Fractional angular momentum in cold atom systems

TL;DR

This paper theoretically demonstrates that pairs of particles in a fractional quantum Hall state can exhibit fractional relative angular momentum, which can be detected through pair correlation measurements in cold atom systems.

Contribution

It introduces the concept of fractional angular momentum in cold atom systems and proposes a method for its experimental detection, linking it to fractional braid statistics and effective magnetic fields.

Findings

Fractional angular momentum can be realized in cold atom systems.

Measurement of pair correlation functions can reveal fractionalization.

Evidence for fractional braid statistics and effective magnetic fields.

Abstract

The quantum statistics of bosons or fermions are manifest through even or odd relative angular momentum of a pair. We show theoretically that, under certain conditions, a pair of certain test particles immersed in a fractional quantum Hall state possesses, effectively, a fractional relative angular momentum, which can be interpreted in terms of fractional braid statistics. We propose that the fractionalization of the angular momentum can be detected directly through the measurement of the pair correlation function in rotating ultra-cold atomic systems in the fractional quantum Hall regime. Such a measurement will also provide direct evidence for the effective magnetic field, resulting from Berry phases arising from attached vortices, and of excitations with fractional particle number, analogous to fractional charge of electron fractional quantum Hall effect.