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arXiv:2001.00545 · Physical Review A

Superfluidity and pairing phenomena in ultracold atomic Fermi gases in one-dimensional optical lattices. I. Balanced case

Jibiao Wang, Leifeng Zhang, Yi Yu, Chaohong Lee, Qijin Chen

Published May 11, 2020• 6 citations
arXivHTMLPDF

Abstract

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 ${T}_{\mathrm{c}}$ decreases with pairing strength in the BEC regime, where it approaches asymptotically ${T}_{\mathrm{c}}=\ensuremath{\pi}an/2m$, with $a$ being the $s$-wave scattering length, and $n$ ($m$) 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 $d/a$. Importantly, ${T}_{\mathrm{c}}$ at unitarity increases with the lattice constant $d$ and hopping integral $t$. The effect of the van Hove singularity on ${T}_{\mathrm{c}}$ is identified. The superfluid density exhibits ${T}^{3/2}$ power laws at low $T$, away from the extreme BCS limit. These predictions can be tested in future experiments.

DOI
10.1103/physreva.101.053617

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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 Tc=\ensuremathπan/2m{T}_{\mathrm{c}}=\ensuremath{\pi}an/2mTc​=\ensuremathπan/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 \ensuremathμ\ensuremath{\mu}\ensuremathμ and pairing gap \ensuremathΔ\mathrm{\ensuremath{\Delta}}\ensuremathΔ, 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.
Abstract Atomic Fermi gases have been an ideal platform for simulating conventional and engineering exotic physical systems owing to their multiple tunable control parameters. Here we investigate the effects of mixed dimensionality on the superfluid and pairing phenomena of a two-component ultracold atomic Fermi gas with a short-range pairing interaction, while one component is confined on a one-dimensional (1D) optical lattice whereas the other is in a homogeneous 3D continuum. We study the phase diagram and the pseudogap phenomena throughout the entire BCS-BEC crossover, using a pairing fluctuation theory. We find that the effective dimensionality of the non-interacting lattice component can evolve from quasi-3D to quasi-1D, leading to strong Fermi surface mismatch. Upon pairing, the system becomes effectively quasi-two dimensional in the BEC regime. The behavior of T c bears similarity to that of a regular 3D population imbalanced Fermi gas, but with a more drastic departure from the regular 3D balanced case, featuring both intermediate temperature superfluidity and possible pair density wave ground state. Unlike a simple 1D optical lattice case, T c in the mixed dimensions has a constant BEC asymptote.
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.
Abstract The superfluid behavior of ultracold atomic Fermi gases with a short range attractive interaction in a two‐dimensional optical lattice (2DOL) is studied using a pairing fluctuation theory, within the context of BCS‐BEC crossover. It is found that the mixing of lattice and continuum dimensions leads to exotic phenomena. For relatively large lattice constant d and small hopping integral t, the superfluid transition temperature exhibits a remarkable reentrant behavior as a function of the interaction strength, and leads to a pair density wave ground state, where vanishes, for a range of intermediate coupling strength. In the unitary and BCS regimes, the nature of the in‐plane and overall pairing changes from particle‐like to hole‐like, with an unexpected nonmonotonic dependence of the chemical potential on the pairing strength. The Bose–Einstein condensation asymptotic behaviors exhibit distinct power law dependencies on the interaction strength compared to cases of pure 3D lattice, 3D continuum, and 1DOL. These predictions can be tested in future experiments.
In this paper, we study the effect of population imbalance and its interplay with pairing strength and lattice effect in atomic Fermi gases in a one-dimensional optical lattice. We compute various phase diagrams as the system undergoes BCS-BEC crossover, using the same pairing fluctuation theory as in Part I of this work [Phys. Rev. A 101, 053617 (2020)]. We find widespread pseudogap phenomena beyond the BCS regime and intermediate temperature superfluid states for relatively low population imbalances. The Fermi surface topology plays an important role in the behavior of Tc{T}_{\mathrm{c}}Tc​. For large ddd and/or small ttt, which yield an open Fermi surface, superfluidity