Quantum signatures of proper time in optical ion clocks

Published

April 20, 2026

Author(s)

Gabriel Sorci, Joshua Foo, Igor Pikovski, Christian Sanner, Dietrich Leibfried

Abstract

Optical clocks based on atoms and ions probe relativistic effects with unprecedented sensitivity by resolving 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 trapped ion clocks can probe effects where a classical description of the proper time dynamics is insufficient. We apply a Hamiltonian formalism to derive time dilation effects in harmonically trapped clock atoms and show how second-order Doppler shifts (SODS) due to the vacuum energy (vSODS), squeezing (sqSODS) and quantum corrections to the dynamics (qSODS) arise. We also demonstrate that the 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 to probe relativistic evolution of clocks for which a quantum description of proper time becomes necessary.

Citation

Physical Review Letters

Pub Type

Journals

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Keywords

quantum mechanics, proper time, second order Doppler shift, atomic clock

Citation

Sorci, G. , Foo, J. , Pikovski, I. , Sanner, C. and Leibfried, D. (2026), Quantum signatures of proper time in optical ion clocks, Physical Review Letters, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=960526 (Accessed September 17, 2026)

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