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arXiv · 2404.03205

Optimal Dynamical Gauge in the Quantum Rabi Model

Yuqi Qing·Wen-Long You·Yueheng Lan·Maoxin Liu
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Abstract

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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Yuqi Qing, Wen-Long You, Yueheng Lan, Maoxin Liu. 2024-04-04. Optimal Dynamical Gauge in the Quantum Rabi Model. https://doi.org/10.1088/0256-307x%2F42%2F2%2F020501

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