Many-body probes for quantum features of spacetime

TL;DR

This paper explores how correlated many-body systems can detect quantum features of spacetime by analyzing modifications in commutation relations, providing analytic solutions and numerical evidence of superquadratic scaling effects.

Contribution

It derives an analytic model for a light-mechanical oscillator system with modified commutation relations and demonstrates superquadratic scaling of non-classical phases in coupled oscillators.

Findings

Analytic derivation of dynamics with modified commutation relations.

Superquadratic scaling of non-classical phase in coupled oscillators.

Numerical evidence supporting the detectability of quantum spacetime features.

Abstract

Many theories of quantum gravity can be understood as imposing a minimum length scale the signatures of which can potentially be seen in precise table top experiments. In this work we inspect the capacity for correlated many body systems to probe non-classicalities of spacetime through modifications of the commutation relations. We find an analytic derivation of the dynamics for a single mode light field interacting with a single mechanical oscillator and with coupled oscillators to first order corrections to the commutation relations. Our solution is valid for any coupling function as we work out the full Magnus expansion. We numerically show that it is possible to have superquadratic scaling of a non-classical phase term, arising from the modification to the commutation relations, with coupled mechanical oscillators.