Selective Interactions in the Quantum Rabi Model

TL;DR

This paper explores how Stark coupling induces selective multi-photon interactions in the quantum Rabi model, providing analytical insights and proposing a trapped ion simulation method with numerical validation.

Contribution

It introduces a new analytical framework for $k$-photon interactions in the quantum Rabi model with Stark coupling and proposes a feasible quantum simulation approach.

Findings

Selective $k$-photon interactions depend on bosonic mode states.

Analytical explanation via time-dependent perturbation theory.

Numerical simulations confirm the simulation method's effectiveness.

Abstract

We demonstrate the emergence of selective $k$-photon interactions in the strong and ultrastrong coupling regimes of the quantum Rabi model with a Stark coupling term. In particular, we show that the interplay between the rotating and counter-rotating terms produces multi-photon interactions whose resonance frequencies depend, due to the Stark term, on the state of the bosonic mode. We develop an analytical framework to explain these $k$-photon interactions by using time-dependent perturbation theory. Finally, we propose a method to achieve the quantum simulation of the quantum Rabi model with a Stark term by using the internal and vibrational degrees of freedom of a trapped ion, and demonstrate its performance with numerical simulations considering realistic physical parameters.