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arXiv:2210.12713

Gravity mediated entanglement between light beams as a table-top test of quantum gravity

Stefan Aimet, Hadrien Chevalier, M. S. Kim

Published Oct 23, 2022• 1 citation
arXivHTMLPDF

Abstract

Over the past century, a large community within theoretical physics has been seeking a unified framework for quantum gravity. Yet, to date, there is still no experimental evidence of any non-classical features of gravity. While traditional experimental proposals would usually require immensely challenging Planck scale experiments, recent table-top protocols based on low-energy quantum control have opened a new avenue into the investigation of non-classical gravity. An approach that has sparked high interest, both in terms of experimental feasibility and of theoretical implications, is the indirect witnessing of non-classical gravity through the detection of its capacity to act as an entangling channel. Most discussions have been centred on the entanglement generation between two gravitationally coupled massive systems. In this work, we instead examine the entangling capacity of the gravitational interaction between two light pulses. We explain the main experimental and theoretical advantages of having a photonic protocol, and lay out the steps leading to the determination of the entangling phase, using the path integral formalism and linearised gravity. We establish a closed form formula for the entangling phase and provide an estimated order of magnitude of the average photon number required for the generation of appreciable phase. Using statistical analysis, we show how entanglement may be certified with lower phase signal.

DOI
10.48550/arxiv.2210.12713

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Over the past century, a large community within theoretical physics has been seeking a unified framework for quantum gravity. Yet, to date, there is still no experimental evidence of any non-classical features of gravity. While traditional experimental proposals would usually require immensely challenging Planck scale experiments, recent table-top protocols based on low-energy quantum control have opened a new avenue into the investigation of non-classical gravity. An approach that has sparked high interest, both in terms of experimental feasibility and of theoretical implications, is the indirect witnessing of non-classical gravity through the detection of its capacity to act as an entangling channel. Most discussions have been centred on the entanglement generation between two gravitationally coupled massive systems. In this work, we instead examine the entangling capacity of the gravitational interaction between two light pulses. We explain the main experimental and theoretical advantages of having a photonic protocol, and lay out the steps leading to the determination of the entangling phase, using the path integral formalism and linearised gravity. We establish a closed form formula for the entangling phase and provide an estimated order of magnitude of the average photon number required for the generation of appreciable phase. Using statistical analysis, we show how entanglement may be certified with lower phase signal.
Detecting gravity-mediated entanglement can provide evidence that the gravitational field obeys quantum mechanics. We report the result of a simulation of the phenomenon using a photonic platform. The simulation tests the idea of probing the quantum nature of a variable by using it to mediate entanglement and yields theoretical and experimental insights, clarifying the operational tools needed for future gravitational experiments. We employ three methods to test the presence of entanglement: the Bell test, entanglement witness, and quantum state tomography. We also simulate the alternative scenario predicted by gravitational collapse models or due to imperfections in the experimental setup and use quantum state tomography to certify the absence of entanglement. The simulation reinforces two main lessons: (1) which path information must be first encoded and subsequently coherently erased from the gravitational field and (2) performing a Bell test leads to stronger conclusions, certifying the existence of gravity-mediated nonlocality.
The quantum nature of gravity is one of physics' greatest unsolved problems, with existing experimental proposals facing formidable challenges in maintaining spatial superpositions of massive objects against decoherence. We propose a fundamentally different approach that bypasses these difficulties. The central insight is that a quantum gravitational field can imprint a gauge-invariant phase on a particle's wavefunction even along an open trajectory, arising from the quantum backreaction of the source. This phase, which manifests prior to the final recombination stage of an interferometer and cannot be generated by a classical gravitational field, provides an operationally direct witness to the quantumness of gravity. Our experimental design uses a single photon whose accumulated gravitational phase due to the Earth is transferred via absorption to auxiliary atoms near the end of the interferometer sequence, preserving the open-path character essential for the test. We scale the interferometer to yield a detectable phase of order 10−310^{-3}10−3 rad and show how non-local correlation measurements on the atoms can access this gauge-invariant signature. Leveraging established quantum optical and atomic techniques, this proposal offers a feasible path to distinguish quantum from classical gravity. A positive result would provide the first experimental evidence for the quantum nature of gravitational fields, with profound implications for quantum gravity theories.
