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Chinese Physics B

Evolution of the vortex state in the BCS–BEC crossover of a quasi two-dimensional superfluid Fermi gas

Xuebing Luo, Kezhao Zhou, Zhang Zhi-dong

Published Nov 1, 2016• 0 citations
Publisher

Abstract

We use the path-integral formalism to investigate the vortex properties of a quasi-two dimensional (2D) Fermi superfluid system trapped in an optical lattice potential. Within the framework of mean-field theory, the cooper pair density, the atom number density, and the vortex core size are calculated from weakly interacting BCS regime to strongly coupled while weakly interacting BEC regime. Numerical results show that the atoms gradually penetrate into the vortex core as the system evolves from BEC to BCS regime. Meanwhile, the presence of the optical lattice allows us to analyze the vortex properties in the crossover from three-dimensional (3D) to 2D case. Furthermore, using a simple re-normalization procedure, we find that the two-body bound state exists only when the interaction is stronger than a critical one denoted by G c which is obtained as a function of the lattice potential’s parameter. Finally, we investigate the vortex core size and find that it grows with increasing interaction strength. In particular, by analyzing the behavior of the vortex core size in both BCS and BEC regimes, we find that the vortex core size behaves quite differently for positive and negative chemical potentials.

DOI
10.1088/1674-1056/25/11/110306

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We use the path-integral formalism to investigate the vortex properties of a quasi-two dimensional (2D) Fermi superfluid system trapped in an optical lattice potential. Within the framework of mean-field theory, the cooper pair density, the atom number density, and the vortex core size are calculated from weakly interacting BCS regime to strongly coupled while weakly interacting BEC regime. Numerical results show that the atoms gradually penetrate into the vortex core as the system evolves from BEC to BCS regime. Meanwhile, the presence of the optical lattice allows us to analyze the vortex properties in the crossover from three-dimensional (3D) to 2D case. Furthermore, using a simple re-normalization procedure, we find that the two-body bound state exists only when the interaction is stronger than a critical one denoted by G c which is obtained as a function of the lattice potential’s parameter. Finally, we investigate the vortex core size and find that it grows with increasing interaction strength. In particular, by analyzing the behavior of the vortex core size in both BCS and BEC regimes, we find that the vortex core size behaves quite differently for positive and negative chemical potentials.
We derive a path-integral description of the vortex state of a fermionic superfluid in the crossover region between the molecular condensate (BEC) regime and the Cooper pairing (BCS) regime. This path-integral formalism, supplemented by a suitable choice for the saddle point value of the pairing field in the presence of a vortex, offers a unified description that encompasses both the BEC and BCS limits. The vortex core size is studied as a function of the tunable interaction strength between the fermionic atoms. We find that in the BEC regime, the core size is determined by the molecular healing length, whereas in the BCS regime, the core size is proportional only to the Fermi wavelength. The observation of such quantized vortices in dilute Fermi gases would provide an unambiguous proof of the realization of superfluidity in these gases.
We analyze the finite temperature phase diagram of fermion mixtures in one-dimensional optical lattices as a function of interaction strength. At low temperatures, the system evolves from an anisotropic three-dimensional Bardeen-Cooper-Schrieffer (BCS) superfluid to an effectively two-dimensional Berezinskii-Kosterlitz-Thouless (BKT) superfluid as the interaction strength increases. We calculate the critical temperature as a function of interaction strength, and identify the region where the dimensional crossover occurs for a specified optical lattice potential. Finally, we show that the dominant vortex excitations near the critical temperature evolve from multiplane elliptical vortex loops in the three-dimensional regime to planar vortex-antivortex pairs in the two-dimensional regime, and we propose a detection scheme for these excitations.
We study the superfluid behavior of ultracold atomic Fermi gases with a short range attractive interaction in a two-dimensional optical lattice (2DOL) using a pairing fluctuation theory, within the context of BCS-BEC crossover. We find that the mixing of lattice and continuum dimensions leads to exotic phenomena. For relatively large lattice constant ddd and small hopping integral ttt, the superfluid transition temperature TcT_cTc​ exhibits a remarkable reentrant behavior as a function of the interaction strength, and leads to a pair density wave ground state, where TcT_cTc​ vanishes, for a range of intermediate coupling strength. In the unitary and BCS regimes, hole-like pairing emerges, with an unexpected nonmonotonic dependence of the chemical potential on the pairing strength. The BEC asymptotic behaviors exhibit distinct power law dependencies on the interaction strength compared to cases of pure 3D lattice, 3D continuum, and 1DOL.
We consider a single vortex in a superfluid Fermi gas in the BCS-BEC crossover regime near a Feshbach resonance. The effect of the molecular Bose-Einstein condensate upon the vortex structure is discussed within the mean field approximation at zero temperature. Using the self-consistent Bogoliubov-de Gennes equation of the fermion-boson coupled model, we calculate density distributions of atoms and molecules. As the number of the molecules increases, both atomic and molecular density changes from BCS-like distribution to BEC-like. We also study the change of the vortex core size in the crossover regime.
The superfluidity and pairing phenomena in ultracold atomic Fermi gases have been of great interest in recent years, with multiple tunable parameters. Here we study the BCS-BEC crossover behavior of balanced two-component Fermi gases in a one-dimensional optical lattice, which is distinct from the simple three-dimensional (3D) continuum and a fully 3D lattice often found in a condensed matter system. We use a pairing fluctuation theory which includes self-consistent feedback effects at finite temperatures and find widespread pseudogap phenomena beyond the BCS regime. As a consequence of the lattice periodicity, the superfluid transition temperature Tc{T}_{\mathrm{c}}Tc​ decreases with pairing strength in the BEC regime, where it approaches asymptotically ${T}_{\mathrm{c}}=\ensuremath{\pi}an/2m$, with aaa being the sss-wave scattering length, and nnn (mmm) the fermion density (mass). In addition, the quasi-two dimensionality leads to fast-growing (absolute value of the) fermionic chemical potential $\ensuremath{\mu}$ and pairing gap $\mathrm{\ensuremath{\Delta}}$, which depends exponentially on the ratio d/ad/ad/a. Importantly, Tc{T}_{\mathrm{c}}Tc​ at unitarity increases with the lattice constant ddd and hopping integral ttt. The effect of the van Hove singularity on Tc{T}_{\mathrm{c}}Tc​ is identified. The superfluid density exhibits T3/2{T}^{3/2}T3/2 power laws at low TTT, away from the extreme BCS limit. These predictions can be tested in future experiments.
We study the zero temperature ground state of a two-dimensional atomic Fermi gas with chemical potential and population imbalance in the mean-field approximation. All calculations are performed in terms of the two-body binding energy B , whose variation allows one to investigate the evolution from the BEC to the BCS regimes. By means of analytical and exact expressions we show that, similarly to what is found in three dimensions, at fixed chemical potentials, BCS is the ground state until the critical imbalance h c , after which there is a first-order phase transition to the normal state. We find that h c , the Chandrasekhar–Clogston limit of superfluidity, has the same value as in three-dimensional systems. We show that for a fixed ratio B / F , where F is the two-dimensional Fermi energy, as the density imbalance m is increased from zero, the ground state evolves from BCS to phase separation to the normal state. At the critical imbalance m c , phase separation is not supported and the normal phase is energetically preferable. The BCS–BEC crossover is discussed in balanced and imbalanced configurations. Possible pictures of what may be found experimentally in these systems are also shown. We also investigate the necessary conditions for the existence of bound states in the balanced and imbalanced normal phase.