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arXiv:1103.3859 · Physical Review A

Topological p x + ip y superfluid phase of fermionic polar molecules

Jesper Levinsen, Nigel R. Cooper, Georgy V. Shlyapnikov

Published Jul 7, 2011• 84 citations
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Abstract

We discuss the topological ${p}_{x}+{\mathit{ip}}_{y}$ 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 ${V}_{0}(r)$ that has an attractive dipole-dipole $1/{r}^{3}$ tail, which provides $p$-wave superfluid pairing at fairly high temperatures. We calculate the amplitude of elastic $p$-wave scattering in the potential ${V}_{0}(r)$ 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 ${T}_{c}$ can be varied within a few orders of magnitude by modifying the short-range part of the potential ${V}_{0}(r)$. 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 $~{10}^{9}$ cm${}^{\ensuremath{-}2}$. This leads to ${T}_{c}$ of up to a few tens of nanokelvins and makes it realistic to obtain the topological ${p}_{x}+{\mathit{ip}}_{y}$ phase in experiments with ultracold polar molecules.

DOI
10.1103/physreva.84.013603

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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{}^{\ensuremath{-}2}\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.
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).
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 study Fermi liquid properties of a weakly interacting 2D gas of single-component fermionic polar molecules with dipole moments ddd oriented perpendicularly to the plane of their translational motion. This geometry allows the minimization of inelastic losses due to chemical reactions for reactive molecules and, at the same time, provides a possibility of a clear description of many-body (beyond mean field) effects. The long-range character of the dipole-dipole repulsive interaction between the molecules, which scales as 1/r31/r^31/r3 at large distances rrr, makes the problem drastically different from the well-known problem of the two-species Fermi gas with repulsive contact interspecies interaction. We solve the low-energy scattering problem and develop a many-body perturbation theory beyond the mean field. The theory relies on the presence of a small parameter kFr∗k_Fr_*kF​r∗​, where kFk_FkF​ is the Fermi momentum, and r∗=md2/ℏ2r_*=md^2/\hbar^2r∗​=md2/ℏ2 is the dipole-dipole length, with mmm being the molecule mass. We obtain thermodynamic quantities as a series of expansion up to the second order in kFr∗k_Fr_*kF​r∗​ and argue that many-body corrections to the ground-state energy can be identified in experiments with ultracold molecules, like it has been recently done for ultracold fermionic atoms. Moreover, we show that only many-body effects provide the existence of zero sound and calculate the sound velocity.
Where Is the ppp-Wave Superfluid? Correlated Phase Diagram of Microwave-Shielded Polar Molecules
Chiral px ⁣± ⁣ipyp_x\!\pm\! i p_ypx​±ipy​ superfluidity in fermionic polar molecules offers a direct route to topological quantum matter with non-Abelian excitations, yet the parameter regime in which pairing survives strong correlations and competing instabilities has remained unresolved. Here we determine this regime for microwave-shielded polar molecules. Under tight confinement along the zzz direction, the microscopic molecular interaction collapses onto a universal quasi-two-dimensional form specified by an interaction length σσσ, defined as the position of its attractive minimum, and a single dimensionless coupling. We combine Fermi-hypernetted-chain Euler--Lagrange theory with correlated-basis pairing theory, thereby treating the correlation hole, density response, stability of the homogeneous fluid, and ppp-wave pairing within one framework. The largest pairing gap occurs immediately on the stable side of a long-wavelength spinodal instability at a two-dimensional density 4×10−2/σ24\times10^{-2}/σ^24×10−2/σ2. Mapping this universal regime onto microscopic shielding schemes exposes an intrinsic limitation of single-microwave dressing: weakening the attraction to the optimal pairing range simultaneously weakens collisional shielding. Dual-microwave dressing removes this constraint by compensating the long-range attraction while retaining a large repulsive core. Imposing explicit requirements on collisional loss, confinement, and microwave-amplitude stability, we identify the regime of molecular mass and dipole moment favorable for ppp-wave superfluidity and determine experimentally realistic microwave and confinement conditions for its realization. These results turn the search for molecular ppp-wave superfluidity into a quantitative optimization problem and define a route toward the topological weak-pairing phase.
We study Fermi-liquid properties of a weakly interacting two-dimensional gas of single-component fermionic polar molecules with dipole moments ddd oriented perpendicularly to the plane of their translational motion. This geometry allows the minimization of inelastic losses due to chemical reactions for reactive molecules and, at the same time, provides a possibility of a clear description of many-body (beyond mean-field) effects. The long-range character of the dipole-dipole repulsive interaction between the molecules, which scales as 1/r31/{r}^{3}1/r3 at large distances rrr, makes the problem drastically different from the well-known problem of the two-species Fermi gas with repulsive contact interspecies interaction. We solve the low-energy scattering problem and develop a many-body perturbation theory beyond the mean field. The theory relies on the presence of a small parameter kFr∗{k}_{F}{r}_{*}kF​r∗​, where kF{k}_{F}kF​ is the Fermi momentum and ${r}_{*}=m{d}^{2}/{\ensuremath{\hbar}}^{2}$ is the dipole-dipole length, with mmm being the molecule mass. We obtain thermodynamic quantities as a series of expansion up to the second order in kFr∗{k}_{F}{r}_{*}kF​r∗​ and argue that many-body corrections to the ground-state energy can be identified in experiments with ultracold molecules, as it has been recently done for ultracold fermionic atoms. Moreover, we show that only many-body effects provide the existence of zero sound and calculate the sound velocity.