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arXiv:1601.03026 · Scientific Reports

Novel p-wave superfluids of fermionic polar molecules

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

Published Jun 9, 2016• 28 citations
arXivHTMLPDF

Abstract

Recently suggested subwavelength lattices offer remarkable prospects for the observation of novel superfluids of fermionic polar molecules. It becomes realistic to obtain a topological p-wave superfluid of microwave-dressed polar molecules in 2D lattices at temperatures of the order of tens of nanokelvins, which is promising for topologically protected quantum information processing. Another foreseen novel phase is an interlayer p-wave superfluid of polar molecules in a bilayer geometry.

DOI
10.1038/srep27448

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Recently suggested subwavelength lattices offer remarkable prospects for the observation of novel superfluids of fermionic polar molecules. It becomes realistic to obtain a topological p-wave superfluid of microwave-dressed polar molecules in 2D lattices at temperatures of the order of tens of nanokelvins, which is promising for topologically protected quantum information processing. Another foreseen novel phase is an interlayer p-wave superfluid of polar molecules in a bilayer geometry.
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.
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 consider fermionic polar molecules in a bilayer geometry where they are oriented perpendicularly to the layers, which permits both low inelastic losses and superfluid pairing. The dipole-dipole interaction between molecules of different layers leads to the emergence of interlayer superfluids. The superfluid regimes range from BCS-like fermionic superfluidity with a high Tc to Bose-Einstein (quasi-)condensation of interlayer dimers, thus exhibiting a peculiar BCS-Bose-Einstein condensation crossover. We show that one can cover the entire crossover regime under current experimental conditions.
We systematically investigate the topological properties of spin polarized Rydberg-dressed fermionic atoms loaded in a bilayer optical lattice. Through tuning the Rydberg coupling strength and the interlayer tunneling amplitude, we identify different types of topological superfluid states generated from the interlayer pairing and relative pairing phase modulation of the coupled two-dimensional ppp-wave superfluids. These phases include gapped/gapless with/without time-reversal symmetry. One of the most interesting states is a gapless paired topological superfluid with both the time-reversal symmetry and particle-hole symmetry, which is a realization of a DIII gapless topological superconductor. The flexibility of experimental manipulation in such Rydberg-dressed fermionic systems therefore becomes a promising system for realizing interesting topological superfluids.
Recent experimental progress in producing ultracold polar molecules with a net electric dipole moment opens up possibilities for realizing quantum phases governed by the long-range and anisotropic dipole-dipole interactions. In this work we predict the existence of experimentally observable broken-symmetry states with spontaneous interlayer coherence in cold polar molecule bilayers. These exotic states, which are manifestations of collective bilayer quantum entanglement, appear due to strong repulsive interlayer interactions and exhibit properties of superfluids, ferromagnets, and excitonic condensates.