Quantum nature of gravity in self-bound quantum droplets

TL;DR

This paper investigates the quantum nature of gravity using ultracold quantum droplets, deriving a generalized uncertainty principle and placing bounds on quantum gravity parameters based on experimental data.

Contribution

It introduces a novel approach to test quantum gravity effects via self-bound quantum droplets and derives a generalized uncertainty principle relevant to this system.

Findings

Derived a generalized uncertainty principle for quantum droplets.

Placed bounds on quantum gravity parameters using experimental data.

Improved upper bounds on the generalized uncertainty principle parameters.

Abstract

We explore the possibility of testing the quantum nature of the gravitational field with an ultracold self-bound quantum droplet of one-dimensional Bose-Bose mixtures. To this end, we solve variationally and numerically the underlying generalized Gross-Pitaevskii equation which includes the effects of quadratic and cubic nonlinearities. We derive the associated generalized uncertainty principle and its corresponding minimal length. The obtained modified uncertainty relation enables us to search for the quantum gravity signatures in both small and large droplets. We place bounds on the parameter using existing experimental data from recent experiment of dilute droplets of potassium. Improved upper bounds on the generalized uncertainty principle parameters are found from our analysis.