The prediction of nonlocal phenomena is a key attribute of quantum mechanics that distinguishes it from classical theories. It was recently suggested that state swapping is one such effect that a fundamentally classical gravitational field cannot give rise to. The reasoning was that the phenomenology of classical fields is restricted to local operations and classical communication (LOCC), whereas swapping is a non-LOCC effect, so gravity must not be a classical channel if it can give rise to such a phenomenon. Here, we show that the Hamiltonian of semiclassical gravity results in an evolution of coherent states that is virtually indistinguishable from swapping them, both theoretically and experimentally. Our results indicate that drawing a definitive conclusion about the nature of gravity based solely on its ability to swap a pair of coherent states would be premature. We discuss the implications of these results regarding proposed experimental tests for the quantum nature of gravity and clarify some conceptual issues.
The prediction of nonlocal phenomena is a key attribute of quantum mechanics that distinguishes it from classical theories. It was recently suggested that state swapping is one such effect that a fundamentally classical gravitational field cannot give rise to. The reasoning was that the phenomenology of classical fields is restricted to local operations and classical communication (LOCC), whereas swapping is a non-LOCC effect, so gravity must not be a classical channel if it can give rise to such a phenomenon. Here, we show that the Hamiltonian of semiclassical gravity results in an evolution of coherent states that is virtually indistinguishable from swapping them, both theoretically and experimentally. Our results indicate that drawing a definitive conclusion about the nature of gravity based solely on its ability to swap a pair of coherent states would be premature. We discuss the implications of these results regarding proposed experimental tests for the quantum nature of gravity and clarify some conceptual issues.
A consistent theory including gravitational effects in quantum mechanics has not been found. Although many different approaches have been proposed for theory of quantum gravity, several authors have suggested that gravity may be fundamentally classical. As there is no experimental evidence for a fundamentally quantum vs. fundamentally classical theory of gravity, it is hoped that investigating the consequences of semiclassical gravity, one may propose an experiment to distinguish between the quantum or classical nature of gravity. As opto- and electromechanical devices allow quantum limited measurement and control over massive, mechanical degrees of freedom, they are ideal systems to test violations of standard quantum mechanics arising from gravitational effects. After a brief introduction to the background theory and literature review, we begin by introducing a semiclassical model of gravity based on quantum measurement and control. We show under which conditions the theory behaves like a collapse model, and how a Newtonian potential is recovered in the multi particle case.We then go on to analyse our semiclassical model in two scenarios: firstly in a cosmological setting, and secondly by considering quantum clocks on the surface of the earth. In the cosmological description, we show that a violation of energy conservation, resulting from our model, can be reinterpreted as a dark energy fluid in the spacetime, suggesting that perhaps local violations of conservations of energy may be resolved in a cosmological framework. Secondly, we derive a minimum, gravitational dephasing rate for quantum clocks under the semiclassical model, which unsurprisingly, is is well below the resolution of current state of the art clocks. The next chapters diverge from analysing the gravitational model, and instead focus on novel methods of manipulating and measuring micromechanical devices, that may be used to experimentally probe the results of the semi-classical theory. Firstly we show that a sequence of coherently controlled pulses in an optomechanical system can be used to directly probe the momentum of an oscillator - opening up the possibility for direct detection of momentum diffusion, which is a consequence of the semiclassical gravity model. Secondly, we introduce an electro-mechanical device, and sequence of control operations, that may be understood as an interferometer for the wave function of a mechanical oscillator coupled to a qubit. We show how the resulting interference pattern can distinguish between unitary evolution, thermalisation/decoherence, and a purely classical description of the mechanical oscillator. We also show how the qubit-oscillator interaction can be used generate arbitrary wave functions of the mechanical oscillator, using only classical qubit driving.
