Weak values obtained from mass-energy equivalence

TL;DR

This paper explores how weak measurement techniques applied to relativistic cold atoms can reveal subtle effects of mass-energy equivalence on atomic momentum, offering a novel experimental approach.

Contribution

It introduces a method to measure weak effects of mass-energy equivalence using weak measurement on cold atoms, linking internal energy to external momentum.

Findings

Weak value can alter atomic momentum uncertainty

Method enables experimental detection of mass-energy effects

Demonstrates coupling between internal energy and external motion

Abstract

Quantum weak measurement, measuring some observable quantities within the selected subensemble of the entire quantum ensemble, can produce many interesting results such as the superluminal phenomena. An outcome of such a measurement is the weak value which has been applied to amplify some weak signals of quantum interactions in lots of previous references. Here, we apply the weak measurement to the system of relativistic cold atoms. According to mass-energy equivalence, the internal energy of an atom will contribute its rest mass and consequently the external momentum of center of mass. This implies a weak coupling between the internal and external degrees of freedom of atoms moving in the free space. After a duration of this coupling, a weak value can be obtained by post-selecting an internal state of atoms. We show that, the weak value can change the momentum uncertainty of atoms and consequently help us to experimentally measure the weak effects arising from mass-energy equivalence.