Gauge Principle and Gauge Invariance in Two-Level Systems

TL;DR

This paper discusses the gauge invariance issues in the quantum Rabi model for two-level systems and introduces a gauge-invariant formulation applicable across different interaction regimes and system configurations.

Contribution

It provides an alternative derivation of a gauge-invariant quantum Rabi model using the gauge principle, extending it to asymmetric systems and multi-mode scenarios.

Findings

Derived a gauge-invariant quantum Rabi model for symmetric two-level systems.

Extended the model to asymmetric two-state systems.

Developed a multi-mode gauge-invariant model beyond the dipole approximation.

Abstract

The quantum Rabi model is a widespread description of the coupling between a two-level system and a quantized single mode of an electromagnetic resonator. Issues about this model's gauge invariance have been raised. These issues become evident when the light-matter interaction reaches the so-called ultrastrong coupling regime. Recently, a modified quantum Rabi model able to provide gauge-invariant physical results (e.g., energy levels, expectation values of observables, quantum probabilities) in any interaction regime was introduced [Nature Physics 15, 803 (2019)]. Here we provide an alternative derivation of this result, based on the implementation in two-state systems of the gauge principle, which is the principle from which all the fundamental interactions in quantum field theory are derived. The adopted procedure can be regarded as the two-site version of the general method used to implement the gauge principle in lattice gauge theories. Applying this method, we also obtain the gauge-invariant quantum Rabi model for asymmetric two-state systems, and the multi-mode gauge-invariant quantum Rabi model beyond the dipole approximation.