  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.
