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arXiv:1906.11184 · The European Physical Journal D

Entanglement dynamics of two mesoscopic objects with gravitational interaction

H. Chau Nguyen, Fabian Bernards

Published Apr 1, 2020• 45 citations
arXivHTMLPDF
DOI
10.1140/epjd/e2020-10077-8

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The gravitational interaction is generally considered to be too weak to be easily submitted to systematic experimental investigation in the quantum, microscopic, domain. In this paper we attempt to remedy this situation by considering the gravitational influence exerted by a crystalline nanosphere of mesoscopic size on itself, in the semi-classical, mean field, regime. We study in depth the self-localisation process induced by the corresponding non-linear potential of (gravitational) self-interaction. In particular, we characterize the stability of the associated self-collapsed ground state and estimate the magnitude of the corrections that are due to the internal structure of the object (this includes size-effects and corrections due to the discrete, atomic, structure of the sphere). Finally, we derive an approximated, gaussian, dynamics which mimics several essential features of the self-gravitating dynamics and, based on numerical results derived from this model, we propose a concrete experimental setting which we believe might, in the foreseeable future, reveal the existence of gravitational self-interaction effects.
The gravitational interaction is generally considered to be too weak to be easily submitted to systematic experimental investigation in the quantum, microscopic, domain.In this paper we attempt to remedy this situation by considering the gravitational influence exerted by a crystalline nanosphere of mesoscopic size on itself, in the semi-classical, mean field, regime.We study in depth the self-localisation process induced by the corresponding non-linear potential of (gravitational) self-interaction.In particular, we characterize the stability of the associated self-collapsed ground state and estimate the magnitude of the corrections that are due to the internal structure of the object (this includes size-effects and corrections due to the discrete, atomic, structure of the sphere).Finally, we derive an approximated, gaussian, dynamics which mimics several essential features of the selfgravitating dynamics and, based on numerical results derived from this model, we propose a concrete experimental setting which we believe might, in the foreseeable future, reveal the existence of gravitational self-interaction effects.
We analytically solve the entangling quantum dynamics of two interacting Stern-Gerlach Interferometers~(SGI). Each SGI exploits an operator-valued force applied by a qubit to create and recombine a non-Gaussian state of matter. The entangling phase between the two qubits generated by the leading-order gravitational interaction of the massive degrees of freedom is found to be mass-independent, both for unitary and open dynamics, irrespective of the temperature and squeezing of the initial states. Further, we show that the solution of the four interferometric paths reveals that the mere presence of the interaction does not allow for a perfect recombination of the centre of mass. This second-order effect, alongside higher-order interaction terms, can be used to bound the mass from above and below, thus restricting the experiment's regime to mesoscopic masses. By solving the open dynamics which includes diffusion and dephasing with initial squeezed thermal states, the bounds are tightened by the inclusion of realistic experimental noise. We discuss diamagnetic levitated masses with embedded NV-centres as a specific physical implementation.