Pairing in ultracold Fermi gases in the lowest Landau level

Details Pairing in ultracold Fermi gases in the lowest Landau level Pairing in ultracold Fermi gases in the lowest Landau level

2008-07-07

arxiv.org/abs/0807.1034v2

Physical Review A79, 033609 (2009)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

12 pages, 9 figs (best viewed in color), published version with additional evidence for a non-Abelian spin singlet state at fi

Scientific paper

10.1103/PhysRevA.79.033609

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 nu =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 structure. 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 wavefunction. By fine tuning of the scattering lengths it is possible to create the non-Abelian critical Haldane-Rezayi state for nu =1/2 and the permanent state of Moore and Read for nu =1. For purely repulsive interactions, we also find evidence for a gapped Halperin state at nu=2/5.

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