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

TL;DR

This paper investigates how gravitational self-interaction, modeled by the Schrödinger-Newton equation, influences the energy states and dynamics of a micron-sized quantum system in a harmonic trap, testing semi-classical gravity theories.

Contribution

It provides a detailed analysis of Schrödinger-Newton effects on trapped quantum systems, bridging theoretical predictions with experimental regimes.

Findings

Gravitational self-interaction modifies energy eigenstates.

Dynamical behavior of squeezed states is affected.

Results are relevant for experimental tests of semi-classical gravity.

Abstract

The Schr\"odinger-Newton equation has gained attention in the recent past as a nonlinear modification of the Schr\"odinger 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 Schr\"odinger-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.