Enhancement of the effects due to the Schr\"odinger-Newton equation

TL;DR

This paper proposes a method to amplify the subtle effects of the Schrödinger-Newton equation in levitated mechanical oscillators by modulating the trapping frequency, making experimental tests of semiclassical gravity more feasible.

Contribution

It introduces a novel modulation protocol to enhance SN effects, enabling potential experimental verification within current magnetic levitation technology.

Findings

SN effects can be amplified by up to six orders of magnitude.

The protocol is feasible with existing magnetic levitation setups.

Measurable quantities like position variance can distinguish SN effects.

Abstract

The Schr\"odinger-Newton (SN) equation introduces a nonlinear self-gravitational term to the standard Schr\"odinger equation, offering a paradigmatic model for semiclassical gravity. However, the small deviations it predicts from standard quantum mechanics pose significant experimental challenges. We propose a novel method to amplify such deviations through periodic modulation of the trapping frequency in a levitated mechanical oscillator. We identify specific regimes where the SN-induced effects on the dynamics of second moments are significantly enhanced-by up to six orders of magnitude compared to unmodulated setups. We show that this protocol remains feasible within current magnetic levitation technologies and enables distinguishability between standard and SN dynamics using measurable quantities such as the position variance. Our results pave the way for a viable experimental test of the SN equation, offering a new route to probe the interface between quantum mechanics and gravity.