Detecting gravity mediated entanglement can provide evidence that the gravitational field obeys quantum mechanics. We report the result of a simulation of the phenomenon using a photonic platform. The simulation tests the idea of probing the quantum nature of a variable by using it to mediate entanglement, and yields theoretical and experimental insights. We employed three methods to test the presence of entanglement: Bell test, entanglement witness and quantum state tomography. We also simulate the alternative scenario predicted by gravitational collapse models or due to imperfections in the experimental setup and use quantum state tomography to certify the absence of entanglement. Two main lessons arise from the simulation: 1) which--path information must be first encoded and subsequently coherently erased from the gravitational field, 2) performing a Bell test leads to stronger conclusions, certifying the existence of gravity mediated nonlocality.
Recently, table-top experiments involving massive quantum systems have been proposed to test the interface of quantum theory and gravity. In particular, the crucial point of the debate is whether it is possible to conclude anything on the quantum nature of the gravitational field, provided that two quantum systems become entangled solely due to the gravitational interaction. Typically, this question has been addressed by assuming a specific physical theory to describe the gravitational interaction, but no systematic approach to characterise the set of possible gravitational theories which are compatible with the observation of entanglement has been proposed. Here, we remedy this by introducing the framework of Generalised Probabilistic Theories (GPTs) to the study of the nature of the gravitational field. This framework enables us to systematically study all theories compatible with the detection of entanglement generated via the gravitational interaction between two systems. We prove a no-go theorem stating that the following statements are incompatible: i) gravity is able to generate entanglement; ii) gravity mediates the interaction between the systems; iii) gravity is classical. We analyse the violation of each condition, in particular with respect to alternative non-linear models such as the Schrödinger-Newton equation and Collapse Models.
No experimental test to date has provided conclusive evidence on the quantum nature of gravity. Recent proposals, such as the Bose-Marletto-Vedral experiment, suggest that generating entanglement could serve as a direct test. Motivated by these proposals, we study a system of three-harmonic oscillator system, with the mediator oscillator operating in two distinct parameter regimes: a heavy mediator regime and a light mediator regime. These regimes induce qualitatively different entanglement dynamics between the terminal oscillators. Crucially, distinguishing these regimes experimentally remains challenging when relying solely on entanglement measures. We demonstrate that the dynamical fidelity susceptibility offers a viable and sensitive probe to contrast the regimes in practice. Our results provide testable signatures for optomechanical and trapped-ion platforms simulating gravitational interactions, and provide new avenues to characterize quantum-gravity-inspired systems beyond entanglement-based protocols.
The paper presents a scheme to detect entanglement arising from the quantum nature of gravity between a spin qubit and photons, using Stokes parameters. One of the crucial tests of the general theory of relativity is the bending of light due to the curvature. Recently, a quantum counterpart of this experiment to test the quantum nature of the gravitational interaction has been proposed, in which the spin-2, massless graviton yields entanglement between matter and a photon sector. Hence, it provides one of the most crucial experimental signatures for testing the quantum nature of gravity in a lab, since only spin-2-induced entanglement can yield the correct deflection of light due to matter. Here, we propose a positive partial-transpose (PPT) witness criterion for witnessing such an entanglement. We scan the entangled states in this context by studying the overlap of the final state, which is proportional to the entanglement phase. We exploit the Stokes observables to measure the photon state and the spins in the matter sector, thereby constructing a witness for the quantum nature of gravity in this setup. To quantify this entanglement, we will couple the photon to a local oscillator, whose phase need to be controlled to probe the orthogonal components of the macroscopic interference in the laser beam. We have shown that for a non-maximally entangled state mediated by the quantum nature of gravity, the witness attains a maximal negativity of −0.052-0.052−0.052. Our findings indicate that this witness effectively detects entanglement within the range 0.71≤∣γ∣<10.71 \leq |γ| < 10.71≤∣γ∣<1, where γγγ is the overlap between the two coherent states of the photon, providing a clear signature of quantum correlations.