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Quantum Signatures of Proper Time in Optical Ion Clocks

Gabriel Sorci1,*, Joshua Foo1,2,*, Dietrich Leibfried3, Christian Sanner4, and Igor Pikovski1,5,†

  • *These authors contributed equally to this work.
  • †Contact author: pikovski@stevens.edu
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Phys. Rev. Lett. 136, 163602 – Published 20 April, 2026

DOI: https://doi.org/10.1103/qhj9-pc2b

Abstract

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.

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Phys. Rev. Lett. 136, 163602– Published 20 April, 2026
  • Received 27 September 2025
  • Accepted 27 February 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by Bibsam.

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