Fractional Spin Hall Effect in Atomic Bose Gases

TL;DR

This paper introduces the fractional spin Hall effect in atomic Bose gases by coupling pseudospin states to optical fields, revealing novel fractional statistics distinct from quantum Hall states.

Contribution

It extends the optically induced spin Hall effect to interacting bosonic systems, proposing new fractional states with unique symmetry and statistics.

Findings

Identifies two types of ground states with fractional wave functions.

Discovers fractional statistics different from FQH states.

Proposes a method to distinguish FSHE from FQH regimes.

Abstract

We propose fractional spin hall effect (FSHE) by coupling pseudospin states of cold bosonic atoms to optical fields. The present scheme is an extension to interacting bosonic system of the recent work \cite{liu,zhu} on optically induced spin hall effect in non-interacting atomic system. The system has two different types of ground states. The 1st type of ground state is a 1/3-factor Laughlin function, and has the property of chiral - anti-chiral interchange antisymmetry, while the 2nd type is shown to be a 1/4-factor wave function with chiral - anti-chiral symmetry. The fractional statistics corresponding to the fractional spin Hall states are studied in detail, and are discovered to be different from that corresponding to the fractional quantum Hall (FQH) states. Therefore the present FSHE can be distinguished from FQH regime in the measurement.