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Physical Review A

Time dilation effects in micron-size rotating optical Ferris-wheel traps

V. E. Lembessis, J. Yuan, Koray Köksal, M. Babiker

Published Aug 25, 2025• 0 citations
Publisher

Abstract

Advances in lasers and atomic clock technologies have enabled delicate measurements to be made of minute relativistic effects. Here, we propose that such developments should lead to the measurement of relativistic effects involving atoms and molecules in dynamic optical traps. Specifically, we make a case for the study of time dilation in the context of atoms and molecules trapped in a rotating optical Ferris wheel. With experimentally relevant examples, we demonstrate how this would extend relativity tests down to the micron scale and would constitute a potential advance toward micron-size Mössbauer-style spectroscopy for trapped atoms and molecules.

DOI
10.1103/5m6c-hfqt

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Advances in lasers and atomic clock technologies have enabled delicate measurements to be made of minute relativistic effects. Here, we propose that such developments should lead to the measurement of relativistic effects involving atoms and molecules in dynamic optical traps. Specifically, we make a case for the study of time dilation in the context of atoms and molecules trapped in a rotating optical Ferris wheel. With experimentally relevant examples, we demonstrate how this would extend relativity tests down to the micron scale and would constitute a potential advance toward micron-size Mössbauer-style spectroscopy for trapped atoms and molecules.
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.
For the past 15 years, tremendous progress within the fields of laser stabilization, optical frequency combs and atom cooling and trapping have allowed the realization of optical atomic clocks with unrivaled performances. These instruments can perform frequency comparisons with fractional uncertainties well below 10-17, finding applications in fundamental physics tests, relativistic geodesy and time and frequency metrology. Even though most optical clocks are currently laboratory setups, several proposals for using these clocks for field measurements or within an optical clock network have been published, and most of time and frequency metrology institutes have started to develop transportable optical clocks. For the purpose of this special issue, we chose to focus on trapped-ion optical clocks. Even though their short-term fractional frequency stability is impaired by a lower signal-to-noise ratio, they offer a high potential for compactness: trapped ions demand low optical powers and simple loading schemes, and can be trapped in small vacuum chambers. We review recent advances on the clock key components, including ion trap and ultra-stable optical cavity, as well as existing projects and experiments which draw the picture of what future transportable, single-ion optical clocks may resemble.
Clock interferometry refers to the coherent splitting of a clock into two different paths and recombining in a way that reveals the proper-time difference between them. Unlike the comparison of two separate clocks, this approach allows testing how nonflat space-time influences quantum coherence. Atomic clocks are currently the most accurate timekeeping devices. Here we propose using optical tweezers to implement clock interferometry. Our proposed clock interferometer employs an alkaline-earth-like atom held in an optical trap at the magic wavelength. Through a combination of adiabatic, tweezer-based splitting and recombining schemes and a modified Ramsey sequence of the clock states, we achieve linear sensitivity to the gravitational time dilation. Moreover, the measurement of the time dilation is insensitive to relative fluctuations in the intensity of the tweezer beams. We analyze the tweezer clock interferometer and show that it is feasible with current technological capabilities. The proposed interferometer could test the effect of gravitational redshift on quantum coherence and implement the quantum twin paradox.