1Department of Physics, Stockholm University, SE-106 91 Stockholm, Sweden
2Institute of Theoretical Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland
3Center for Theoretical Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland
4Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck, Austria
5Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria
6Department of Physics, Saint Anselm College, Manchester, New Hampshire 03102, USA
7Department of Physics and Astronomy, Dartmouth College, Hanover, New Hampshire 03755, USA
8Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543 Singapore, Singapore
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Abstract
According to relativity, the reading of an ideal clock is interpreted as the elapsed proper time along its classical trajectory through spacetime. In contrast, quantum theory allows the association of many simultaneous trajectories with a single quantum clock, each weighted appropriately. Here, we investigate how the superposition principle affects the gravitational time dilation observed by a simple clock – a decaying two-level atom. Placing such an atom in a superposition of positions enables us to analyze a quantum contribution to a classical time dilation manifest in spontaneous emission. In particular, we show that the emission rate of an atom prepared in a coherent superposition of separated wave packets in a gravitational field is different from the emission rate of an atom in a classical mixture of these packets, which gives rise to a quantum gravitational time dilation effect. We demonstrate that this nonclassical effect also manifests in a fractional frequency shift of the internal energy of the atom that is within the resolution of current atomic clocks. In addition, we show the effect of spatial coherence on the atom’s emission spectrum.
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Cited by
[1] Kacper Dębski, Piotr T. Grochowski, Rafał Demkowicz-Dobrzański, and Andrzej Dragan, “Universality of quantum time dilation”, arXiv:2211.02425, (2022).
[2] Simone Rijavec, “Robustness of the Page-Wootters construction across different pictures, states of the universe, and system-clock interactions”, Physical Review D 108 6, 063507 (2023).
[3] Takeshi Chiba and Shunichiro Kinoshita, “Quantum clocks, gravitational time dilation, and quantum interference”, Physical Review D 106 12, 124035 (2022).
[4] Joshua Foo and Magdalena Zych, “Superpositions of thermalisation states in relativistic quantum field theory”, arXiv:2307.02593, (2023).
[5] Jerzy Paczos and Luis C. Barbado, “Hawking radiation for detectors in superposition of locations outside a black hole”, Physical Review D 108 12, 125015 (2023).
[6] Jiatong Yan and Baocheng Zhang, “Influence of gravitational waves on quantum multibody states”, Physical Review D 108 10, 105015 (2023).
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On Crossref’s cited-by service no data on citing works was found (last attempt 2024-05-07 23:14:31).
This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.
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