Given a unitary evolution U on a multipartite quantum system and an ensemble of initial states, how well can U be simulated by local operations and classical communication (LOCC) on that ensemble? We answer this question by establishing a general, efficiently computable upper bound on the maximal LOCC simulation fidelity—what we call an “LOCC inequality.” We then apply our findings to the fundamental setting where U implements a quantum Newtonian Hamiltonian over a gravitationally interacting system. Violation of our LOCC inequality can rule out the LOCCness of the underlying evolution, thereby establishing the nonclassicality of the gravitational dynamics, which can no longer be explained by a local classical field. As a prominent application of this scheme we study systems of quantum harmonic oscillators initialized in coherent states following a normal distribution and interacting via Newtonian gravity, and discuss a possible physical implementation with torsion pendula. One of our main technical contributions is the analytical calculation of the above LOCC inequality for this family of systems. As opposed to existing tests based on the detection of gravitationally mediated entanglement, our proposal works with coherent states alone, and thus it does not require the generation of largely delocalized states of motion nor the detection of entanglement, which is never created at any point in the process. Published by the American Physical Society 2024
Abstract Several approaches to quantum gravity lead to nonlocal modifications of fields’ dynamics. This, in turn, can give rise to nonlocal modifications of quantum mechanics at non-relativistic energies. Here, we analyze the nonlocal Schrödinger evolution of a quantum harmonic oscillator in one such scenario, where the problem can be addressed without the use of perturbation theory. We demonstrate that although deviations from standard quantum predictions occur at low occupation numbers, where they could potentially be detected or constrained by high-precision experiments, the classical limits of quantum probability densities and free energy remain unaffected up to energies comparable with the nonlocality scale. These results provide an example of nonlocal quantum dynamics compatible with classical predictions, suggesting massive quantum objects as a promising avenue for testing some phenomenological aspects of quantum 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 10−3 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.
The possibility that a classical space-time and quantum matter cohabit at the deepest level, i.e., the possibility of having a fundamental and not phenomenological semiclassical gravity, is often disregarded for lack of a good candidate theory. The standard semiclassical theory suffers from fundamental inconsistencies (e.g., Schr\"odinger cat sources, faster-than-light communication and violation of the Born rule) which can only be ignored in simple typical situations. We harness the power of spontaneous localization models, historically constructed to solve the measurement problem in quantum mechanics, to build a consistent theory of (stochastic) semiclassical gravity in the Newtonian limit. Our model makes quantitative and potentially testable predictions: we recover the Newtonian pair potential up to a short distance cutoff (hence, we predict no one-particle self-interaction) and uncover an additional gravitational decoherence term which depends on the specifics of the underlying spontaneous localization model considered. We hint at a possible program to go past the Newtonian limit, towards a consistent general relativistic semiclassical gravity.
We argue that semiclassical gravity can be made consistent if quantum systems source gravity only when they participate in non-gravitational interactions that can lead to environment-induced decoherence, and which select conditional states that lead them to source such a field. If they do not participate in those interactions, systems do not contribute their stress-energy to the semiclassical equations, where regions lacking a gravitational field may remain flat. This proposal of conditional gravity is testable by probing the gravitational field sourced by systems, which should depend entirely on environment-induced decoherence in this context; by gravity not mediating entanglement in the Bose-Marletto-Vedral (BMV) experiment; and by how the reversibility of the initial state in this experiment would depend solely on this decoherence, distinguishing it from competing approaches. Our approach involves different theories. A distinct one involves chains of causally ordered interactions between quantum matter fields, which may show how gravity arises from QFT, and provide benefits to other areas of physics. To distinguish between the different theories that our approach allows for, and possibly test them, we present a generalization of the process operator and quantum causal models, which is applicable to quantum measurements in QFT implemented via the Fewster-Verch framework. However, we will also propose another approach. These different theories can be seen as arising from different ways quantum operations are classically controlled, since outcomes obtained along this chain determine which quantum operations are implemented next. We propose an experiment to test them using quantum circuits, which may allow us to probe how precisely gravity arises from quantum systems. We thus propose another application of quantum computers, which is to control the sourcing of gravity by quantum systems.