Gauge Principle and Gauge Invariance in Quantum Two-Level Systems

TL;DR

This paper explores gauge invariance in quantum two-level systems, providing an alternative derivation of a gauge-invariant quantum Rabi model applicable across interaction regimes, including asymmetric and multi-mode cases.

Contribution

It introduces a gauge principle-based derivation for the gauge-invariant quantum Rabi model, extending it to asymmetric systems and multi-mode interactions beyond the dipole approximation.

Findings

Derived a gauge-invariant quantum Rabi model using gauge principles.

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 for 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 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.