Gauge ambiguities in ultrastrong coupling QED

Ultrastrong-coupling between two-level systems and radiation is important for both fundamental and applied quantum electrodynamics (QED). Such regimes are identified by the breakdown of the rotating-wave approximation, which applied to the quantum Rabi model (QRM) yields the apparently less fundamental Jaynes-Cummings model (JCM). We show that when truncating the material system to two levels, each gauge gives a different description whose predictions vary significantly for ultrastrong-coupling. QRMs are obtained through specific gauge choices, but so too is a JCM without needing the rotating-wave approximation. Analysing a circuit QED setup, we find that this JCM provides more accurate predictions than the QRM for the ground state, and often for the first excited state as well.

More generally, even in the absence of two-level approximations, gauge-freedom implies that there are many different definitions of light and matter as quantum subsystems, which only coincide when interactions vanish. Considering time-dependent light-matter interactions, we show that in the absence of an argument to choose a particular gauge when promoting the coupling parameter to a time-dependent function, the description that results is essentially ambiguous. For sufficiently strong and non-adiabatic (i.e. fast switching) interactions, the qualitative physical predictions of final subsystem properties, such as entanglement and photon number, depend on the gauge chosen. This occurs even when the coupling vanishes at the preparation and measurement stages of the protocol, at which times the subsystems are unique and experimentally addressable.