Quantum time dilation in atomic spectra

Quantum time dilation occurs when a clock moves in a superposition of relativistic momentum wave packets. The lifetime of an excited hydrogenlike atom can be used as a clock, which we use to demonstrate how quantum time dilation manifests in a spontaneous emission process. The resulting emission rate differs when compared with 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 with the effect of quantum time dilation. We argue that spectroscopic experiments offer a technologically feasible platform to explore the effects of quantum time dilation.