can be readily destroyed by a small amount of population imbalance ppp. The superfluid phase, especially in the BEC regime, can exist only for a highly restricted volume of the parameter space. An open Fermi surface often leads to destruction of the superfluid ground state in the BEC regime. Due to the continuum-lattice mixing, population imbalance gives rise to a new mechanism for pair hopping, as assisted by excessive majority fermions, which may lead to significant enhancement of Tc{T}_{\mathrm{c}}Tc​ on the BEC side of the Feshbach resonance, and also render Tc{T}_{\mathrm{c}}Tc​ approaching a constant asymptote in the BEC limit, when it exists. Furthermore, we find that not all minority fermions will be paired up in BEC limit, unlike the 3D continuum case. These predictions can be tested in future experiments.
We study the ground-state phase diagram of population balanced and imbalanced ultracold atomic Fermi gases with a short-range attractive interaction throughout the crossover from BCS to Bose-Einstein condensation (BEC), in a two-dimensional (2D) optical lattice comprised of a 2D array of 1D lines. We find that the mixing of lattice and continuum dimensions, together with population imbalance, has an extraordinary effect on pairing and the superfluidity of atomic Fermi gases. In the balanced case, the superfluid ground state prevails over the majority of the phase space. However, for relatively small lattice hopping integral ttt and large lattice constant ddd, a pair density wave (PDW) emerges unexpectedly at intermediate coupling strength, and the nature of the in-plane and overall pairing changes from particlelike to holelike in the BCS and unitary regimes, associated with an abnormal increase in the Fermi volume with the pairing strength. In the imbalanced case, the stable polarized superfluid phase shrinks to only a small portion of the entire phase space spanned by t,dt, dt,d, imbalance ppp, and interaction strength UUU, mainly in the bosonic regime of low ppp, moderately strong pairing, relatively large ttt, and small ddd. Due to the Pauli exclusion between paired and excessive fermions within the confined momentum space, a PDW phase emerges and the overall pairing evolves from particlelike into holelike, as the pairing strength grows stronger in the BEC regime. In both cases, the ground-state property is largely governed by the Fermi surface topology. These findings are very different from the cases of a pure 3D continuum, a 3D lattice, or a 1D optical lattice.
In this thesis, we discuss ultracold quantum gases both in continuum and optical lattices. For the continuum Fermi gases in BCS-BEC crossover, we present an effective field theory study on the recently discovered puzzling damping phenomena on the BCS side of the crossover. We find that in contrast to the previous proposed pair-breaking mechanism of damping, the damping process is due to the interaction between superfluid phonons and thermally excited fermionic quasi particles. Results from our effective field theory are compared quantitatively with experiments, showing a good agreement. For the ultracold fermionic atoms in optical lattices, we propose two novel quantum phases. Firstly, we show that a novel superconducting pairing occurs for spin-imbalanced Fermi gases with the spin up and down Fermi levels lying within the px- and s- orbital bands of a quasi-one-dimensional optical lattice. The pairs condense at a finite momentum equal to the sum of the two Fermi momenta of spin up and down fermions, and form a p-orbital condensate. The phase diagram shows that the p-orbital pair condensate occurs in a wide range of fillings. Secondly, we study instabilities of single-species fermionic atoms in the p-orbital bands in two-dimensional square optical lattices. From the nearly-perfect nesting Fermi surfaces, charge density wave and orbital density wave orderings with stripe or checkerboard patterns are found for attractive and repulsive interactions, respectively. The superconducting phase, usually expected of attractively interacting fermions, is strongly suppressed. We also use field theory to analyze the possible liquid crystal phases in our system. For bosons, we study ultracold bosonic atoms loaded in a one-dimensional optical lattice of two-fold p-orbital degeneracy at each site, and find an anti-ferro-orbital, a homogeneous px Mott insulator phase and two kinds of superfluid phases distinguished by the orbital ordering.