Density and spin response of a strongly-interacting Fermi gas in the attractive and quasi-repulsive regime

Recent experimental advances in ultra-cold Fermi gases allow for exploring response functions under different dynamical conditions. In particular, the issue of obtaining a "quasi-repulsive" regime starting from a Fermi gas with an attractive inter-particle interaction while avoiding the formation of the two-body bound state is currently debated. Here, we provide a calculation of the density and spin response for a wide range of temperature and coupling both in the attractive and quasi-repulsive regime, whereby the system is assumed to evolve non-adiabatically toward the "upper branch" of the Fermi gas. A comparison is made with the available experimental data for these two quantities.Comment: 8 pages, 7 figures, to appear on Phys. Rev. Let

Size shrinking of composite bosons for increasing density in the BCS to Bose-Einstein crossover

We consider a system of fermions in the continuum case at zero temperature, in the strong-coupling limit of a short-range attraction when composite bosons form as bound-fermion pairs. We examine the density dependence of the size of the composite bosons at leading order in the density ("dilute limit"), and show on general physical grounds that this size should decrease with increasing density, both in three and two dimensions. We then compare with the analytic zero-temperature mean-field solution, which indeed exhibits the size shrinking of the composite bosons both in three and two dimensions. We argue, nonetheless, that the two-dimensional mean-field solution is not consistent with our general result in the "dilute limit", to the extent that mean field treats the scattering between composite bosons in the Born approximation which is known to break down at low energy in two dimensions.Comment: Revised version to be published on Eur. Phys. Jour. B, 7 pages, 1 figur

Extracting the condensate density from projection experiments with Fermi gases

A debated issue in the physics of the BCS-BEC crossover with trapped Fermi atoms is to identify characteristic properties of the superfluid phase. Recently, a condensate fraction was measured on the BCS side of the crossover by sweeping the system in a fast (nonadiabatic) way from the BCS to the BEC sides, thus ``projecting'' the initial many-body state onto a molecular condensate. We analyze here the theoretical implications of these projection experiments, by identifying the appropriate quantum-mechanical operator associated with the measured quantities and relating them to the many-body correlations occurring in the BCS-BEC crossover. Calculations are presented over wide temperature and coupling ranges, by including pairing fluctuations on top of mean field.Comment: 4 pages, 4 figure

From superconducting fluctuations to the bosonic limit in the response functions above the critical temperature

We investigate the density, current, and spin response functions above the critical temperature for a system of three-dimensional fermions interacting via an attractive short-range potential. In the strong-coupling (bosonic) limit of this interaction, we identify the dominant diagrammatic contributions for a ``dilute'' system of composite bosons which form as bound-fermion pairs, and compare them with the usual (Aslamazov-Larkin, Maki-Thompson, and density-of-states) terms occurring in the theory of superconducting fluctuations above the critical temperature for a clean system in the weak-coupling limit. We show that, at the zeroth order in the diluteness parameter for the composite bosons, the Aslamazov-Larkin term still represents formally the dominant contribution to the density and current response functions, while the Maki-Thompson and density-of-states terms are strongly suppressed. Corrections to the Aslamazov-Larkin term are then considered at the next order in the diluteness parameter for the composite bosons. The spin response function is also examined, and it is found to be exponentially suppressed in the bosonic limit only when appropriate sets of diagrams are considered simultaneously.Comment: 10 pages, 6 figure

Gap equation with pairing correlations beyond mean field and its equivalence to a Hugenholtz-Pines condition for fermion pairs

The equation for the gap parameter represents the main equation of the pairing theory of superconductivity. Although it is formally defined through a single-particle property, physically it reflects the pairing correlations between opposite-spin fermions. Here, we exploit this physical connection and cast the gap equation in an alternative form which explicitly highlights these two-particle correlations, by showing that it is equivalent to a Hugenholtz-Pines condition for fermion pairs. At a formal level, a direct connection is established in this way between the treatment of the condensate fraction in condensate systems of fermions and bosons. At a practical level, the use of this alternative form of the gap equation is expected to make easier the inclusion of pairing fluctuations beyond mean field. As a proof-of-concept of the new method, we apply the modified form of the gap equation to the long-pending problem about the inclusion of the Gorkov-Melik-Barkhudarov correction across the whole BCS-BEC crossover, from the BCS limit of strongly overlapping Cooper pairs to the BEC limit of dilute composite bosons, and for all temperatures in the superfluid phase. Our numerical calculations yield excellent agreement with the recently determined experimental values of the gap parameter for an ultra-cold Fermi gas in the intermediate regime between BCS and BEC, as well as with the available quantum Monte Carlo data in the same regime.Comment: 24 pages, 13 figure

Temperature dependence of a vortex in a superfluid Fermi gas

The temperature dependence of an isolated quantum vortex, embedded in an otherwise homogeneous fermionic superfluid of infinite extent, is determined via the Bogoliubov-de Gennes (BdG) equations across the BCS-BEC crossover. Emphasis is given to the BCS side of this crossover, where it is physically relevant to extend this study up to the critical temperature for the loss of the superfluid phase, such that the size of the vortex increases without bound. To this end, two novel techniques are introduced. The first one solves the BdG equations with "free boundary conditions", which allows one to determine with high accuracy how the vortex profile matches its asymptotic value at a large distance from the center, thus avoiding a common practice of constraining the vortex in a cylinder with infinite walls. The second one improves on the regularization procedure of the self-consistent gap equation when the inter-particle interaction is of the contact type, and permits to considerably reduce the time needed for its numerical integration, by drawing elements from the derivation of the Gross-Pitaevskii equation for composite bosons starting from the BdG equations.Comment: 18 pgaes, 16 figure

Anisotropy probe of galactic and extra-galactic Dark Matter annihilations

We study the flux and the angular power spectrum of gamma-rays produced by Dark Matter (DM) annihilations in the Milky Way (MW) and in extra-galactic halos. The annihilation signal receives contributions from: a) the smooth MW halo, b) resolved and unresolved substructures in the MW, c) external DM halos at all redshifts, including d) their substructures. Adopting a self-consistent description of local and extra-galactic substructures, we show that the annihilation flux from substructures in the MW dominates over all the other components for angles larger than O(1) degrees from the Galactic Center, unless an extreme prescription is adopted for the substructures concentration. We also compute the angular power spectrum of gamma-ray anisotropies and find that, for an optimistic choice of the particle physics parameters, an interesting signature of DM annihilations could soon be discovered by the Fermi LAT satellite at low multipoles, l<100, where the dominant contribution comes from MW substructures with mass M>10^4 solar masses. For the substructures models we have adopted, we find that the contribution of extra-galactic annihilations is instead negligible at all scales.Comment: 14 pages, 7 figure

Bose-Fermi mixtures in the molecular limit

We consider a Bose-Fermi mixture in the molecular limit of the attractive interaction between fermions and bosons. For a boson density smaller or equal to the fermion density, we show analytically how a T-matrix approach for the constituent bosons and fermions recovers the expected physical limit of a Fermi-Fermi mixture of molecules and atoms. In this limit, we derive simple expressions for the self-energies, the momentum distribution function, and the chemical potentials. By extending these equations to a trapped system, we determine how to tailor the experimental parameters of a Bose-Fermi mixture in order to enhance the 'indirect Pauli exclusion effect' on the boson momentum distribution function. For the homogeneous system, we present finally a Diffusion Monte Carlo simulation which confirms the occurrence of such a peculiar effect.Comment: 13 pages, 7 figures; final versio