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Ultrastrong-coupling between two-level systems and radiation is important forboth fundamental and applied quantum electrodynamics (QED). Such regimes areidentified by the breakdown of the rotating-wave approximation, which appliedto the quantum Rabi model (QRM) yields the apparently less fundamentalJaynes-Cummings model (JCM). We show that when truncating the material systemto two levels, each gauge gives a different description whose predictions varysignificantly for ultrastrong-coupling. QRMs are obtained through specificgauge choices, but so too is a JCM without needing the rotating-waveapproximation. Analysing a circuit QED setup, we find that this JCM providesmore accurate predictions than the QRM for the ground state, and often for thefirst excited state as well. Thus, Jaynes-Cummings physics is not restricted tolight-matter coupling below the ultrastrong limit. Among the many implicationsis that the system's ground state is not necessarily highly entangled, which isusually considered a hallmark of ultrastrong-coupling.

Gauge ambiguities imply Jaynes-Cummings physics remains valid in ultrastrong coupling QED