Effects of Newtonian gravitational self-interaction in harmonically trapped quantum systems

Abstract

The Schrödinger-Newton equation has gained attention in the recent past as a nonlinear modification of the Schrödinger equation due to a gravitational self-interaction. Such a modification is expected from a fundamentally semi-classical theory of gravity, and can therefore be considered a test case for the necessity of the quantisation of the gravitational field. Here we provide a thorough study of the effects of the Schrödinger-Newton equation for a micron-sized sphere trapped in a harmonic oscillator potential. We discuss both the effect on the energy eigenstates and the dynamical behaviour of squeezed states, covering the experimentally relevant parameter regimes.

arXiv comment22 pages, 14 figures

References in corpus (12)

• Gravitation and quantummechanical localization of macroobjects
• Is Quantum Gravity Necessary?
• The Schrödinger-Newton equation and its foundations
• The Schrödinger-Newton equation as non-relativistic limit of self-gravitating Klein-Gordon and Dirac fields
• Macroscopic Quantum Mechanics in a Classical Spacetime
• Gravitationally induced inhibitions of dispersion according to the Schrödinger-Newton Equation
• Problems with the Newton-Schrödinger Equations
• Optomechanical test of the Schrödinger-Newton equation
• Schrödinger-Newton "collapse" of the wave function
• Centre-of-mass motion in multi-particle Schroedinger-Newton dynamics
• Gravitationally induced inhibitions of dispersion according to a modified Schrödinger-Newton equation for a homogeneous-sphere potential
• Crucial tests of macrorealist and semi-classical gravity models with freely falling mesoscopic nanospheres

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• Propagators in the Correlated Worldline Theory of Quantum Gravity
• Disfavoring the Schroedinger-Newton equation
• Correlations and signaling in the Schrödinger-Newton model
• Self-gravitational dephasing of quasi-classical Stern-Gerlach trajectories
• Probing the Schroedinger-Newton equation in a Stern-Gerlach interferometer
• Emergence of Classicality in Stern-Gerlach Experiment via Self-Gravity
• Newtonian self-gravity in trapped quantum systems and experimental tests
• Dephasing and inhibition of spin interference from semi-classical self-gravitation