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arXiv:cond-mat/0502148

Exotic p-wave superfluidity of single hyperfine state Fermi gases in optical lattices

M. Iskin, C. A. R. Sá de Melo

Published Feb 5, 2005• 0 citations
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Abstract

We consider p-wave (triplet) pairing of single hyperfine state ultracold atomic gases trapped in quasi-two-dimensional optical lattices. We find that the critical temperatures in the lattice model is considerably higher and experimentally attainable around half-filling in contrast to the predictions of continuum model for p-wave superfluids. In tetragonal lattices, we show that the atomic compressibility and spin susceptibility have a peak at low temperatures exactly at the half-filling, but this peak splits into two in the orthorhombic lattices. These peaks reflect the p-wave structure of the order parameter for superfluidity and they disappear as the critical temperature is approached from below. We also calculate the superfluid density tensor, and show that for the orthorhombic case there is no off-diagonal component, however in the tetragonal case an off-diagonal component develops, and becomes a key signature of the exotic p-wave state.

DOI
10.48550/arxiv.cond-mat/0502148

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We consider p-wave (triplet) pairing of single hyperfine state ultracold atomic gases trapped in quasi-two-dimensional optical lattices. We find that the critical temperatures in the lattice model is considerably higher and experimentally attainable around half-filling in contrast to the predictions of continuum model for p-wave superfluids. In tetragonal lattices, we show that the atomic compressibility and spin susceptibility have a peak at low temperatures exactly at the half-filling, but this peak splits into two in the orthorhombic lattices. These peaks reflect the p-wave structure of the order parameter for superfluidity and they disappear as the critical temperature is approached from below. We also calculate the superfluid density tensor, and show that for the orthorhombic case there is no off-diagonal component, however in the tetragonal case an off-diagonal component develops, and becomes a key signature of the exotic p-wave state.
We consider ppp-wave pairing of single hyperfine state and sss-wave pairing of two hyperfine states ultracold atomic gases trapped in quasi-two-dimensional optical lattices. First, we analyze superfluid properties of ppp-wave and sss-wave symmetries in the strictly weak coupling BCS regime where we discuss the order parameter, chemical potential, critical temperature, atomic compressibility, and superfluid density as a function of filling factor for tetragonal and orthorhombic optical lattices. Second, we analyze superfluid properties of ppp-wave and sss-wave superfluids in the evolution from the BCS to Bose-Einstein condensation regimes at low temperatures $(T\ensuremath{\approx}0)$, where we discuss the changes in the quasiparticle excitation spectrum, chemical potential, atomic compressibility, Cooper pair size, and momentum distribution as a function of filling factor and interaction strength for tetragonal and orthorhombic optical lattices.
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.
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.
Many-body effects on superfluidity and transition temperatures are calculated for optical lattices and uniform systems with ultracold multi-component Fermi gases. The induced interactions depend sensitively on the interactions between the multi-components and their densities. The s- and d-wave pairing gaps and critical temperatures are calculated for optical lattices at low (dilute) filling as well as near half filling to leading orders in the interaction strength with and without induced interactions. They can deviate strongly from dilute two-component systems and affect the phase diagram. In two dimensional optical lattices the induced interactions are singular at half filling and strongly affect s- and d-wave superfluidity.
We propose an experimental protocol to study ppp-wave superfluidity in a spin-polarized cold Fermi gas tuned by an sss-wave Feshbach resonance. A crucial ingredient is to add a quasi-one-dimensional optical lattice and tune the fillings of two spins to the sss and ppp band, respectively. The pairing order parameter is confirmed to inherit ppp-wave symmetry in its center-of-mass motion. We find that it can further develop into a state of unexpected $\ensuremath{\pi}$-phase modulation in a broad parameter regime. Experimental signatures are predicted in the momentum distributions, density of states, and spatial densities for a realistic experimental setup with a shallow trap. The $\ensuremath{\pi}$-phase ppp-wave superfluid is reminiscent of the $\ensuremath{\pi}$ state in superconductor-ferromagnet heterostructures but differs in symmetry and physical origin. The spatially varying phases of the superfluid gap provide an approach to synthetic magnetic fields for neutral atoms. It would represent another example of ppp-wave pairing, first discovered in 3He^{3}\mathrm{He}3He liquids.
This is a study of ultra-cold Fermi gases in different systems. This thesis is focused on exotic superfluid states, for an example on the three component Fermi gas and the FFLO phase in optical lattices. In the two-components case, superfluidity is studied mainly in the case of the spin population imbalanced Fermi gases and the phase diagrams are calculated from the mean-field theory. Different methods to detect different phases in optical lattices are suggested. In the three-component case, we studied also the uniform gas and harmonically trapped system. In this case, the BCS theory is generalized to three-component gases. It is also discussed how to achieve the conditions to get an SU(3)-symmetric Hamiltonian in optical lattices. The thesis is divided in chapters as follows: Chapter 1 is an introduction to the field of cold quantum gases. In chapter 2 optical lattices and their experimental characteristics are discussed. Chapter 3 deals with two-components Fermi gases in optical lattices and the paired states in lattices. In chapter 4 three-component Fermi gases with and without a harmonic trap are explored, and the pairing mechanisms are studied. In this chapter, we also discuss three-component Fermi gases in optical lattices. Chapter 5 devoted to the higher order correlations, and what they can tell about the paired states. Chapter 6 concludes the thesis.