

arXiv:2506.18763•Physical Review A•Nov 20, 2025•1 citation
We present a semi-analytical framework for studying interactions between quantum emitters and general electromagnetic resonators. The method relies on the Lippmann-Schwinger equation to calculate the complex resonance frequencies of the coupled system based only on a single calculation for the electromagnetic resonator without the quantum emitter and with no fitting parameters. This is in stark contrast to standard approaches in the literature, in which the properties of the coupled system are fitted from calculated spectra. As an application example, we consider a recent dielectric cavity design featuring deep subwavelength confinement of light. We find the expected anti-crossing of the emitter and cavity resonance frequencies, and comparing to independent reference calculations, we find an extraordinary quantitative agreement with a relative error below one part in ten thousand. In order to unambiguously connect with the Jaynes-Cummings model, we derive an explicit expression relating the classical description of the emitter, as modeled by a spherical inclusion with a Lorentzian material response, to the dipole moment of the corresponding quantum optical model. The combined framework therefore enables classical calculations to be used for evaluating the coupling strength entering quantum optical theories in a transparent way.
We present a modal analysis of a popular modeling framework for studying light-matter interaction between quantum emitters and general electromagnetic resonators, in which the active materials are modeled via Lorentzian material responses. The method relies on the Lippmann-Schwinger equation to calculate the complex resonance frequencies of the coupled system based only on a single calculation for the electromagnetic resonator without the active material and without fitting to calculated spectra. As an application example, we consider a recent dielectric cavity design featuring deep subwavelength confinement of light. We find the expected anticrossing of the emitter and cavity resonance frequencies, and comparing with independent reference calculations, we find an extraordinary quantitative agreement with a relative error below one part in ten thousand. To connect with the Jaynes-Cummings model, we relate the classical description of the emitter to the dipole moment in the corresponding quantum optical model. The combined framework therefore enables classical calculations to be used for evaluating the coupling strength entering quantum optical theories in a transparent way. The methodology is expected to be useful in the design and interpretation of ongoing and future experiments and devices involving single-photon sources for quantum information and quantum communication technology.
We theoretically examine the interaction between a single quantum emitter (QE) and a general electromagnetic resonator and provide a semi-analytical approach to calculate the coupling strength in the combined system. The model relies on the Lippmann-Schwinger equation to calculate the quasi-normal modes of the coupled system with no fitting parameters. This is in stark contrast to standard approaches in the literature, in which the properties of the coupled system are typically fitted from scattering spectra.
The interaction of an ensemble of NNN two-level quantum emitters with a single-mode electromagnetic field is described by the Tavis-Cummings model. There, the collectively enhanced light-matter coupling strength is given by gN=Ng‾1{g}_{N}=\sqrt{N}{\overline{g}}_{1}gN​=N​g​1​, where g‾1{\overline{g}}_{1}g​1​ is the ensemble-averaged single-emitter coupling strength. This model has been employed to describe and to analyze numerous cavity-based experiments. Here, we show that this is only justified if the effective scattering rate into noncavity modes is negligible compared to the cavity's free-spectral range. In terms of experimental parameters, this requires that the optical depth of the ensemble is low, a condition that is violated in several state-of-the-art experiments. We give quantitative conditions for the validity of the Tavis-Cummings model and derive a more general Hamiltonian description that takes into account the cascaded interaction of the photons with all consecutive emitters. We show that the predictions of our cascaded model can differ quantitatively and even qualitatively from those obtained with the Tavis-Cummings model. Finally, we present experimental data, for which the deviation from the predictions of the Tavis-Cummings model is apparent. Our findings are relevant for all experiments in which optically dense ensembles of quantum emitters are coupled to an optical resonator.
Strong coupling between a single resonator mode and a single quantum emitter is key to a plethora of experiments and applications in quantum science and technology and is commonly described by means of the Jaynes-Cummings model. Here, we show that the Jaynes-Cummings model only applies when the cavity does not significantly change the emitter's emission rate into free-space. Most notably, the predictions made by the Jaynes-Cummings model become increasingly wrong when approaching the ideal emitter-resonator systems with no free-space decay channels. We present a Hamiltonian that provides, within the validity range of the rotating wave approximation, a correct theoretical description that applies to all regimes. As minimizing the coupling to free-space modes is paramount for many cavity-based applications, a correct description of strong light-matter interaction is therefore crucial for developing and optimizing quantum protocols.
Strong coupling between a single resonator mode and a single quantum emitter is key to a plethora of experiments and applications in quantum science and technology and is commonly described by means of the Jaynes–Cummings model. Here, we show that the Jaynes–Cummings model only applies when the cavity does not significantly change the emitter’s decay rate into free-space. Most notably, the predictions made by the Jaynes–Cummings model become increasingly wrong when approaching the ideal emitter-resonator systems with no free-space decay channels. We present a Hamiltonian that provides, within the validity range of the rotating wave approximation, a correct theoretical description that applies to all regimes. As minimizing the coupling to free-space modes is paramount for many cavity-based applications, a correct description of strong light-matter interaction is therefore crucial for developing and optimizing quantum protocols.
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.