Hartree-Fock-Bogoliubov theory versus local-density approximation for superfluid trapped fermionic atoms

We investigate a gas of superfluid fermionic atoms trapped in two hyperfine states by a spherical harmonic potential. We propose a new regularization method to remove the ultraviolet divergence in the Hartree-Fock-Bogoliubov equations caused by the use of a zero-range atom-atom interaction. Compared with a method used in the literature, our method is simpler and has improved convergence properties. Then we compare Hartree-Fock-Bogoliubov calculations with the semiclassical local-density approximation. We observe that for systems containing a small number of atoms shell effects, which cannot be reproduced by the semiclassical calculation, are very important. For systems with a large number of atoms at zero temperature the two calculations are in quite good agreement, which, however, is deteriorated at non-zero temperature, especially near the critical temperature. In this case the different behavior can be explained within the Ginzburg-Landau theory.Comment: 12 pages, 8 figures, revtex; v2: references and clarifying remarks adde

All the colours of the rainbow.

Our perception of colour has always been a source of fascination, so it's little wonder that studies of the phenomenon date back hundreds of years. What, though, can modern scientists learn from medieval literature — and how do we go about it

Density wave instabilities of tilted fermionic dipoles in a multilayer geometry

We consider the density wave instability of fermionic dipoles aligned by an external field, and moving in equidistant layers at zero temperature. Using a conserving Hartree-Fock approximation, we show that correlations between dipoles in different layers significantly decrease the critical coupling strength for the formation of density waves when the distance between the layers is comparable to the inter-particle distance within each layer. This effect, which is strongest when the dipoles are oriented perpendicular to the planes, causes the density waves in neighboring layers to be in-phase for all orientations of the dipoles. We furthermore demonstrate that the effects of the interlayer interaction can be understood from a classical model. Finally, we show that the interlayer correlations are important for experimentally relevant dipolar molecules, including the chemically stable $^{23}$Na$^{40}$K and $^{40}$K$^{133}$Cs, where the density wave regime is within experimental reach.Comment: 18 pages, 11 figures; new version with expanded discussion on experimental relevance including one new figur

Three-body recombination rates near a Feshbach resonance within a two-channel contact interaction model

We calculate the three-body recombination rate into a shallow dimer in a gas of cold bosonic atoms near a Feshbach resonance using a two-channel contact interaction model. The two-channel model naturally describes the variation of the scattering length through the Feshbach resonance and has a finite effective range. We confront the theory with the available experimental data and show that the two-channel model is able to quantitatively describe the existing data. The finite effective range leads to a reduction of the scaling factor between the recombination minima from the universal value of 22.7. The reduction is larger for larger effective ranges or, correspondingly, for narrower Feshbach resonances.Comment: 9 pages, 7 figure

Metastability in spin polarised Fermi gases and quasiparticle decays

We investigate the metastability associated with the first order transition from normal to superfluid phases in the phase diagram of two-component polarised Fermi gases.We begin by detailing the dominant decay processes of single quasiparticles.Having determined the momentum thresholds of each process and calculated their rates, we apply this understanding to a Fermi sea of polarons by linking its metastability to the stability of individual polarons, and predicting a region of metastability for the normal partially polarised phase. In the limit of a single impurity, this region extends from the interaction strength at which a polarised phase of molecules becomes the groundstate, to the one at which the single quasiparticle groundstate changes character from polaronic to molecular. Our argument in terms of a Fermi sea of polarons naturally suggests their use as an experimental probe. We propose experiments to observe the threshold of the predicted region of metastability, the interaction strength at which the quasiparticle groundstate changes character, and the decay rate of polarons

Microscopic Structure of a Vortex Line in a Superfluid Fermi Gas

The microscopic properties of a single vortex in a dilute superfluid Fermi gas at zero temperature are examined within the framework of self-consistent Bogoliubov-de Gennes theory. Using only physical parameters as input, we study the pair potential, the density, the energy, and the current distribution. Comparison of the numerical results with analytical expressions clearly indicates that the energy of the vortex is governed by the zero-temperature BCS coherence length.Comment: 4 pages, 4 embedded figures. Added references. To be published in Physical Review Letter

Resonance superfluidity in a quantum degenerate Fermi gas

We consider the superfluid phase transition that arises when a Feshbach resonance pairing occurs in a dilute Fermi gas. We apply our theory to consider a specific resonance in potassium-40, and find that for achievable experimental conditions, the transition to a superfluid phase is possible at the high critical temperature of about 0.5 T_F. Observation of superfluidity in this regime would provide the opportunity to experimentally study the crossover from the superfluid phase of weakly-coupled fermions to the Bose-Einstein condensation of strongly-bound composite bosons.Comment: 4 pages, 3 figure

Ginzburg-Landau-Gor'kov Theory of Magnetic oscillations in a type-II 2-dimensional Superconductor

We investigate de Haas-van Alphen (dHvA) oscillations in the mixed state of a type-II two-dimensional superconductor within a self-consistent Gor'kov perturbation scheme. Assuming that the order parameter forms a vortex lattice we can calculate the expansion coefficients exactly to any order. We have tested the results of the perturbation theory to fourth and eight order against an exact numerical solution of the corresponding Bogoliubov-de Gennes equations. The perturbation theory is found to describe the onset of superconductivity well close to the transition point $H_{c2}$. Contrary to earlier calculations by other authors we do not find that the perturbative scheme predicts any maximum of the dHvA-oscillations below $H_{c2}$. Instead we obtain a substantial damping of the magnetic oscillations in the mixed state as compared to the normal state. We have examined the effect of an oscillatory chemical potential due to particle conservation and the effect of a finite Zeeman splitting. Furthermore we have investigated the recently debated issue of a possibility of a sign change of the fundamental harmonic of the magnetic oscillations. Our theory is compared with experiment and we have found good agreement.Comment: 39 pages, 8 figures. This is a replacement of supr-con/9608004. Several sections changed or added, including a section on the effect of spin and the effect of a conserved number of particles. To be published in Phys. Rev.

Asymmetric Fermi superfluid in a harmonic trap

We consider a dilute two-component atomic fermion gas with unequal populations in a harmonic trap potential using the mean field theory and the local density approximation. We show that the system is phase separated into concentric shells with the superfluid in the core surrounded by the normal fermion gas in both the weak-coupling BCS side and near the Feshbach resonance. In the strong-coupling BEC side, the composite bosons and left-over fermions can be mixed. We calculate the cloud radii and compare axial density profiles systemically for the BCS, near resonance and BEC regimes.Comment: 15 pages, 5 figure

Exact particle and kinetic energy densities for one-dimensional confined gases of non-interacting fermions

We propose a new method for the evaluation of the particle density and kinetic pressure profiles in inhomogeneous one-dimensional systems of non-interacting fermions, and apply it to harmonically confined systems of up to N=1000 fermions. The method invokes a Green's function operator in coordinate space, which is handled by techniques originally developed for the calculation of the density of single-particle states from Green's functions in the energy domain. In contrast to the Thomas-Fermi (local density) approximation, the exact profiles under harmonic confinement show negative local pressure in the tails and a prominent shell structure which may become accessible to observation in magnetically trapped gases of fermionic alkali atoms.Comment: 8 pages, 3 figures, accepted for publication in Phys. Rev. Let