Fractional quantum Hall states of a Bose gas with spin-orbit coupling

TL;DR

This paper investigates fractional quantum Hall states in a spin-orbit coupled Bose gas under artificial gauge fields, revealing how degeneracies and interactions influence the emergence and stability of various quantum Hall phases.

Contribution

It introduces a detailed analysis of Landau level crossings and their impact on quantum Hall phases in spin-orbit coupled Bose gases, including the characterization of states at different filling factors.

Findings

Degeneracy points lead to the disappearance of incompressible phases at =1/2.

Gapped phases are observed at =3/2 and =2.

Connection to non-Abelian spin singlet states at =2/3 and =4/3.

Abstract

We study the fractional quantum Hall phases of a pseudospin-1/2 Bose gas in an artificial gauge field. In addition to an external magnetic field, the gauge field also mimics an intrinsic spin-orbit coupling of the Rashba type. While the spin degeneracy of the Landau levels is lifted by the spin-orbit coupling, the crossing of two Landau levels at certain coupling strengths gives rise to a new degeneracy. We therefore take into account two Landau levels, and perform exact diagonalization of the many-body Hamiltonian. We study and characterize the quantum Hall phases which occur in the vicinity of the degeneracy point. Notably, we describe the different states appearing at the Laughlin filling, \nu=1/2. While for this filling incompressible phases disappear at the degeneracy point, denser systems at \nu=3/2 and \nu=2 are found to be clearly gapped. For filling factors \nu=2/3 and \nu=4/3, we discuss the connection of the exact ground state to the non-Abelian spin singlet states, obtained as the ground state of k+1 body contact interactions.