Testing the weak equivalence principle for nonclassical matter with torsion balances

TL;DR

This paper proposes a novel method to test the weak equivalence principle using quantum superpositions in torsion balances, analyzing both mean and variance of acceleration to detect potential violations.

Contribution

It introduces a quantum model for WEP testing with superposition states and a dynamical setup to improve detection of violations.

Findings

Variance of acceleration reveals WEP violations due to quantum coherence.

A torsion balance setup can measure mean and variance of torque to test WEP.

Time-dependent gravitational fields enhance sensitivity to violations.

Abstract

We propose tests of the weak equivalence principle (WEP) using a torsion balance, in which superposition of energy eigenstates are created in a controllable way for the test masses. After general considerations on the significance of tests of the WEP using quantum states and the need for considering inertial and gravitational masses as operators, we develop a model to derive the matrix elements of the free-fall operator, showing that the variance of the acceleration operator, in addition to its mean, enables estimation of violations of the WEP due to quantum coherence in a way that is robust with respect to shot-to-shot fluctuations. Building on this analysis, we demonstrate how the validity of the WEP may be tested in a torsion balance setup, by accessing the mean and variance of a torque operator we introduce and quantize. Due to the long acquisition times of the signal as compared to the timescale on which coherent superposition states may survive, we further propose a dynamical setting, where the torsion balance is subject to a time-dependent gravitational field, and measurements of angular acceleration encode possible violations of the WEP.