Generalization of the Tavis-Cummings model for multi-level anharmonic systems

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. 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.

arXiv comment37 pages, 4 figures

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• Vibropolaritonic Reaction Rates in the Collective Strong Coupling Regime: Pollak-Grabert-Hänggi Theory
• Permutational symmetry for identical multi-level systems: a second quantized approach
• Cooperative molecular structure in polaritonic and dark states
• Crafting the dynamical structure of synchronization by harnessing bosonic multilevel cavity QED
• Semi-empirical Quantum Optics for Mid-Infrared Molecular Nanophotonics
• Singly-excited resonant open quantum system Tavis-Cummings model with quantum circuit mapping
• The role of dark polariton states for electronic strong coupling in molecules
• A little bit of self-correction
• Coherent nonlinear optical probe for cavity-dressed vibrational mode mixing: Multidimensional double-quantum coherence and photon-echo spectroscopy