Ultrastrong time-dependent light-matter interactions are gauge relative

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 nonequivalence between gauges. We provide a physical example in which each different nonequivalent 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 nonadiabatic even if the coupling vanishes at the preparation and measurement stages of the protocol, at which times the subsystems are unique and experimentally addressable.