Fulde-Ferrell-Larkin-Ovchinnikov state of two-dimensional imbalanced Fermi gases

The ground-state phase diagram of attractively-interacting Fermi gases in two dimensions with a population imbalance is investigated. We find the regime of stability for the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, in which pairing occurs at finite wave vector, and determine the magnitude of the pairing amplitude $\Delta$ and FFLO wavevector $q$ in the ordered phase, finding that $\Delta$ can be of the order of the two-body binding energy. Our results rely on a careful analysis of the zero temperature gap equation for the FFLO state, which possesses nonanalyticities as a function of $\Delta$ and $q$, invalidating a Ginzburg-Landau expansion in small $\Delta$.Comment: 16 pages. 14 figure files. Submitted to Physical Review

Comment on "Superfluid stability in the BEC-BCS crossover"

We point out an error in recent work by Pao, Wu, and Yip [Phys. Rev.B {\bf 73}, 132506 (2006)], that stems from their use of a necessary but not sufficient condition [positive compressibility (magnetic susceptibility) and superfluid stiffness] for the stability of the ground state of a polarized Fermi gas. As a result, for a range of detunings their proposed ground-state solution is a local maximum rather than a minimum of the ground state energy, which thereby invalidates their proposed phase diagram for resonantly interacting fermions under an imposed population difference.Comment: 4 pages, 2 figures. Version in PR

Density profiles and collective modes of a Bose-Einstein condensate with light-induced spin-orbit coupling

The phases of a Bose-Einstein condensate (BEC) with light-induced spin-orbit coupling (SOC) are studied within the mean-field approximation. The mixed BEC phase, in which the system condenses in a superposition of two plane wave states, is found to be stable for sufficiently small light-atom coupling, becoming unstable in a continuous fashion with increasing light-atom coupling. The structure of the phase diagram at fixed chemical potential for bosons with SOC is shown to imply an unusual density dependence for a trapped mixed BEC phase, with the density of one dressed spin state increasing with increasing radius, providing a unique experimental signature of this state. The collective Bogoliubov sound mode is shown to also provide a signature of the mixed BEC state, vanishing as the boundary to the regime of phase separation is approached.Comment: 9 pages, 4 figures. Published Versio

Intrinsic resistivity and the SO(5) theory of high-temperature superconductors

The topological structure of the order parameter in Zhang's SO(5) theory of superconductivity allows for an unusual type of dissipation mechanism via which current-carrying states can decay. The resistivity due to this mechanism, which involves orientation rather than amplitude order-parameter fluctuations, is calculated for the case of a thin superconducting wire. The approach is a suitably modified version of that pioneered by Langer and Ambegaokar for conventional superconductors.Comment: 4 pages, including 1 figure (REVTEX); references added, minor corrections mad

Feynman path-integral approach to the QED3 theory of the pseudogap

In this work the connection between vortex condensation in a d-wave superconductor and the QED$_3$ gauge theory of the pseudogap is elucidated. The approach taken circumvents the use of the standard Franz-Tesanovic gauge transformation, borrowing ideas from the path-integral analysis of the Aharonov-Bohm problem. An essential feature of this approach is that gauge-transformations which are prohibited on a particular multiply-connected manifold (e.g. a superconductor with vortices) can be successfully performed on the universal covering space associated with that manifold.Comment: 15 pages, 1 Figure. Int. J. Mod. Phys. B 17, 4509 (2003). Minor changes from previous versio

Quantum decoupling transition in a one-dimensional Feshbach-resonant superfluid

We study a one-dimensional gas of fermionic atoms interacting via an s-wave molecular Feshbach resonance. At low energies the system is characterized by two Josephson-coupled Luttinger liquids, corresponding to paired atomic and molecular superfluids. We show that, in contrast to higher dimensions, the system exhibits a quantum phase transition from a phase in which the two superfluids are locked together to one in which, at low energies, quantum fluctuations suppress the Feshbach resonance (Josephson) coupling, effectively decoupling the molecular and atomic superfluids. Experimental signatures of this quantum transition include the appearance of an out-of-phase gapless mode (in addition to the standard gapless in-phase mode) in the spectrum of the decoupled superfluid phase and a discontinuous change in the molecular momentum distribution function.Comment: 4 RevTeX pages, 1 figure, submitted to PR

Topological phases of topological insulator thin films

We study the properties of a thin film of topological insulator material. We treat the coupling between helical states at opposite surfaces of the film in the properly-adapted tunneling approximation, and show that the tunneling matrix element oscillates as function of both the film thickness and the momentum in the plane of the film for Bi$_2$Se$_3$ and Bi$_2$Te$_3$. As a result, while the magnitude of the matrix element at the center of the surface Brillouin Zone gives the gap in the energy spectrum, the sign of the matrix element uniquely determines the topological properties of the film, as demonstrated by explicitly computing the pseudospin textures and the Chern number. We find a sequence of transitions between topological and non-topological phases, separated by semimetallic states, as the film thickness varies. In the topological phase the edge states of the film always exist but only carry a spin current if the edge potentials break particle-hole symmetry. The edge states decay very slowly away from the boundary in Bi$_2$Se$_3$, making Bi$_{2}$Te$_{3}$, where this scale is shorter, a more promising candidate for the observation of these states. Our results hold for free-standing films as well as heterostructures with large-gap insulators

Pairing correlations in a trapped one-dimensional Fermi gas

We use a BCS-type variational wavefunction to study attractively-interacting quasi one-dimensional (1D) fermionic atomic gases, motivated by cold-atom experiments that access the 1D regime using an anisotropic harmonic trapping potential (with trapping frequencies $\omega_x = \omega_y \gg \omega_z$) that confines the gas to a cigar-shaped geometry. To handle the presence of the trap along the $z$-direction, we construct our variational wavefunction from the harmonic oscillator Hermite functions that are the eigenstates of the single-particle problem. Using an analytic determination of the effective interaction among harmonic oscillator states along with a numerical solution of the resulting variational equations, we make specific experimental predictions for how pairing correlations would be revealed in experimental probes like the local density and the momentum correlation function.Comment: 8 pages, 6 figures. Published in Phys. Rev.

A self-consistent Hartree-Fock approach for interacting bosons in optical lattices

A theoretical study of interacting bosons in a periodic optical lattice is presented. Instead of the commonly used tight-binding approach (applicable near the Mott insulating regime of the phase diagram), the present work starts from the exact single-particle states of bosons in a cubic optical lattice, satisfying the Mathieu equation, an approach that can be particularly useful at large boson fillings. The effects of short-range interactions are incorporated using a self-consistent Hartree-Fock approximation, and predictions for experimental observables such as the superfluid transition temperature, condensate fraction, and boson momentum distribution are presented.Comment: 12 pages, 15 figure file