Composite fermion theory of rapidly rotating two-dimensional bosons

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 ν = p/(p + 1), both by spectral analysis and by direct comparison with trial wavefunctions. 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 wavefunction.