Two-fluid model for a rotating trapped Fermi gas in the BCS phase

We investigate the dynamical properties of a superfluid gas of trapped fermionic atoms in the BCS phase. As a simple example we consider the reaction of the gas to a slow rotation of the trap. It is shown that the currents generated by the rotation can be understood within a two-fluid model similar to the one used in the theory of superconductors, but with a position dependent ratio of normal and superfluid densities. The rather general result of this paper is that already at very low temperatures, far below the critical one, an important normal-fluid component appears in the outer regions of the gas. This renders the experimental observation of superfluidity effects more difficult and indicates that reliable theoretical predictions concerning other dynamical properties, like the frequencies of collective modes, can only be made by taking into account temperature effects.Comment: 6 pages, 4 figure

Hopping on the Bethe lattice: Exact results for densities of states and dynamical mean-field theory

We derive an operator identity which relates tight-binding Hamiltonians with arbitrary hopping on the Bethe lattice to the Hamiltonian with nearest-neighbor hopping. This provides an exact expression for the density of states (DOS) of a non-interacting quantum-mechanical particle for any hopping. We present analytic results for the DOS corresponding to hopping between nearest and next-nearest neighbors, and also for exponentially decreasing hopping amplitudes. Conversely it is possible to construct a hopping Hamiltonian on the Bethe lattice for any given DOS. These methods are based only on the so-called distance regularity of the infinite Bethe lattice, and not on the absence of loops. Results are also obtained for the triangular Husimi cactus, a recursive lattice with loops. Furthermore we derive the exact self-consistency equations arising in the context of dynamical mean-field theory, which serve as a starting point for studies of Hubbard-type models with frustration.Comment: 14 pages, 9 figures; introduction expanded, references added; published versio

Dynamics of a trapped Fermi gas in the BCS phase

We derive semiclassical transport equations for a trapped atomic Fermi gas in the BCS phase at temperatures between zero and the superfluid transition temperature. These equations interpolate between the two well-known limiting cases of superfluid hydrodynamics at zero temperature and the Vlasov equation at the critical one. The linearized version of these equations, valid for small deviations from equilibrium, is worked out and applied to two simple examples where analytical solutions can be found: a sound wave in a uniform medium and the quadrupole excitation in a spherical harmonic trap. In spite of some simplifying approximations, the main qualitative results of quantum mechanical calculations are reproduced, which are the different frequencies of the quadrupole mode at zero and the critical temperature and strong Landau damping at intermediate temperatures. In addition we suggest a numerical method for solving the semiclassical equations without further approximations.Comment: 15 pages, 4 figures; v2: discussion and references adde

Spin textures in slowly rotating Bose-Einstein Condensates

Slowly rotating spin-1 Bose-Einstein condensates are studied through a variational approach based upon lowest Landau level calculus. The author finds that in a gas with ferromagnetic interactions, such as $^{87}$Rb, angular momentum is predominantly carried by clusters of two different types of skyrmion textures in the spin-vector order parameter. Conversely, in a gas with antiferromagnetic interactions, such as $^{23}$Na, angular momentum is carried by $\pi$-disclinations in the nematic order parameter which arises from spin fluctuations. For experimentally relevant parameters, the cores of these $\pi$-disclinations are ferromagnetic, and can be imaged with polarized light.Comment: 14 pages, 12 low resolution bitmapped figures, RevTeX4. High resolution figures available from author. Suplementary movies available from autho

Vortex phase diagram in rotating two-component Bose-Einstein condensates

We investigate the structure of vortex states in rotating two-component Bose-Einstein condensates with equal intracomponent but varying intercomponent coupling constants. A phase diagram in the intercomponent-coupling versus rotation-frequency plane reveals rich equilibrium structures of vortex states. As the ratio of intercomponent to intracomponent couplings increases, the interlocked vortex lattices undergo phase transitions from triangular to square, to double-core lattices, and eventually develop interwoven "serpentine" vortex sheets with each component made up of chains of singly quantized vortices.Comment: 4 pages, 4 figures, revtex

