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arXiv:cond-mat/0502487 · Physical Review Letters

Two-Component Fermi Gas on Internal-State-Dependent Optical Lattices

Miguel A. Cazalilla, A. F. Ho, Thierry Giamarchi

Published Nov 23, 2005• 74 citations
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Abstract

We study the phase diagram of a one-dimensional, two-component (i.e., pseudo-"spin"-(1/2)) ultracold atomic Fermi gas. The two atom species can have different hopping or mass. A very rich phase diagram for equal densities of the species is found, containing Mott insulators and superfluids. We also discuss coupling such 1D systems and the experimental signatures of the phases. In particular, we compute the spin-structure factor at small momentum, which should reveal a spin gap.

DOI
10.1103/physrevlett.95.226402

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An ultracold gas of coupled two-component atoms in an optical field is studied. Due to the internal two-level structure of the atoms, three competing energy terms exist: atomic kinetic, atomic internal, and atom-atom interaction energies. A novel outcome of this interplay, not present in the regular Bose-Hubbard model, is that in the single band and tight-binding approximations four different phases appear: two superfluid and two Mott phases. When passing through the critical point between the two superfluid or the two Mott phases, a swapping of the internal atomic populations takes place. By means of the strong-coupling expansion, we find the full phase diagram for the four different phases.
We show that an interesting kind of pairing occurs for spin-imbalanced Fermi gases under a specific experimental condition---the spin up and spin down Fermi levels lying within the px{p}_{x}px​ and sss orbital bands of an optical lattice, respectively. The pairs condense at a finite momentum equal to the sum of the two Fermi momenta of spin up and spin down fermions and form a ppp-orbital pair condensate. This 2kF2{k}_{F}2kF​ momentum dependence has been seen before in spin- and charge-density waves, but it differs from the usual ppp-wave superfluids such as 3He^{3}\mathrm{He}3He, where the orbital symmetry refers to the relative motion within each pair. Our conclusion is based on the density matrix renormalization group analysis for the one-dimensional (1D) system and mean-field theory for the quasi-1D system. The phase diagram of the quasi-1D system is calculated, showing that the ppp-orbital pair condensate occurs in a wide range of fillings. In the strongly attractive limit, the system realizes an unconventional BEC beyond Feynman's no-node theorem. The possible experimental signatures of this phase in molecule projection experiment are discussed.
Two-component coupled Bose gas in a 1D optical lattice is examined. In addition to the postulated Mott insulator and Superfluid phases, multiple bosonic components manifest spin degrees of freedom. Coupling of the components in the Bose gas within same site and neighboring sites leads to substantial change in the previously observed spin phases revealing fascinating remarkable spin correlations. In the presence of strong interactions it gives rise to unconventional effective ordering of the spins leading to unprecedented spin phases: site-dependent z-xz\textsf{-}xz-x spin configuration with tunable (by hopping parameter) proclivity of spin alignment along zzz. Exact analysis and Variational Monte Carlo (VMC) along with stochastic minimization on Entangled Plaquette State (EPS) bestow a unique and enhanced perspective into the system beyond the scope of mean-field treatment. The physics of complex intra-component tunneling and inter-component coupling and filling factor greater than unity are discussed.
Advances in pure optical trapping techniques now allow the creation of degenerate Bose gases with internal degrees of freedom. Systems such as 87Rb,39K^{87}\mathrm{Rb},\phantom{\rule{0.16em}{0ex}}^{39}\mathrm{K}87Rb,39K, or 23Na^{23}\mathrm{Na}23Na in the F=1F=1F=1 hyperfine state offer an ideal platform for studying the interplay of superfluidity and quantum magnetism. Motivated by the experimental developments, we study ground-state phases of a two-component Bose gas loaded on an optical lattice. The system is described effectively by the Bose-Hubbard Hamiltonian with on-site and near-neighbor spin-spin interactions. An important feature of our investigation is the inclusion of interconversion (spin-flip) terms between the two species, which has been observed in optical lattice experiments. Using mean-field theory and quantum Monte Carlo simulations, we map out the phase diagram of the system. A rich variety of phases is identified, including antiferromagnetic (AF) Mott insulators and ferromagnetic and AF superfluids.