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arXiv:2107.05985 · Classical and Quantum Gravity

Dephasing and inhibition of spin interference from semi-classical self-gravitation

André Großardt

Published Nov 4, 2021• 5 citations
arXivHTMLPDF

Abstract

Abstract We present a detailed derivation of a model to study effects of self-gravitation from semi-classical gravity, described by the Schrödinger–Newton equation, employing spin superposition states in inhomogeneous magnetic fields, as proposed recently for experiments searching for gravity induced entanglement. Approximations for the experimentally relevant limits are discussed. Results suggest that spin interferometry could provide a more accessible route towards an experimental test of quantum aspects of gravity than both previous proposals to test semi-classical gravity and the observation of gravitational spin entanglement.

DOI
10.1088/1361-6382/ac36a6

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Abstract We present a detailed derivation of a model to study effects of self-gravitation from semi-classical gravity, described by the Schrödinger–Newton equation, employing spin superposition states in inhomogeneous magnetic fields, as proposed recently for experiments searching for gravity induced entanglement. Approximations for the experimentally relevant limits are discussed. Results suggest that spin interferometry could provide a more accessible route towards an experimental test of quantum aspects of gravity than both previous proposals to test semi-classical gravity and the observation of gravitational spin entanglement.
Abstract Bose et al and Marletto and Vedral proposed an experiment to test whether gravity can induce entanglement between massive systems, arguing that the capacity to do so would imply the quantum nature of gravity. In this work, a class of semi-classical models is examined that treat gravity classically, through some potential in the Schrödinger equation, and it is shown that these models do not generate entanglement. This class includes the Newton–Schrödinger model, where gravity is sourced by the wave function, the Bohmian analogue, where gravity is sourced by actual point-particles, and an interpolating model proposed by Döner and Großardt. These models are analyzed in the context of the proposed experiment and contrasted with the standard Newtonian potential, which does generate entanglement.
The Schr\"odinger-Newton equation has frequently been studied as a nonlinear modification of the Schr\"odinger equation incorporating gravitational self-interaction. However, there is no evidence yet as to whether nature actually behaves this way. This work investigates a possible way to experimentally test gravitational self-interaction. The effect of self-gravity on the interference of massive particles is studied by numerically solving the Schr\"odinger-Newton equation for a particle passing through a double-slit. The results show that the presence of gravitational self-interaction has an effect on the fringe width of the interference that can be tested in matter-wave interferometry experiments. Notably, this approach can distinguish between gravitational self-interaction and environment-induced decoherence, as the latter does not affect the fringe width. This result will also provide a way to test if gravity requires to be quantized on the scale of ordinary quantum mechanics.
No experimental evidence exists, to date, whether or not the gravitational field must be quantised. Theoretical arguments in favour of quantisation are inconclusive. The most straightforward alternative to quantum gravity, a coupling between classical gravity and quantum matter according to the semi-classical Einstein equations, yields a nonlinear modification of the Schrödinger equation. Here, effects of this so-called Schrödinger-Newton equation are discussed, which allow for technologically feasible experimental tests.
Gravity-induced entanglement has been proposed as a method for testing the non-classical nature of gravity via tabletop experiments. While most existing proposals are restricted to the Newtonian limit, the frame dragging effect offers access to genuinely post-Newtonian features of the gravitational interaction and remains comparatively less explored. Here, we study gravity-induced entanglement generated by frame dragging in an interferometric setting and compute the entanglement phase between the rotational degrees of freedom of a source mass and the paths of a particle in two complementary ways: (i) via Schrödinger evolution with a quantized Lense-Thirring Hamiltonian in the large angular momentum limit, and (ii) via the on-shell action of linearized quantum gravity within the stationary phase approximation. Both approaches yield the same entanglement phase, consistent with the proper time difference between the interferometer arms. The path integral derivation further reveals how gravitational retardation modifies the entanglement phase, thereby making the local, relativistically causal linearized-gravity description explicit. Under the standard locality/mediator assumptions used in existing arguments, the resulting entanglement would witness non-classicality of the gravitational interaction.
Abstract The experimental observation of a clear quantum signature of gravity is believed to be out of the grasp of current technology. However, several recent promising proposals to test the possible existence of non-classical features of gravity seem to be accessible by the state-of-art table-top experiments. Among them, some aim at measuring the gravitationally induced entanglement between two masses which would be a distinct non-classical signature of gravity. We explicitly study, in two of these proposals, the effects of decoherence on the system’s dynamics by monitoring the corresponding degree of entanglement. We identify the required experimental conditions necessary to perform successfully the experiments. In parallel, we account also for the possible effects of the continuous spontaneous localization (CSL) model, which is the most known among the models of spontaneous wavefunction collapse. We find that any value of the parameters of the CSL model would completely hinder the generation of gravitationally induced entanglement.
The interplay between gravity and quantum mechanics remains a central open problem in modern physics. In this talk, I will discuss how a fundamentally classical, local gravitational interaction necessarily induces a diffusive modification of quantum dynamics. This diffusion leads to measurable noise even in the classical regime and provides a novel, experimentally accessible signature that does not require macroscopic quantum superpositions. I will derive a lower bound on the gravitational noise required to prevent entanglement generation and outline an experimental proposal based on torsion pendulums to test this bound. Next, I will consider the Schrödinger-Newton equation—a paradigmatic model of semiclassical gravity—which predicts nonlinear, self-induced gravitational effects. I will show how a periodic modulation of the trap frequency in levitated mechanical oscillators can amplify these otherwise negligible deviations by up to six orders of magnitude. The protocol remains feasible within current technologies and opens new pathways to experimentally test the SN dynamics through precise monitoring of the system’s position variance.