Abstract
Finding a feasible scheme for testing the quantum mechanical nature of the gravitational interaction has been attracting an increasing level of attention. Gravity mediated entanglement generation so far appears to be the key ingredient for a potential experiment. In a recent proposal [D. Carney et al., PRX Quantum 2, 030330 (2021)] combining an atom interferometer with a low-frequency mechanical oscillator, a coherence revival test is proposed for verifying this entanglement generation. With measurements performed only on the atoms, this protocol bypasses the need for correlation measurements. Here, we explore formulations of such a protocol, and specifically find that in the envisioned regime of operation with high thermal excitation, semiclassical models, where there is no concept of entanglement, also give the same experimental signatures. We elucidate in a fully quantum mechanical calculation that entanglement is not the source of the revivals in the relevant parameter regime. We argue that, in its current form, the suggested test is only relevant if the oscillator is nearly in a pure quantum state, and in this regime the effects are too small to be measurable. We further discuss potential open ends. The results highlight the importance and subtleties of explicitly considering how the quantum case differs from the classical expectations when testing for the quantum mechanical nature of a physical system.
Highlights
Testing the quantum mechanical nature of the gravitational field has long been a subject of interest [1–4]
We showed that in the high-temperature limit of the sensing protocol under discussion, the experimentally observable signatures are identical to those predicted by a semiclassical model
Note that our analysis does not indicate any contradiction with utilizing the protocol for nearly pure initial states of the oscillator, experimental feasibility of observing visibility variations in the coupled atom-oscillator system requires high initial oscillator temperature, rendering the oscillator astronomically far from the pure state limit
Summary
Testing the quantum mechanical nature of the gravitational field has long been a subject of interest [1–4]. We explore formulations of such a protocol both in the semiclassical and in the fully quantum domains, and explicitly illustrate that entanglement is not responsible for the coherence revivals in the configurations required for experimental feasibility—namely, the high thermal excitation requirement. This emphasizes the importance and subtleties of explicitly considering how the quantum case differs from the classical one for potential experiments aiming at testing the quantum mechanical nature of the gravitational interaction. The results highlight the quantum-to-classical transition where the origin of the loss and gain of quantum coherence changes nature, going from entanglement to classical correlations
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