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arxiv: 2509.09573 · v2 · submitted 2025-09-11 · 🪐 quant-ph · gr-qc· physics.atom-ph

Quantum signatures of proper time in optical ion clocks

Gabriel Sorci , Joshua Foo , Dietrich Leibfried , Christian Sanner , Igor Pikovski This is my paper

Pith reviewed 2026-05-18 17:28 UTC · model grok-4.3

classification 🪐 quant-ph gr-qcphysics.atom-ph
keywords proper timetime dilationoptical ion clockssecond-order Doppler shiftquantum entanglementtrapped ionsrelativistic quantum mechanicsproper time interferometry
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The pith

Atomic clocks can detect relativistic effects that require a quantum description of proper time.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that optical ion clocks have the precision to measure time dilation where a classical proper time parameter is no longer sufficient. Modeling atoms in harmonic traps with a Hamiltonian approach reveals extra frequency shifts from vacuum energy, from squeezing the atomic motion, and from quantum corrections to the dynamics. When the motion is strongly squeezed, entanglement between the atom's position and its internal clock state becomes detectable, which would enable a form of proper time interferometry. A reader would care because this moves quantum-relativistic clock effects from theory into the range of near-term experiments with existing trapped-ion technology.

Core claim

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 (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.

What carries the argument

Hamiltonian formalism for harmonically trapped clock atoms that isolates vacuum, squeezing, and quantum contributions to second-order Doppler shifts and renders motion-clock entanglement observable under strong squeezing.

If this is right

  • Vacuum energy produces a measurable contribution to the second-order Doppler shift in trapped clocks.
  • Squeezing of the atomic motion generates an additional, observable second-order Doppler shift.
  • Quantum corrections to the clock dynamics appear as detectable frequency shifts.
  • Strong squeezing renders the entanglement between atomic motion and internal clock evolution measurable, enabling proper time interferometry.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Confirmation would supply a concrete metrological route to test how quantum mechanics alters the notion of proper time in relativistic regimes.
  • The same squeezing techniques could be adapted to other precision systems such as neutral-atom clocks or matter-wave interferometers.
  • Observing these signatures would also benchmark the level of motional control needed for future quantum-relativistic sensing protocols.

Load-bearing premise

State-of-the-art ion traps can achieve the strong squeezing of atomic motion required to make the entanglement between motion and clock evolution observable.

What would settle it

A trapped-ion experiment that reaches the required squeezing level yet measures no deviation from classical proper-time predictions for the second-order Doppler shift or entanglement signature would falsify the claim that quantum proper-time effects are detectable.

Figures

Figures reproduced from arXiv: 2509.09573 by Christian Sanner, Dietrich Leibfried, Gabriel Sorci, Igor Pikovski, Joshua Foo.

Figure 1
Figure 1. Figure 1: FIG. 1. Illustration of classical, semiclassical, and quan [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Illustration of time-dilation induced entanglement [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
read the original 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 atomic 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper applies a Hamiltonian formalism to harmonically trapped optical clock ions to derive relativistic time-dilation corrections beyond classical proper time. It identifies three distinct quantum contributions to second-order Doppler shifts (vSODS from vacuum energy, sqSODS from motional squeezing, and qSODS from quantum dynamics) and argues that strong squeezing of the atomic motion can render motion-clock entanglement observable, enabling proper-time interferometry in state-of-the-art ion traps.

Significance. If the derivations are robust and the experimental parameters are shown to be attainable, the work would provide a concrete route to testing quantum aspects of proper time using precision metrology. The systematic Hamiltonian treatment and the explicit naming of three quantum signatures constitute a clear advance over purely classical treatments of clock time dilation.

major comments (2)
  1. [Abstract (final paragraph)] The final paragraph of the abstract claims that strong squeezing renders motion-clock entanglement observable in current ion traps, yet no quantitative estimates of achievable squeezing parameters, their compatibility with typical clock interrogation times, or signal-to-noise above decoherence are provided. This assumption is load-bearing for the central experimental claim.
  2. [Hamiltonian derivation (main text)] The transition from the derived Hamiltonian to the explicit expressions for vSODS, sqSODS and qSODS should be checked for any post-hoc choices or approximations that could alter the claimed quantum character of the corrections; the manuscript does not appear to include a parameter-free derivation or falsifiable prediction that would strengthen this step.
minor comments (2)
  1. [Notation and definitions] Clarify the precise definition of the quantum proper-time operator versus the classical parameter throughout the derivations to avoid notational ambiguity.
  2. [Discussion] Add a short discussion or reference to existing experimental limits on motional squeezing in ion traps used for optical clocks.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments. We address each major comment below.

