Ultrastrong Coupling of a Qubit with a Nonlinear Optical Resonator

TL;DR

This paper investigates the interaction between a two-level atom and a nonlinear optical resonator in the ultrastrong coupling regime, addressing gauge invariance issues and proposing a consistent quantum Rabi model.

Contribution

It develops a gauge-invariant nonlinear-resonator quantum Rabi model suitable for ultrastrong coupling regimes, overcoming limitations of previous models.

Findings

Identifies problems with gauge invariance in high coupling regimes.

Proposes a new gauge-consistent nonlinear Rabi model.

Provides a framework for accurate modeling of ultrastrong light-matter interactions.

Abstract

We study the interaction of a two-level atom with a single-mode nonlinear electromagnetic resonator, considering coupling strengths ranging from zero to the so-called deep strong coupling regime. When the qubit-resonator coupling is very strong, the standard Kerr model for the resonator becomes questionable. Moreover, recently, it has been shown that extra care is needed when constructing gauge-independent theories in the presence of approximations as the truncation of the Hilbert space of the matter system. Such a truncation can ruin gauge invariance leading to non-physical results, especially when the light-matter interactions strength is very high. Here we face and solve this issues to provide a consistent nonlinear-resonator quantum Rabi model satisfying the gauge principle.