Composite fermion theory of rapidly rotating two-dimensional bosons

N. Regnault 1, C. C. Chang 2, Th. Jolicoeur 1, 3, J. K. Jain 2

Journal of Physics B 39 (2006) S89-S99

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.

  • 1. Laboratoire Pierre Aigrain (LPA),
    CNRS : UMR8551 – Université Paris VI – Pierre et Marie Curie – Université Paris VII – Paris Diderot – Ecole Normale Supérieure de Paris – ENS Paris
  • 2. Department of Physics, 104 Davey Laboratory,
    The Pennsylvania State University
  • 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
    CNRS : UMR8626 – Université Paris XI – Paris Sud
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