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arXiv:2006.10084 · Physical Review Research

Quantum time dilation in atomic spectra

Piotr T. Grochowski, Alexander R. H. Smith, Andrzej Dragan, Kacper Dębski

Published Apr 19, 2021• 19 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevresearch.3.023053

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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.
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Relativistic time dilation implies that an accelerating excited atom would have its lifetime prolonged in the lab frame. In this paper, we demonstrate a complementary effect: Longer-lived excited atoms turn out to have been accelerated. We propose the following experiment. An excited atom is prepared in a superposition of momenta. Due to relativistic time dilation, in the lab frame, the decay rate of components with higher momentum is diminished. As time passes without the atom emitting a photon, higher-momentum components become more probable. This results in a time-dependent shift of the expectation value of momentum. Taking into account first-order relativistic corrections, we calculate the force and acceleration undergone by the atom due to the fact that it did not emit a photon.
Optical clocks based on atoms and ions probe relativistic effects with unprecedented sensitivity. They resolve time dilation due to atom motion or different positions in the gravitational potential through frequency shifts. However, all measurements of time dilation so far can be explained effectively as the result of dynamics with respect to a classical proper time parameter. Here we show that atomic clocks can probe effects where a classical description of the proper time dynamics is insufficient as superpositions of proper time emerge. We apply a Hamiltonian formalism to derive time dilation effects in harmonically trapped clock atoms and show how second-order Doppler shifts due to the vacuum energy, squeezing, and quantum corrections to the dynamics arise. We also demonstrate that time-dilation-induced entanglement between motion and clock evolution can become observable in state-of-the-art clocks when the motion of the atoms is strongly squeezed, realizing proper time interferometry. Our results show that experiments with trapped ion clocks are within reach of probing relativistic evolution of clocks for which a quantum description of proper time becomes necessary.
Abstract At the intersection of quantum theory and relativity lies the possibility of a clock experiencing a superposition of proper times. We consider quantum clocks constructed from the internal degrees of relativistic particles that move through curved spacetime. The probability that one clock reads a given proper time conditioned on another clock reading a different proper time is derived. From this conditional probability distribution, it is shown that when the center-of-mass of these clocks move in localized momentum wave packets they observe classical time dilation. We then illustrate a quantum correction to the time dilation observed by a clock moving in a superposition of localized momentum wave packets that has the potential to be observed in experiment. The Helstrom-Holevo lower bound is used to derive a proper time-energy/mass uncertainty relation.
At the intersection of quantum theory and relativity lies the possibility of a clock experiencing a superposition of proper times. We consider quantum clocks constructed from the internal degrees of relativistic particles that move through curved spacetime. The probability that one clock reads a given proper time conditioned on another clock reading a different proper time is derived. From this conditional probability distribution, it is shown that when the center-of-mass of these clocks move in localized momentum wave packets they observe classical time dilation. We then illustrate a quantum correction to the time dilation observed by a clock moving in a superposition of localized momentum wave packets that has the potential to be observed in experiment. The Helstrom-Holevo lower bound is used to derive a proper time-energy/mass uncertainty relation.