Rydberg atoms and relativistic charged spectator

Abstract The gauge dependence of physical observables was first noticed by Lamb and has sparked widespread discussion. Subsequently, many authors used the ‘gauge-invariant’ Hamiltonian to define atomic states, claiming that it can solve the problem of gauge dependence. Here, by calculating the spontaneous radiation spectrum of Rydberg atoms in the electromagnetic fields produced by a cluster of relativistic charged particles (referred to as ‘Relativistic Charged Spectator’ in this paper), we reveal this kind of gauge dependence that cannot be resolved by the previous methods. The obtained peak frequency can differ by about 6 MHz or larger for the commonly used Coulomb, Lorentz, and multipolar gauges, which can be distinguished through experiments. This result is important not only for understanding the physical significance of gauge potential, but also for practical applications such as the timing accuracy of atomic clocks under the influence of the moving charged particles.