Quantum time dilation in atomic spectra

TL;DR

This paper demonstrates quantum time dilation effects in atomic spectra using a hydrogen-like atom as a clock, revealing differences in emission rates and spectral shifts due to quantum superpositions of momentum, with implications for experimental exploration.

Contribution

It introduces a method to observe quantum time dilation effects in atomic spectra through spontaneous emission, highlighting quantum corrections to Doppler shifts and decay rates.

Findings

Quantum time dilation affects atomic emission rates.

Quantum coherence modifies Doppler shift in spectra.

Spectroscopic experiments can observe quantum time dilation effects.

Abstract

Quantum time dilation occurs when a clock moves in a superposition of relativistic momentum wave packets. We utilize the lifetime of an excited hydrogen-like atom as a clock to demonstrate how quantum time dilation manifests in a spontaneous emission process. The resulting emission rate differs when compared to the emission rate of an atom prepared in a mixture of momentum wave packets at order $v^2/c^2$. This effect is accompanied by a quantum correction to the Doppler shift due to the coherence between momentum wave packets. This quantum Doppler shift affects the spectral line shape at order $v/c$. However, its effect on the decay rate is suppressed when compared to the effect of quantum time dilation. We argue that spectroscopic experiments offer a technologically feasible platform to explore the effects of quantum time dilation.