Pairing in ultracold Fermi gases in the lowest Landau level

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 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.

arXiv comment12 pages, 9 figs (best viewed in color), published version with additional evidence for a non-Abelian spin singlet state at filling nu=2/3

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Cited by in corpus (5)

• Infinite density matrix renormalization group for multicomponent quantum Hall systems
• The structure of spinful quantum Hall states: a squeezing perspective
• Creating a bosonic fractional quantum Hall state by pairing fermions
• Two-dimensional fermionic superfluids, pairing instability and vortex liquids in the absence of time reversal symmetry
• Are smooth pseudopotentials a good choice for representing short-range interactions?