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arXiv:1710.08695

When Cavendish meets Feynman: A quantum torsion balance for testing the quantumness of gravity

Matteo Carlesso, Mauro Paternostro, Hendrik Ulbricht, Angelo Bassi

Published Oct 24, 2017• 20 citations
arXivHTMLPDF

Abstract

We propose a thought experiment, based on a mechanism that is reminiscent of Cavendish's torsion balance, to investigate the possible quantum nature of the gravitational field generated by the quantum superposition state of a massive system. Our proposal makes use of the dynamics of a ultra-stable optically levitated nanomechanical rotor endowed with a spin to generate a quantum angular superposition that is then tested through standard Ramsey-like scheme. Gravity manifests itself as an effective decoherence mechanism, whose strength is different-and, as we show, appreciable-in the classical and quantum case. By incorporating both the source for decoherence and the mechanism to probe it, the experiment that we propose allows for a much reduced degree of control and dynamical engineering.

DOI
10.48550/arxiv.1710.08695

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We propose a thought experiment, based on a mechanism that is reminiscent of Cavendish's torsion balance, to investigate the possible quantum nature of the gravitational field generated by the quantum superposition state of a massive system. Our proposal makes use of the dynamics of a ultra-stable optically levitated nanomechanical rotor endowed with a spin to generate a quantum angular superposition that is then tested through standard Ramsey-like scheme. Gravity manifests itself as an effective decoherence mechanism, whose strength is different-and, as we show, appreciable-in the classical and quantum case. By incorporating both the source for decoherence and the mechanism to probe it, the experiment that we propose allows for a much reduced degree of control and dynamical engineering.
The inclusion of gravitation within the framework of quantum theory remains one of the most prominent open problem in physics. To date, the absence of empirical evidence hampers conclusions regarding the fundamental nature of gravity -- whether it adheres to quantum principles or remains a classical field manifests solely in the macroscopic domain. This article presents a though experiment aimed at discerning the quantum signature of gravity through the lens of macroscopic nonlocality. The experiment integrates a standard Bell test with a classical Cavendish experiment. We illustrate that the measurement apparatuses employed in a Bell experiment, despite lacking entanglement, defy classical descriptions; their statistical behaviors resist explanations through local hidden variable models. Extending this argument to encompass the massive objects in the Cavendish experiment allows for further disputing classical models of the gravitational field. Under favorable conditions and in light of corroborating evidence from the recent loophole-free Bell experiments, the quantum character of gravity is essentially substantiated.
The probing of the quantum nature of a macroscopic object is an open problem. Approaches in preparing quantum superposition towards a larger scale, which has been progressively accessible in a variety of experimental implementations, may detect new physics or extend the boundary of quantum theory. Development on a nano-mechanical system in the framework of quantum optics and information theory has opened new research directions. It paves ways to manipulate the wavefunction of a massive particle over a large spatial range and probe its quantum behavior to an unprecedented precision. In this thesis, quantum superposition on a mechanical system is studied theoretically in the light of possible implementations under current techniques in order to test superposition principle and the quantum nature of gravity in the mesoscopic region. The work includes two lines of study. In the first line, the motion of the center of mass (c.m.) of the mechanical system is coupled to its internal spin system magnetically, and a Ramsey scheme is developed based on coherent spin control. The wavepacket of the test object, under a spin-dependent force, may then be delocalized to a macroscopic scale. A gravity induced dynamical phase (accrued solely on the spin state, and measured through a Ramsey scheme) is used to reveal the above spatially delocalized superposition of the spin-nano-object composite system that arises during the scheme. A remarkable immunity to the motional noise in the c.m. (initially in a thermal state with moderate cooling) and also a dynamical decoupling nature of the scheme itself is revealed. A careful examination of the perturbation effect due to setup imperfection and environment-induced decoherence is performed, which shows that the Ramsey fringes have a high tolerance on those unwanted faults under realistic experimental conditions. The scheme also facilitates a gravimetry protocol that potentially could be developed for a novel on-chip gravimeter with a precision of 10−6g/Hz10^{-6}g/\sqrt{\text{Hz}}10−6g/Hz​. In the second line, an opto-mechanical experiment is proposed to entangle the motion of two mechanical oscillators through their mutual gravitational interaction. The feasibility of such an experiment is critically examined within the framework of cavity optomechanics. It is shown that within the decoherence time of mechanical noise and potentially gravitational induced state collapse, entanglement between mirrors could be obtained when the initial state of the cavity field is prepared in some particular states. Strategies that give enhancement to entanglement generation rate are studied in light of quantum estimation theory. It is shown that for a cavity initially in a coherent state, the resulting entanglement generation rate would be enhanced linearly with the amplitude of the coherent state. Lastly, it shows that in the proposed setup Casimir effect would significantly affect the gravity-induced entanglement. A proper shield can eliminate the detrimental effect of Casimir force, which, however, will constrain the closest distance between the mirrors in its implementation.
The question of whether gravity is fundamentally quantum remains one of the deepest open problems in modern physics. A recently explored approach consists of testing gravity's ability to entangle quantum systems, which requires preparing and controlling massive quantum states - a formidable experimental challenge. We propose an alternative strategy that circumvents the need for quantum state engineering. We show that, if gravity is classical, it must necessarily modify momentum statistics in a non-unitary way. We consider the corresponding linearized master equation for two harmonically trapped objects interacting gravitationally and establish a lower bound on the noise that any classical gravitational interaction must induce. We then outline an experimental protocol based on a high-precision torsion pendulum at millikelvin temperatures, showing that the predicted diffusion, if present, is in principle detectable with near-term technology. Our approach offers a novel route to testing the classical versus quantum nature of gravity without requiring macroscopic quantum superpositions or precise control of the system's quantum state, thereby significantly reducing the experimental complexity.
Abstract One of the outstanding questions in modern physics is how to test whether gravity is classical or quantum in a laboratory. Recently there has been a proposal to test the quantum nature of gravity by creating quantum superpositions of two nearby neutral masses, close enough that the quantum nature of gravity can entangle the two quantum systems, but still sufficiently far away that all other known Standard Model interactions remain negligible. However, preparing superposition states of a neutral mass (the light system) requires the vicinity of laboratory apparatus (the heavy system). We will suppose that such a heavy system can be modelled as another quantum system; since gravity is universal, the lighter system can get entangled with the heavier system, providing an inherent source of gravitational decoherence. In this paper, we will consider a toy model composed of two light and two heavy quantum oscillators prepared in the motional ground state, forming pairs of probe-detector systems, and study under what conditions the entanglement between two light systems evades the decoherence induced by the heavy systems. We conclude by estimating the decoherence in the proposed experiment for testing the quantum nature of gravity.
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.
Abstract What gravitational field is generated by a massive quantum system in a spatial superposition? Despite decades of intensive theoretical and experimental research, we still do not know the answer. On the experimental side, the difficulty lies in the fact that gravity is weak and requires large masses to be detectable. However, it becomes increasingly difficult to generate spatial quantum superpositions for increasingly large masses, in light of the stronger environmental effects on such systems. Clearly, a delicate balance between the need for strong gravitational effects and weak decoherence should be found. We show that such a trade off could be achieved in an optomechanics scenario that allows to witness whether the gravitational field generated by a quantum system in a spatial superposition is in a coherent superposition or not. We estimate the magnitude of the effect and show that it offers perspectives for observability.