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Frontiers in Physics

Tavis-Cummings model revisited: A perspective from macroscopic quantum electrodynamics

Yi-Ting Chuang, Ming‐Wei Lee, Liang‐Yan Hsu

Published Oct 7, 2022• 14 citations
Publisher

Abstract

The Tavis-Cummings (TC) model has been widely used to investigate the collective coupling effect in hybrid light-matter systems; however, the TC model neglects the effect of a dielectric environment (the spectral structure of photonic bath), and it remains unclear whether the TC model can adequately depict the light-matter interaction in a non-homogeneous, dispersive, and absorbing medium. To clarify the ambiguity, in this work, we first connect the macroscopic quantum electrodynamics and the TC model with dissipation. Based on the relationship between these two theoretical frameworks, we develop a guideline that allows us to examine the applicability of the TC model with dissipation. The guideline states that if 1) the generalized spectral densities are independent of the positions of molecules and 2) the generalized spectral densities resemble a Lorentzian function, then the hybrid light-matter system can be properly described by the TC model with dissipation. In order to demonstrate how to use the guideline, we examine the position dependence and the lineshape of the generalized spectral densities in three representative systems, including a silver Fabry-Pérot cavity, a silver surface, and an aluminum spherical cavity. We find that only the aluminum spherical cavity meets the two conditions, i.e., position independence and Lorentzian lineshape, required for the utilization of the dissipative TC model. Our results indicate that the use of the TC model with dissipation to study the collective coupling effect should be done with care, providing an important perspective on resonance energy transfer and polariton chemistry.

