On the origin of force sensitivity in tests of quantum gravity with delocalised mechanical systems

Abstract

The detection of the quantum nature of gravity in the low-energy limit hinges on achieving an unprecedented degree of force sensitivity with mechanical systems. Against this background, we explore the relationship between the sensitivity of mechanical systems to external forces and the properties of the quantum states they are prepared in. We establish that the main determinant of the force sensitivity in pure quantum states is their spatial delocalisation and we link the force sensitivity to the rate at which two mechanical systems become entangled under a quantum force. We exemplify this at the hand of two commonly considered configurations. One that involves gravitationally interacting objects prepared in non-Gaussian states such as Schrödinger-cat states, where the generation of entanglement is typically ascribed to the accumulation of a dynamical phase between components in superposition. The other prepares particles in Gaussian states that are strongly squeezed in momentum and delocalised in position where entanglement generation is attributed to accelerations. We offer a unified description of these two arrangements using the phase-space representation and link their entangling rate to their force sensitivity, showing that both configurations get entangled at the same rate provided that they are equally delocalised in space. Our description in phase space and the established relation between force sensitivity and entanglement sheds light on the intricacies of why the equivalence between these two configurations holds, something that is not always evident in the literature, due to the distinct physical and analytical methods employed to study each of them. Notably, we demonstrate that while the conventional computation of entanglement via the dynamical phase remains accurate for Schrödinger-cat states, it yields erroneous estimations for systems in squeezed cat states.

Invited contribution to Contemporary Physics. 16 pages (+ bibliography), 6 figures

References in corpus (17)

• A Spin Entanglement Witness for Quantum Gravity
• Gravitationally-induced entanglement between two massive particles is sufficient evidence of quantum effects in gravity
• Levitodynamics: Levitation and control of microscopic objects in vacuum
• Gravitationally Mediated Entanglement: Newtonian Field vs. Gravitons
• Large Quantum Delocalization of a Levitated Nanoparticle using Optimal Control: Applications for Force Sensing and Entangling via Weak Forces
• Why Eppley and Hannah's Experiment Isn't
• Light Microscopy: An ongoing contemporary revolution
• Enhancing Gravitational Interaction between Quantum Systems by a Massive Mediator
• Quantum experiments with microscale particles
• Enhanced force sensitivity and entanglement in periodically driven optomechanics
• What gravity mediated entanglement can really tell us about quantum gravity
• On inference of quantization from gravitationally induced entanglement
• Gravity entanglement, quantum reference systems, degrees of freedom
• On the Significance of Interferometric Revivals for the Fundamental Description of Gravity
• Three little paradoxes: making sense of semiclassical gravity
• When Cavendish meets Feynman: A quantum torsion balance for testing the quantumness of gravity
• On tests of the quantum nature of gravitational interactions in presence of non-linear corrections to quantum mechanics

Cited by in corpus (8)

• Massive quantum systems as interfaces of quantum mechanics and gravity
• Testing the quantum nature of gravity without entanglement
• Dark Matter Searches with Levitated Sensors
• Classical theories of gravity produce entanglement
• Optically Hyperpolarized Materials for Levitated Optomechanics
• Angular Momentum Entanglement Mediated By General Relativistic Frame Dragging
• Quantum-to-Classical Transition via Single-Shot Generalized Measurements
• Beyond Entanglement: Diagnosing quantum mediator dynamics in gravitationally mediated experiments