Pairing in ultracold Fermi gases in the lowest Landau level

G. Möller, Th. Jolicoeur, and N. Regnault
Phys. Rev. A 79, 033609 – Published 11 March 2009

Abstract

We study a rapidly rotating gas of unpolarized spin-1/2 ultracold fermions in the two-dimensional regime when all atoms reside in the lowest Landau level. Due to the presence of the spin degree of freedom both s-wave and p-wave interactions are allowed at ultralow temperatures. We investigate the phase diagram of this system as a function of the filling factor in the lowest Landau level and in terms of the ratio between s- and p-wave interaction strengths. We show that the presence of attractive interactions induces a wide regime of phase separation with formation of maximally compact droplets that are either fully polarized or composed of spin-singlets. In the regime with no phase separation, we give evidence for fractional quantum Hall states. Most notably, we find two distinct singlet states at the filling ν=2/3 for different interactions. One of these states is accounted for by the composite fermion theory, while the other one is a paired state for which we identify two competing descriptions with different topological structures. This paired state may be an Abelian liquid of composite spin-singlet Bose molecules with Laughlin correlations. Alternatively, it may be a known non-Abelian paired state, indicated by good overlaps with the corresponding trial wave function. By fine tuning of the scattering lengths it is possible to create the non-Abelian critical Haldane-Rezayi state for ν=1/2 and the permanent state of Moore and Read for ν=1. For purely repulsive interactions, we also find evidence for a gapped Halperin state at ν=2/5.

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  • Received 9 July 2008

DOI:https://doi.org/10.1103/PhysRevA.79.033609

©2009 American Physical Society

Authors & Affiliations

G. Möller1, Th. Jolicoeur2, and N. Regnault3

  • 1Cavendish Laboratories, J.J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
  • 2Laboratoire de Physique Théorique et Modèles Statistiques, Université Paris-Sud, 91405 Orsay, France
  • 3Département de Physique, Laboratoire Pierre Aigrain, ENS, CNRS, 24 rue Lhomond, Paris F-75005, France

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Issue

Vol. 79, Iss. 3 — March 2009

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