Thermodynamically consistent equilibrium properties of normal-liquid Helium-3

The high-precision data for the specific heat C_{V}(T,V) of normal-liquid Helium-3 obtained by Greywall, taken together with the molar volume V(T_0,P) at one temperature T_0, are shown to contain the complete thermodynamic information about this phase in zero magnetic field. This enables us to calculate the T and P dependence of all equilibrium properties of normal-liquid Helium-3 in a thermodynamically consistent way for a wide range of parameters. The results for the entropy S(T,P), specific heat at constant pressure C_P(T,P), molar volume V(T,P), compressibility kappa(T,P), and thermal expansion coefficient alpha(T,P) are collected in the form of figures and tables. This provides the first complete set of thermodynamically consistent values of the equilibrium quantities of normal-liquid Helium-3. We find, for example, that alpha(T,P) has a surprisingly intricate pressure dependence at low temperatures, and that the curves alpha(T,P) vs T do not cross at one single temperature for all pressures, in contrast to the curves presented in the comprehensive survey of helium by Wilks. Corrected in cond-mat/9906222v3: The sign of the coefficient d_0 was misprinted in Table I of cond-mat/9906222v1 and v2. It now correctly reads d_0=-7.1613436. All results in the paper were obtained with the correct value of d_0. (We would like to thank for E. Collin, H. Godfrin, and Y. Bunkov for finding this misprint.)Comment: 19 pages, 19 figures, 9 tables; published version; note added in proof; v3: misprint correcte

Stability conditions and Fermi surface topologies in a superconductor

Candidate homogeneous, isotropic superfluid or superconducting states of paired fermion species with different chemical potentials, can lead to quasiparticle excitation energies that vanish at either zero, one, or two spheres in momentum space. With no zeroes, we have a conventional BCS superconductor. The other two cases, ``gapless'' superconductors, appear in mean field theory for sufficiently large mismatches and/or sufficiently large coupling strengths. Here we examine several stability criteria for those candidate phases. Positivity of number susceptibility appears to provide the most powerful constraint, and renders all the two-zero states that we have examined mechanically unstable. Our results should apply directly to ultracold fermionic atom systems.Comment: 18 pages, 7 figures; v2: some clarifications in Sec. IIC; references added; version accepted for publication in Phys. Rev.

Quark description of the Nambu-Goldstone bosons in the color-flavor locked phase

We investigate the color-singlet order parameters and the quark description of the Nambu-Goldstone (NG) bosons in the color-flavor locked (CFL) phase. We put emphasis on the NG boson (phason) called ``H'' associated with the $\mathrm{U_B(1)}$ symmetry breaking. We qualitatively argue the nature of H as the second sound in the hydrodynamic regime. We articulate, based on a diquark picture, how the structural change of the condensates and the associated NG bosons occurs continuously from hadronic to CFL quark matter if the quark-hadron continuity is realized. We sharpen the qualitative difference between the flavor octet pions and the singlet phason. We propose a conjecture that superfluid H matter undergoes a crossover to a superconductor with tightly-bound diquarks, and then a crossover to superconducting matter with diquarks dissociated.Comment: 14 pages, 1 table, 1 figure and confusing statements are correcte

Critical Velocity of Vortex Nucleation in Rotating Superfluid 3He-A

We have measured the critical velocity v_c at which 3He-A in a rotating cylinder becomes unstable against the formation of quantized vortex lines with continuous (singularity-free) core structure. We find that v_c is distributed between a maximum and minimum limit, which we ascribe to a dependence on the texture of the orbital angular momentum l(r) in the cylinder. Slow cool down through T_c in rotation yields l(r) textures for which the measured v_c's are in good agreement with the calculated instability of the expected l texture.Comment: 4 pages, 3 figure

Magnetism in one-dimensional quantum dot arrays

We employ the density functional Kohn-Sham method in the local spin-density approximation to study the electronic structure and magnetism of quasi one-dimensional periodic arrays of few-electron quantum dots. At small values of the lattice constant, the single dots overlap, forming a non-magnetic quantum wire with nearly homogenous density. As the confinement perpendicular to the wire is increased, i.e. as the wire is squeezed to become more one-dimensional, it undergoes a spin-Peierls transition. Magnetism sets in as the quantum dots are placed further apart. It is determined by the electronic shell filling of the individual quantum dots. At larger values of the lattice constant, the band structure for odd numbers of electrons per dot indicates that the array could support spin-polarized transport and therefore act as a spin filter.Comment: 11 pages, 6 figure