# Ultrastrong time-dependent light-matter interactions are gauge-relative

## TL;DR

This paper reveals that strong, non-adiabatic, time-dependent light-matter interactions are gauge-dependent, challenging the common assumption of gauge invariance in modeling such systems, especially under rapid switching conditions.

## Contribution

It demonstrates the gauge dependence of time-dependent light-matter interactions in non-adiabatic regimes and provides physical examples illustrating this non-equivalence.

## Key findings

- Final-time predictions depend on the gauge used.
- Gauge non-equivalence occurs with strong, rapid coupling changes.
- Different gauges correspond to different experimental scenarios.

## Abstract

Time-dependent light-matter interactions are a widespread means by which to describe controllable experimental operations. They can be viewed as an approximation in which a third system - the control system - is treated as external within the Hamiltonian. We demonstrate that this results in non-equivalence between gauges. We provide a physical example in which each different non-equivalent model coincides with a gauge-invariant description applied in a different experimental situation. The qualitative final-time predictions obtained from these models, including entanglement and photon number, depend on the gauge within which the time-dependent coupling assumption is made. This occurs whenever the interaction switching is sufficiently strong and non-adiabatic even if the coupling vanishes at the preparation and measurement stages of the protocol, at which times the subsystems are unique and experimentally addressable.