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arXiv:0802.2101 · Physical Review Letters

Stability of Superflow for Ultracold Fermions in Optical Lattices

A. A. Burkov, Arun Paramekanti

Published Jun 25, 2008• 25 citations
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Abstract

We investigate the stability of superflow of paired fermions in an optical lattice. We show that there are two distinct dynamical instabilities which limit the superflow in this system. One dynamical instability occurs when the superfluid stiffness becomes negative; this evolves, with increasing pairing interaction, from the fermion pair breaking instability to the well-known dynamical instability of lattice bosons. The second, more interesting, dynamical instability is marked by the emergence of a transient atom density wave. Both dynamical instabilities can be experimentally accessed by tuning the pairing interaction and the fermion density.

DOI
10.1103/physrevlett.100.255301

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We investigate the stability of superflow of paired fermions in an optical lattice. We show that there are two distinct dynamical instabilities which limit the superflow in this system. One dynamical instability occurs when the superfluid stiffness becomes negative; this evolves, with increasing pairing interaction, from the fermion pair breaking instability to the well-known dynamical instability of lattice bosons. The second, more interesting, dynamical instability is marked by the emergence of a transient atom density wave. Both dynamical instabilities can be experimentally accessed by tuning the pairing interaction and the fermion density.
We study the superfluid phase of the one-band attractive Hubbard model of fermions as a prototype of a strongly correlated sss-wave fermion superfluid on a lattice. We show that the collective mode spectrum of this superfluid exhibits, in addition to the long wavelength sound mode, a sharp roton mode over a wide range of densities and interaction strengths. We compute the sound velocity and the roton gap within a generalized random phase approximation (GRPA) and show that the GRPA results are in good agreement, at strong coupling, with a spin-wave analysis of the appropriate strong-coupling pseudospin model. We also investigate, using this two-pronged approach, the breakdown of superfluidity in the presence of a supercurrent. We find that the superflow can break down at a critical flow momentum via several distinct mechanisms---depairing, Landau instabilities or dynamical instabilities---depending on the dimension, the interaction strength and the fermion density. The most interesting of these instabilities is a charge modulation dynamical instability which is distinct from previously studied dynamical instabilities of Bose superfluids. The charge order associated with this instability can be of two types: (i) a commensurate checkerboard modulation driven by softening of the roton mode at the Brillouin zone corner, or, (ii) an incommensurate density modulation arising from superflow-induced finite momentum pairing of Bogoliubov quasiparticles. We elucidate the dynamical phase diagram showing the critical flow momentum of the leading instability over a wide range of fermion densities and interaction strengths and point out implications of our results for experiments on cold atom fermion superfluids in an optical lattice.
We analyze the dynamical and energetic instabilities of spin currents in a system of two-component bosons in an optical lattice, with a particular focus on the N\'eel state. We consider both the weakly interacting superfluid and the strongly interacting Mott insulating limits as well as the regime near the superfluid-insulator transition and establish the criteria for the onset of these instabilities. We use Bogoliubov theory to treat the weakly interacting superfluid regime. Near the Mott transition, we calculate the stability phase diagram within a variational Gutzwiller wave-function approach. In the deep Mott limit we discuss the emergence of the Heisenberg model and calculate the stability diagram within this model. Though the Bogoliubov theory and the Heisenberg model (appropriate for the deep superfluid and the deep Mott-insulating phase, respectively) predict no dynamical instabilities, we find, interestingly, that between these two limiting cases there is a regime of dynamical instability. This result is relevant for the ongoing experimental efforts to realize a stable N\'eel-ordered state in multicomponent ultracold bosons.
We study the stability of superfluid flow of two-component Fermi gases in one-dimensional optical lattices. We find that the density fluctuation mode, the so-called Anderson-Bogoliubov mode, has the roton-like structure as seen in superfluid 4 He. With increasing supercurrent, one of the roton-like minima reaches zero before the pair breaking occurs. This means that the instability of the superfluid Fermi gas is due to the spontaneous emission of the roton-like excitations of the Anderson-Bogoliubov mode instead of due to the Cooper pair breaking. We calculate the critical velocity determined by the roton-like structure for one-dimensional optical lattices.
We study the stability of superflow of Bose gases in optical lattices by analyzing the Bose-Hubbard model within the Gutzwiller mean-field approximation. We calculate the excitation spectra of the homogeneous Bose-Hubbard model at unit filling to determine the critical momenta for the Landau and dynamical instabilities. These two critical momenta are shown to approach each other when the on-site interaction increases towards the Mott transition point. In order to make a direct connection with realistic experiments, we next take into account a parabolic trapping potential and compute the real-time dynamics of dipole oscillations induced by suddenly displacing the trap center. We consider the following two cases: standard soft-core bosons, whose interparticle interactions include the on-site one only; and hard-core bosons with long-range dipole-dipole interactions. For both cases, we show that the dipole oscillation is significantly damped when the maximum local momentum exceeds a certain threshold, which quantitatively agrees with the critical momentum for the dynamical instability in the homogeneous system. In the case of dipolar hard-core bosons, the dynamical instability of dipole oscillations leads to the formation of checkerboard density waves in the superfluid phase near the boundary to the supersolid phase.
We investigate many-body phase diagrams of atomic boson-fermion mixtures loaded in the two-dimensional optical lattice. Bosons mediate an attractive, finite-range interaction between fermions, leading to fermion pairing phases of different orbital symmetries. Specifically, we show that by properly tuning atomic and lattice parameters it is possible to create superfluids with sss-, ppp-, and ddd-wave pairing symmetry as well as spin and charge density wave phases. These phases and their stability are analyzed within the mean-field approximation for systems of $^{40}\mathrm{K}\text{\ensuremath{-}}^{87}\mathrm{Rb}$ and $^{40}\mathrm{K}\text{\ensuremath{-}}^{23}\mathrm{Na}$ mixtures. For the experimentally accessible regime of parameters, superfluids with unconventional fermion pairing have transition temperature around a percent of the Fermi energy.