Optimal Dynamical Gauge in the Quantum Rabi Model

We have investigated the gauge dependence of physical observables in a quantum Rabi model under different potential fields arising from the Hilbert space truncation of the atomic degrees of freedom. In both the square-well and harmonic potentials, the optimal gauge for the ground-state energy depends on the cavity frequency, which is optimal in the low-frequency limit, whereas the Coulomb gauge is optimal in the high-frequency limit. For a dynamic quantity, such as an out-of-time-order correlator, we have demonstrated the necessity of introducing an optimal dynamic gauge. This study provides deeper insight into the intricate relationship between gauge choice and the dynamics of quantum electrodynamics systems, resulting in more accurate theoretical frameworks.