read point-by-point responses

  1. Referee: [Abstract (final paragraph)] The final paragraph of the abstract claims that strong squeezing renders motion-clock entanglement observable in current ion traps, yet no quantitative estimates of achievable squeezing parameters, their compatibility with typical clock interrogation times, or signal-to-noise above decoherence are provided. This assumption is load-bearing for the central experimental claim.

    Authors: We agree that the experimental claim would be strengthened by quantitative estimates. In the revised manuscript we will add estimates of achievable motional squeezing (drawing on reported values of 10–15 dB in ion traps), discuss compatibility with typical interrogation times of order 1 s, and provide order-of-magnitude signal-to-noise estimates that incorporate known decoherence rates. These additions will be placed in a new paragraph of the main text together with appropriate experimental references. revision: yes

  2. Referee: [Hamiltonian derivation (main text)] The transition from the derived Hamiltonian to the explicit expressions for vSODS, sqSODS and qSODS should be checked for any post-hoc choices or approximations that could alter the claimed quantum character of the corrections; the manuscript does not appear to include a parameter-free derivation or falsifiable prediction that would strengthen this step.

    Authors: The three contributions emerge directly from a perturbative expansion of the unitary time-evolution operator generated by the Hamiltonian; no additional approximations or post-hoc selections are introduced. The vacuum term (vSODS) arises from the zero-point energy, the squeezing term (sqSODS) from the quadratic squeezing operator, and the dynamical correction (qSODS) from the next order in the Magnus expansion. To make the derivation fully transparent we will insert an expanded step-by-step calculation in the main text (or as a new appendix) that shows each term without intermediate choices. The resulting expressions yield falsifiable signatures: the sqSODS scales linearly with the squeezing parameter while the qSODS exhibits a distinct temperature dependence, both of which can be tested by varying the motional state. revision: partial

Circularity Check

0 steps flagged

No circularity: standard Hamiltonian derivation with independent observability assumption

full rationale

The paper applies a standard Hamiltonian formalism for harmonically trapped ions to derive vSODS, sqSODS, and qSODS directly from the equations of motion and vacuum energy contributions. These quantities emerge from the relativistic expansion and squeezing operators without being fitted to the target signatures or defined in terms of themselves. The entanglement observability claim is conditioned on an external experimental assumption (strong squeezing in state-of-the-art traps) rather than reducing to a self-referential fit or self-citation chain. No uniqueness theorems, ansatzes smuggled via prior work, or renaming of known results are invoked as load-bearing steps. The derivation remains self-contained against external benchmarks in quantum optics and ion-trap physics.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the applicability of a non-relativistic Hamiltonian to the trapped-ion system plus standard quantum-optics assumptions about squeezing; no new entities are postulated.

axioms (2)
  • domain assumption The motion of the trapped ion can be treated with a quantum harmonic-oscillator Hamiltonian coupled to the internal clock states.
    Invoked when the authors apply the Hamiltonian formalism to derive the time-dilation effects.
  • domain assumption Strong motional squeezing is experimentally achievable in current ion traps without destroying clock coherence.
    Required for the observability of entanglement and proper-time interferometry.

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Reference graph

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    Quantum signatures of proper time in optical ion clocks

    After perform- ing the sum overk, the off-diagonal element in polar form is given by 2ρeg = e−i(ωct−arctan(tan(ε)(2¯n+1))) q cos2(ε) + sin2(ε)(2¯n+ 1)2 (B2) having here definedε=ε cωt/4. We can read off from this expression the frequency shift ∆ω c and the visibility 2|ρeg|. In the regimeε¯n≪1, we obtain toO(ε¯n) the usual SODS as in the main text: 2ρeg ≃...

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