Metrics and properties of optimal gauges in multimode cavity QED

Multimode cavity quantum electrodynamics describes, for example, the coupling between an atom and a multimode electromagnetic resonator. The gauge choice is important for practical calculations in truncated Hilbert spaces, because the exact gauge invariance is recovered only in the whole space. An optimal gauge can be defined as the one predicting the most accurate observables for the same number of atomic levels and modes. Different metrics quantifying the gauge performance can be introduced depending on the observable of interest. In this paper we demonstrate that the optimal choice is generally mode dependent, i.e., a different gauge is needed for each cavity mode. While the choice of gauge becomes more important for increasing light-matter interaction, we also show that the optimal gauge does not correspond to the situation where the entanglement between light and matter is the smallest.