Breakdown of gauge invariance in ultrastrong-coupling cavity QED

TL;DR

This paper examines how gauge choices affect the validity of the two-level approximation in ultrastrong-coupling cavity QED, revealing breakdowns in the Coulomb gauge that challenge common modeling assumptions.

Contribution

It demonstrates the gauge-dependent validity of the two-level approximation in ultrastrong coupling regimes, highlighting potential inaccuracies in standard models.

Findings

Two-level approximation validity depends on gauge choice in ultrastrong coupling.

The approximation can fail in Coulomb gauge even with highly anharmonic spectra.

Extensive analysis across different systems confirms the gauge-dependent breakdown.

Abstract

We revisit the derivation of Rabi- and Dicke-type models, which are commonly used for the study of quantum light-matter interactions in cavity and circuit QED. We demonstrate that the validity of the two-level approximation, which is an essential step in this derivation, depends explicitly on the choice of gauge once the system enters the ultrastrong coupling regime. In particular, while in the electric dipole gauge the two-level approximation can be performed as long as the Rabi frequency remains much smaller than the energies of all higher-lying levels, it can dramatically fail in the Coulomb gauge, even for systems with an extremely anharmonic spectrum. We extensively investigate this phenomenon both in the single-dipole (Rabi) and multi-dipole (Dicke) case, and considering the specific examples of dipoles confined by double-well and by square-well potentials, and of circuit QED systems with flux qubits coupled to an LC resonator.