title: 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.
authors.affiliation: Department of Physics, University of Trieste, 34151 Miramare-Trieste, Italy.|Istituto Nazionale di Fisica Nucleare, Sezione di Trieste, Via Valerio 2, 34127 Trieste, Italy.
authors.forename: André
authors.initials: A
authors.lastname: Großardt
authors.affiliation: School of Physics and Astronomy, University of Southampton, SO17 1BJ, United Kingdom.|Department of Physics, College of Science, Swansea University, Swansea SA2 8PP, United Kingdom.
authors.forename: James
authors.initials: J
authors.lastname: Bateman
authors.affiliation: School of Physics and Astronomy, University of Southampton, SO17 1BJ, United Kingdom.
authors.forename: Hendrik
authors.initials: H
authors.lastname: Ulbricht
authors.affiliation: Department of Physics, University of Trieste, 34151 Miramare-Trieste, Italy.|Istituto Nazionale di Fisica Nucleare, Sezione di Trieste, Via Valerio 2, 34127 Trieste, Italy.
authors.forename: Angelo
authors.initials: A
authors.lastname: Bassi