Quantum time dilation in atomic spectra
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 v2/c2. 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.