Optimal Dynamical Gauge in the Quantum Rabi Model
arxiv(2024)
摘要
In this paper, we investigate the gauge dependence of various physical
observables in the quantum Rabi model (QRM) under different potential fields,
arising from the Hilbert-space truncation of the atomic degree of freedom. We
discover that in both the square-well potential and oscillator potential,the
optimal gauges for the ground-state energy of the QRM vary with respect to the
cavity frequency, with the dipole gauge being optimal in the low-frequency
limit and the Coulomb gauge in the high-frequency limit of the cavity
frequency. Additionally, for higher energy levels, the optimal gauge
asymptotically approaches the dipole gauge. However, for the dynamical quantity
out-time-order correlator (OTOC), we find the necessity to introduce an optimal
dynamical gauge. We determine the optimal dynamical gauge by minimizing the
mean error between the two-level OTOC and the full Hamiltonian one. We expect
that this study will contribute to a more profound understanding of the subtle
relation between gauge choice and the dynamics of QED systems.
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