Generalization of the Tavis-Cummings model for multi-level anharmonic systems: insights on the second excitation manifold

Abstract

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 (TC) 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 a gigantic $N^2\times N^2$ Hamiltonian (where $N=10^6-10^{10}$, as experiments suggest) to the diagonalization of, at most, $4\times 4$ matrices. 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 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.

arXiv comment15 pages, 6 figures

References in corpus (29)

• Cavity quantum electrodynamics for superconducting electrical circuits: an architecture for quantum computation
• Molecular polaritons for controlling chemistry with quantum optics
• Open quantum systems with local and collective incoherent processes: Efficient numerical simulation using permutational invariance
• Quantum theory of collective strong coupling of molecular vibrations with a microcavity mode
• Superabsorption of light via quantum engineering
• Dark state semilocalization of quantum emitters in a cavity
• Catalysis by Dark States in Vibropolaritonic Chemistry
• Comparative quantum and semi-classical analysis of Atom-Field Systems II: Chaos and regularity
• Triplet harvesting in the polaritonic regime: a variational polaron approach
• Two-dimensional Infrared Spectroscopy of vibrational polaritons of molecules in an optical cavity
• Multi-level quantum Rabi model for anharmonic vibrational polaritons
• Multimode Organic Polariton Lasing
• Cavity molecular dynamics simulations of vibrational polariton enhanced molecular nonlinear absorption
• 2D Fourier Transform Spectroscopy of exciton-polaritons and their interactions
• The Excitation Ladder of Cavity Polaritons
• The Shape of the Electric Dipole Function Determines the Sub-Picosecond Dynamics of Anharmonic Vibrational Polaritons
• Enhanced optical nonlinearities under strong light-matter coupling
• Driving chemical reactions with polariton condensates
• Raman scattering with strongly coupled vibron-polaritons
• Large Random Arrowhead Matrices: Multifractality, Semi-Localization, and Protected Transport in Disordered Quantum Spins Coupled to a Cavity
• One-photon Solutions to Multiqubit Multimode quantum Rabi model
• Generalization of the Tavis-Cummings model for multi-level anharmonic systems
• A semi-classical versus quantum description of the ground state of three-level atoms interacting with a one-mode electromagnetic field
• Exact solutions for a family of spin-boson systems
• Permutational symmetry for identical multi-level systems: a second quantized approach
• Collective strong coupling in a plasmonic nanocavity
• Semi-empirical Quantum Optics for Mid-Infrared Molecular Nanophotonics
• Condensation of Photons coupled to a Dicke Field in an Optical Microcavity
• Algebraic approach to the Tavis-Cummings model with three modes of oscillation

Cited by in corpus (10)

• Swinging between shine and shadow: Theoretical advances on thermally-activated vibropolaritonic chemistry (a perspective)
• Dissociation dynamics of a diatomic molecule in an optical cavity
• Crafting the dynamical structure of synchronization by harnessing bosonic multilevel cavity QED
• Nonlinear semiclassical spectroscopy of ultrafast molecular polariton dynamics
• Enhancing the efficiency of polariton OLEDs in and beyond the single-excitation subspace
• Tunable photon-mediated interactions between spin-1 systems
• 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
• Permutationally invariant processes in open multiqudit systems
• Impact of light-matter coupling strength on the efficiency of microcavity OLEDs: A unified quantum master equation approach