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

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-Perot 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.