Composite fermion theory of rapidly rotating two-dimensional bosons

TL;DR

This paper applies composite fermion theory to rapidly rotating 2D bosons, demonstrating their fractional quantum Hall-like states and revealing a transition to paired states described by the Moore-Read wave function.

Contribution

It extends composite fermion theory to bosonic systems, providing numerical evidence and analyzing the transition to paired states in rapidly rotating 2D bosons.

Findings

Composite fermions form in rotating bosons at specific filling fractions.

Bosons exhibit statistical transmutation into composite fermions.

Residual interactions lead to paired states described by Moore-Read wave functions.

Abstract

Ultracold neutral bosons in a rapidly rotating atomic trap have been predicted to exhibit fractional quantum Hall-like states. We describe how the composite fermion theory, used in the description of the fractional quantum Hall effect for electrons, can be applied to interacting bosons. Numerical evidence supporting the formation of composite fermions, each being the bound state of a boson and one flux quantum, is shown for filling fractions of the type nu=p/(p+1), both by spectral analysis and by direct comparison with trial wave functions. The rapidly rotating system of two-dimensional bosons thus constitutes an interesting example of "statistical transmutation," with bosons behaving like composite fermions. We also describe the difference between the electronic and the bosonic cases when p approaches infinity. Residual interactions between composite fermions are attractive in this limit, resulting in a paired composite-fermion state described by the Moore-Read wave function.