Bound State of an Electron on a $^4$He Superfluid Droplet as a Test for Quantum Gravity

TL;DR

This paper explores the potential for observable quantum gravitational effects in a system where an electron is bound to a superfluid helium droplet, calculating the first-order correction to binding energy due to graviton exchange.

Contribution

It introduces a novel system involving helium droplets to test quantum gravity effects and computes the first-order radiative correction to the electron's binding energy in this context.

Findings

Relative difference in binding energies is about 1% for two helium droplets differing by one microgram.

First-order radiative correction due to graviton exchange is calculable using standard quantum-field methods.

The proposed system could serve as a testbed for measurable quantum gravitational effects.

Abstract

We address the problem of finding a system in which there would be measurable quantum gravitational effects. Following standard quantum-field methods, we have calculated the first-order radiative correction of graviton exchange on the binding energy of an electron with an ultra cold superfluid droplet of $^4$He with mass about the Planck mass. For two $^4$He droplets with a mass difference of about one microgram, we show that the relative difference in the binding energies is about one percent.