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arXiv:1711.01849 · AIP conference proceedings

Superfluidity of identical fermions in an optical lattice: Atoms and polar molecules

Aleksey K. Fedorov, Vladimir I. Yudson, Georgy V. Shlyapnikov

Published Jan 1, 2018• 0 citations
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Abstract

In this work we discuss the emergence of p-wave superfluids of identical fermions in 2D lattices. The optical lattice potential manifests itself in an interplay between an increase in the density of states on the Fermi surface and the modification of the fermion-fermion interaction (scattering) amplitude. The density of states is enhanced due to an increase of the effective mass of atoms. In deep lattices, for short-range interacting atoms the scattering amplitude is strongly reduced compared to free space due to a small overlap of wavefunctions of fermions sitting in the neighboring lattice sites, which suppresses the p-wave superfluidity. However, we show that for a moderate lattice depth there is still a possibility to create atomic p-wave superfluids with sizable transition temperatures. The situation is drastically different for fermionic polar molecules. Being dressed with a microwave field, they acquire a dipole-dipole attractive tail in the interaction potential. Then, due to a long-range character of the dipole-dipole interaction, the effect of the suppression of the scattering amplitude in 2D lattices is absent. This leads to the emergence of a stable topological px + ipy superfluid of identical microwave-dressed polar molecules.

DOI
10.1063/1.5025460

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In this work we discuss the emergence of p-wave superfluids of identical fermions in 2D lattices. The optical lattice potential manifests itself in an interplay between an increase in the density of states on the Fermi surface and the modification of the fermion-fermion interaction (scattering) amplitude. The density of states is enhanced due to an increase of the effective mass of atoms. In deep lattices, for short-range interacting atoms the scattering amplitude is strongly reduced compared to free space due to a small overlap of wavefunctions of fermions sitting in the neighboring lattice sites, which suppresses the p-wave superfluidity. However, we show that for a moderate lattice depth there is still a possibility to create atomic p-wave superfluids with sizable transition temperatures. The situation is drastically different for fermionic polar molecules. Being dressed with a microwave field, they acquire a dipole-dipole attractive tail in the interaction potential. Then, due to a long-range character of the dipole-dipole interaction, the effect of the suppression of the scattering amplitude in 2D lattices is absent. This leads to the emergence of a stable topological px + ipy superfluid of identical microwave-dressed polar molecules.
We discuss the emergence of ppp-wave superfluidity of identical atomic fermions in a two-dimensional optical lattice. The optical lattice potential manifests itself in an interplay between an increase in the density of states on the Fermi surface and the modification of the fermion-fermion interaction (scattering) amplitude. The density of states is enhanced due to an increase of the effective mass of atoms. In deep lattices the scattering amplitude is strongly reduced compared to free space due to a small overlap of wave functions of fermions sitting in the neighboring lattice sites, which suppresses the ppp-wave superfluidity. However, for moderate lattice depths the enhancement of the density of states can compensate the decrease of the scattering amplitude. Moreover, the lattice setup significantly reduces inelastic collisional losses, which allows one to get closer to a ppp-wave Feshbach resonance. This opens possibilities to obtain the topological px+ipy{p}_{x}+i{p}_{y}px​+ipy​ superfluid phase, especially in the recently proposed subwavelength lattices. We demonstrate this for the two-dimensional version of the Kronig-Penney model allowing a transparent physical analysis.
We study a system of ultracold fermionic polar molecules in a two-dimensional square lattice interacting via both the long-range dipole-dipole interaction and a short-range on-site attractive interaction. Singlet-superfluid, change density wave, and supersolid phases are found to exist in the system. We map out the zero-temperature phase diagram and find that the supersolid phase is considerably stabilized by the dipole-dipole interaction and thus can exist over a large region of filling factors. We study the melting of the supersolid phase with increasing temperature, map out a finite-temperature phase diagram of the system at fixed filling, and determine the parameter region where the supersolid phase can possibly be observed in experiments.
We show that single-component fermionic polar molecules confined to a 2D geometry and dressed by a microwave field may acquire an attractive 1/r(3) dipole-dipole interaction leading to superfluid p-wave pairing at sufficiently low temperatures even in the BCS regime. The emerging state is the topological p(x) + ip(y) phase promising for topologically protected quantum information processing. The main decay channel is via collisional transitions to dressed states with lower energies and is rather slow, setting a lifetime of the order of seconds at 2D densities approximately 10(8) cm(-2).
We discuss the topological px+ipy{p}_{x}+{\mathit{ip}}_{y}px​+ipy​ superfluid phase in a two-dimensional (2D) gas of single-component fermionic polar molecules dressed by a circularly polarized microwave field. This phase emerges because the molecules may interact with each other via a potential V0(r){V}_{0}(r)V0​(r) that has an attractive dipole-dipole 1/r31/{r}^{3}1/r3 tail, which provides ppp-wave superfluid pairing at fairly high temperatures. We calculate the amplitude of elastic ppp-wave scattering in the potential V0(r){V}_{0}(r)V0​(r) taking into account both the anomalous scattering due to the dipole-dipole tail and the short-range contribution. This amplitude is then used for the analytical and numerical solution of the renormalized BCS gap equation which includes the second-order Gor'kov-Melik-Barkhudarov corrections and the correction related to the effective mass of the quasiparticles. We find that the critical temperature Tc{T}_{c}Tc​ can be varied within a few orders of magnitude by modifying the short-range part of the potential V0(r){V}_{0}(r)V0​(r). The decay of the system via collisional relaxation of molecules to dressed states with lower energies is rather slow due to the necessity of a large momentum transfer. The presence of a constant transverse electric field reduces the inelastic rate, and the lifetime of the system can be of the order of seconds even at 2D densities  109~{10}^{9} 109 cm${}^{\ensuremath{-}2}$. This leads to Tc{T}_{c}Tc​ of up to a few tens of nanokelvins and makes it realistic to obtain the topological px+ipy{p}_{x}+{\mathit{ip}}_{y}px​+ipy​ phase in experiments with ultracold polar molecules.
Abstract In this manuscript, we discuss the emergence of p-wave superfluidity in a dipolar Fermi gas confined in a double layer array of parallel optical lattices in two dimensions. The dipole moments of the molecules placed at the sites of the optical lattices, separated a distance L and pointing in opposite directions produce an effective attractive interaction among them, except between those dipoles situated one on top of the other. Such interaction between dipoles is precisely the origin of the non-conventional superfluid state. We present the analysis for the ground state of the many-body system within the mean-field scheme. In particular, we study the stable regions, as a function of the system parameters, namely the effective interaction between dipoles and the filling factor n, for which the superfluid state can exist. Following the BKT scheme, we estimate the critical temperature of the superfluid state.