# Multi-level quantum Rabi model for anharmonic vibrational polaritons

## TL;DR

This paper develops a multi-level quantum Rabi model to describe anharmonic vibrational polaritons in cavity QED, revealing complex spectral features and bond length modifications with potential chemical implications.

## Contribution

It introduces a novel multi-level quantum Rabi model for anharmonic molecular vibrations interacting with infrared cavities, extending beyond the rotating-wave approximation.

## Key findings

- Spectrum shows dense level crossings governed by pseudo parity.
- Vibrational polariton bond length is never greater than the bare Morse oscillator.
- Bond hardening occurs due to virtual photon creation, affecting chemical reactivity.

## Abstract

We propose a cavity QED approach to describe light-matter interaction between an individual anharmonic molecular vibration and an infrared cavity field. Starting from a generic Morse oscillator with quantized nuclear motion, we derive a multi-level quantum Rabi model to study vibrational polaritons beyond the rotating-wave approximation. We analyze the spectrum of vibrational polaritons in detail and compare with available experiments. For high excitation energies, the spectrum exhibits a dense manifold of true and avoided level crossings as the light-matter coupling strength and cavity frequency are tuned. These crossings are governed by a pseudo parity selection rule imposed by the cavity field. We also analyze polariton eigenstates in nuclear coordinate space. We show that the bond length of a vibrational polariton at a given energy is never greater than the bond length of a bare Morse oscillator with the same energy. This type of bond hardening of vibrational polaritons occurs at the expense of the creation of virtual infrared cavity photons, and may have implications in chemical reactivity.