DOI
10.3389/fphy.2022.980167

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The Tavis-Cummings (TC) model has been widely used to investigate the collective coupling effect in hybrid light-matter systems; however, the TC model neglects the effect of a dielectric environment (the spectral structure of photonic bath), and it remains unclear whether the TC model can adequately depict the light-matter interaction in a non-homogeneous, dispersive, and absorbing medium. To clarify the ambiguity, in this work, we first connect the macroscopic quantum electrodynamics and the TC model with dissipation. Based on the relationship between these two theoretical frameworks, we develop a guideline that allows us to examine the applicability of the TC model with dissipation. The guideline states that if 1) the generalized spectral densities are independent of the positions of molecules and 2) the generalized spectral densities resemble a Lorentzian function, then the hybrid light-matter system can be properly described by the TC model with dissipation. In order to demonstrate how to use the guideline, we examine the position dependence and the lineshape of the generalized spectral densities in three representative systems, including a silver Fabry-Pérot cavity, a silver surface, and an aluminum spherical cavity. We find that only the aluminum spherical cavity meets the two conditions, i.e., position independence and Lorentzian lineshape, required for the utilization of the dissipative TC model. Our results indicate that the use of the TC model with dissipation to study the collective coupling effect should be done with care, providing an important perspective on resonance energy transfer and polariton chemistry.
Abstract The interaction between anharmonic quantum emitters (e.g. molecular vibrations) and confined electromagnetic fields gives rise to quantum states with optical and chemical properties that are different from those of their precursors. The exploration of these properties has been typically constrained to the first excitation manifold, the harmonic approximation, ensembles of two-level systems [Tavis–Cummings (TC) model], or the anharmonic single-molecule case. The present work studies, for the first time, a collective ensemble of identical multi-level anharmonic emitters and their dipolar interaction with a photonic cavity mode, which is an exactly solvable many-body problem. The permutational properties of the system allow identifying symmetry classified submanifolds in the energy spectrum. Notably, in this approach, the number of particles, typically in the order of several millions, becomes only a parameter from the operational standpoint, and the size of the dimension of the matrices to diagonalize is independent of it. The formalism capabilities are illustrated by showing the energy spectrum structure, up to the third excitation manifold, and the calculation of the photon contents as a permutationally invariant quantity. Emphasis is placed on (a) the collective (superradiant) scalings of light–matter couplings and the various submanifolds of dark (subradiant) states with no counterpart in the single-molecule case, as well as (b) the delocalized modes containing more than one excitation per molecule with no equivalent in the TC model. We expect these findings to be applicable in the study of non-linear spectroscopy and chemistry of polaritons.
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.
This work investigates the emergent thermalization regimes in a chaotic Tavis-Cummings (TC) model and their implications in quantum spectroscopy. While the TC model is a cornerstone of cavity quantum electrodynamics, traditional treatments often overlook many-body effects that arise in the thermodynamic limit. We utilize the Eigenstate Thermalization Hypothesis to demonstrate that a non-integrable excitonic Hamiltonian within the material manifold drives local thermalization. By tuning the polariton splitting ggg, we observe two dynamical regimes: a thermalizing regime at low interactions driven by quantum chaos and ergodicity, and a non-thermalizing regime at high interactions where strong coupling suppresses ergodicity. We further show that these regimes have direct implications on output photon statistics, specifically influencing the correlation times τcτ_cτc​ of the cavity population and the second-order correlation function g(2)(t+τ)g^{(2)}(t+τ)g(2)(t+τ). We propose that entangled-biphoton spectroscopy serves as an ideal experimental platform to probe these effects and to allow the characterization of the underlying many-body exciton-coupling disorder σσσ through coincidence measurements of the output. Taken together, these results exploit a naturally occurring many-body phenomenon to bridge theoretical predictions with experimental observables.
Dynamics of nonclassicality in a generalized Tavis Cummings model with XY spin (1/2,1)(1/2,1)(1/2,1) atomic interactions
We investigate the dynamics of nonclassicality, quantified by the Wigner Yanase skew information, in generalized Jaynes Cummings (JC) and Tavis Cummings (TC) models describing light matter interactions in cavity quantum electrodynamics. We first analyze a generalized JC model consisting of a single bosonic cavity mode coupled to a spin 1 atom, focusing on the temporal evolution of nonclassicality in both the cavity field and the atomic subsystem. We then extend this framework to a generalized TC model by introducing an additional spin 1/21/21/2 atom, enabling us to examine the influence of collective atomic degrees of freedom. The global dynamics are investigated both with and without an XYXYXY spin interaction. Our results show that, under resonance conditions, the system exhibits efficient excitation exchange between the cavity field and the atomic subsystem, resulting in regular, coherent nonclassicality dynamics and enhanced field nonclassicality generation. Conversely, an increasing longitudinal magnetic field acts primarily as an effective detuning parameter rather than a direct exchange interaction. In this off resonant regime, the atom field coupling is substantially weakened, localizing excitations within the atomic subsystem. This localization suppresses coherent energy transfer to the cavity field, leading to a pronounced reduction in field nonclassicality, while the atomic subsystem retains the majority of the quantum correlations. Notably, atomic superposition states exhibit highly irregular spin dynamics, reflecting a detuning-induced redistribution of quantum correlations. These findings demonstrate that the dynamics of spin and field nonclassicality are governed primarily by interaction mediated excitation flow and resonance conditions rather than the initial energy distribution alone, ..
Confined electromagnetic modes strongly couple to collective excitations in ensembles of quantum emitters, producing light–matter hybrid states known as polaritons. Under such conditions, the discrete multilevel spectrum of molecular systems offers an appealing playground for exploring multiphoton processes. This work contrasts predictions from the Tavis–Cummings model in which the material is a collection of two-level systems, with the implications of considering additional energy levels with harmonic and anharmonic structures. We discuss the exact eigenspectrum, up to the second excitation manifold, of an arbitrary number N of oscillators collectively coupled to a single cavity mode in the rotating-wave approximation. Elaborating on our group-theoretic approach [New J. Phys. 23, 063081 (2021)], we simplify the brute-force diagonalization of N2 × N2 Hamiltonians to the eigendecomposition of, at most, 4 × 4 matrices for arbitrary N. We thoroughly discuss the eigenstates and the consequences of weak and strong anharmonicities. Furthermore, we find resonant conditions between bipolaritons and anharmonic transitions where two-photon absorption can be enhanced. Finally, we conclude that energy shifts in the polaritonic states induced by anharmonicities become negligible for large N. Thus, calculations with a single or few quantum emitters qualitatively fail to represent the nonlinear optical response of the collective strong coupling regime. Our work highlights the rich physics of multilevel anharmonic systems coupled to cavities absent in standard models of quantum optics. We also provide concise tabulated expressions for eigenfrequencies and transition amplitudes, which should serve as a reference for future spectroscopic studies of molecular polaritons.
Strong coupling of organic molecules to the vacuum field of a nanoscale cavity can be used to modify their chemical and physical properties. We extend the Tavis-Cummings model for molecular ensembles and show that the often neglected interaction terms arising from the static dipole moment and the dipole self-energy are essential for a correct description of the light-matter interaction in polaritonic chemistry. On the basis of a full quantum description, we simulate the excited-state dynamics and spectroscopy of MgH+ molecules resonantly coupled to an optical cavity. We show that the inclusion of static dipole moments and the dipole self-energy is necessary to obtain a consistent model. We construct an efficient two-level system approach that reproduces the main features of the real molecular system and may be used to simulate larger molecular ensembles.