Witnessing mass-energy equivalence with trapped atom interferometers

Jerzy Paczos; Joshua Foo; Magdalena Zych

doi:10.22331/q-2025-08-08-1827

Witnessing mass-energy equivalence with trapped atom interferometers

Jerzy Paczos¹, Joshua Foo^2,3,4, and Magdalena Zych^1,5

¹Department of Physics, Stockholm University, SE-106 91 Stockholm, Sweden
²Centre for Quantum Computation and Communication Technology, School of Mathematics and Physics, University of Queensland, St. Lucia, Queensland 4072, Australia
³Department of Physics, Stevens Institute of Technology, Castle Point Terrace, Hoboken, New Jersey 07030, USA
⁴Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1
⁵Centre for Engineered Quantum Systems, School of Mathematics and Physics, The University of Queensland, St. Lucia, Queensland, 4072, Australia

Published:	2025-08-08, volume 9, page 1827
Editor:	Maximilian Lock
Eprint:	arXiv:2406.19037v3
Doi:	https://doi.org/10.22331/q-2025-08-08-1827
Citation:	Quantum 9, 1827 (2025).

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Abstract

We propose an experimental setup to probe the interplay between the quantum superposition principle and gravitational time dilation arising from the mass-energy equivalence. It capitalizes on state-of-the-art atom interferometers that can keep atoms trapped in a superposition of heights in Earth's gravitational field for exceedingly long times, reaching the minute scale. Our proposal consists of adding two additional laser pulses to the existing experiments that would set up a clock trapped at a superposition of heights, reading a quantum superposition of relativistic proper times. We develop a method to include relativistic corrections to Bloch oscillations, which describe the trapped part of the interferometer. We derive the trajectories and corresponding phases acquired in each arm of the interferometer. We then show that a superposition of proper times manifests in the interference pattern in two ways: visibility modulations and a shift of the atom's resonant frequency. We argue that the latter might be observable with current technology.

Featured image: Proposed trapped-atom clock-interferometer. Blue wavy lines are $\pi/2$ Bragg pulses that split and later recombine the atomic wavepacket. Red wavy lines are $\pi/2$ clock pulses (Ramsey-type) acting only on the internal transition. Between them, an optical lattice (not shown for clarity) holds the atom in a spatial superposition of two heights, so that the internal clock simultaneously samples two proper times.

Popular summary

State‑of‑the‑art trapped‑atom interferometers can now hold single atoms in a superposition of heights for durations comparable to a minute, while optical atomic clocks have achieved sensitivities sufficient to resolve gravitational redshifts over height differences of just a millimeter. These advances bring us closer to a regime where both quantum mechanics and general relativity are simultaneously relevant. In our proposal, we combine these capabilities by applying Ramsey interferometry to atoms trapped in a superposition of heights, effectively operating a quantum clock that experiences a superposition of proper times. When the superposed paths are recombined, this dual reading of time shows up as slow oscillations in the interference contrast and, more prominently, as a tiny shift in the clock’s resonant frequency — large enough to be within reach of today’s best atomic clocks. Experimentally demonstrating that a single atom can read out a superposition of proper times would provide direct evidence that time itself can exist in a quantum superposition. This would constitute a landmark experiment and open the door to further tests of the currently inaccessible intersection of quantum theory and relativistic gravitation.

► BibTeX data

@article{Paczos2025witnessingmass,
  doi = {10.22331/q-2025-08-08-1827},
  url = {https://doi.org/10.22331/q-2025-08-08-1827},
  title = {Witnessing mass-energy equivalence with trapped atom interferometers},
  author = {Paczos, Jerzy and Foo, Joshua and Zych, Magdalena},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1827},
  month = aug,
  year = {2025}
}

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