From Narrow to Broad Feshbach Resonances: Condensate Fraction of Cooper Pairs and Preformed Molecules

We extend our previous investigations of fermionic condensation in broad Feshbach resonances by using the two-channel model developed for narrow Feshbach resonances. We investigate two crossovers: the BCS-BEC crossover by changing the s-wave scattering length and the crossover from a narrow to a broad resonance by changing the atom-molecule coupling. At zero temperature we analyze, as a function of both atom-molecule coupling and s-wave scattering length, the chemical potential, the energy gap, and the condensate fraction of atoms. In particular, we predict the contribution of Cooper pairs and preformed molecules to the total condensate density along the two crossovers.Comment: 5 pages, 2 figures, accepted for publication in Phys. Rev.

Fermionic condensation in ultracold atoms, nuclear matter and neutron stars

We investigate the Bose-Einstein condensation of fermionic pairs in three different superfluid systems: ultracold and dilute atomic gases, bulk neutron matter, and neutron stars. In the case of dilute gases made of fermionic atoms the average distance between atoms is much larger than the effective radius of the inter-atomic potential. Here the condensation of fermionic pairs is analyzed as a function of the s-wave scattering length, which can be tuned in experiments by using the technique of Feshbach resonances from a small and negative value (corresponding to the Bardeen-Cooper-Schrieffer (BCS) regime of Cooper Fermi pairs) to a small and positive value (corresponding to the regime of the Bose-Einstein condensate (BEC) of molecular dimers), crossing the unitarity regime where the scattering length diverges. In the case of bulk neutron matter the s-wave scattering length of neutron-neutron potential is negative but fixed, and the condensate fraction of neutron-neutron pairs is studied as a function of the total neutron density. Our results clearly show a BCS-quasiunitary-BCS crossover by increasing the neutron density. Finally, in the case of neutron stars, where again the neutron-neutron scattering length is negative and fixed, we determine the condensate fraction as a function of the distance from the center of the neutron star, finding that the maximum condensate fraction appears in the crust of the neutron star.Comment: 9 pages, 3 figures, presented to the 22nd International Laser Physics Workshop, to be published in the Proceeding

Formation of multi-solitons and vortex bright solitons in Bose-condensed alkali-metal atoms

Formation of multi-solitons and vortex bright solitons in Bose-condensed alkali-metal atoms is analyzed by using the nonpolynomial Schordinger equation. A train of bright solitons is obtained from an axially homogeneous Bose-Einstein condensate by a sudden change of the scattering length from repulsive to attractive. We derive an analytical expression for the number of bright solitons generated by using this mechanism. The formula generalizes a previous formula obtained with the 1D Gross-Pitaevskii equation. In the second part we consider vortex bright solitons, namely cigar-shaped bright solitons with a nonzero angular quantum number $k$ along the axial direction. By using a variational approach we determine the shape of vortex bright solitons, showing that the critical number of atoms for the collapse of the vortex soliton increases with a larger $k$. Finally we calculate monopole and quadrupole collective oscillations of these vortex bright solitons.Comment: presented to the XII International Laser Physics Workshop, August 24-29 2003, Hamburg (Germany); to be published in Laser Physic

Condensate fraction in metallic superconductors and ultracold atomic vapors

We investigate the condensate density and the condensate fraction of conduction electrons in weak-coupling superconductors by using the BCS theory and the concept of off-diagonal-long-range-order. We discuss the analytical formula of the zero-temperature condensate density of Cooper pairs as a function of Debye frequency and energy gap, and calculate the condensate fraction for some metals. We study the density of Cooper pairs also at finite temperature showing its connection with the gap order parameter and the effects of the electron-phonon coupling. Finally, we analyze similarities and differences between superconductors and ultracold Fermi atoms in the determination of their condensate density by using the BCS theory.Comment: 14 pages, 1 figure, 1 table, to be published in 'Fermions: Flavors, Properties, and Types' (Nova Science Publishers, New York)

Reply to a Comment on "the Role of Dimensionality in the Stability of a Confined Condensed Bose Gas"

As pointed out by the authors of the comment quant-ph/9712046, in our paper quant-ph/9712030 we studied in detail the metastability of a Bose-Einstein Condensate (BEC) confined in an harmonic trap with zero-range interaction. As well known, the BEC with attractive zero-range interaction is not stable but can be metastable. In our paper we analyzed the role of dimensionality for the metastability of the BEC with attractive and repulsive interaction.Comment: 4 pages, Latex, no figure

Instabilities, Point Attractors and Limit Cycles in a Inflationary Universe

We study the stability of a scalar inflaton field and analyze its point attractors in the phase space. We show that the value of the inflaton field in the vacuum is a bifurcation parameter and prove the possible existence of a limit cycle by using analytical and numerical arguments.Comment: Latex, 11 pages, 3 figures (available upon request), to be published in Modern Physics Letters

Shock waves in a quasi one-dimensional Bose-Einstein condensate

We study analytically and numerically the generation of shock waves in a quasi one-dimensional Bose-Einstein condensate (BEC) made of dilute and ultracold alkali-metal atoms. For the BEC we use an equation of state based on a 1D nonpolynomial Schrodinger equation (1D NPSE), which takes into account density modulations in the transverse direction and generalizes the familiar 1D Gross-Pitaevskii equation (1D GPE). Comparing 1D NPSE with 1D GPE we find quantitative differences in the dynamics of shock waves regarding the velocity of propagation, the time of formation of the shock, and the wavelength of after-shock dispersive ripples.Comment: 11 pages, 4 figures, a typo in Eq. (3) has been corrected, analysis of after-shock dynamics added (with two figures). Title and abstract changed. To be published in European Physical Journal Plu

Low-temperature thermodynamics of the unitary Fermi gas: superfluid fraction, first sound and second sound

We investigate the low-temperature thermodynamics of the unitary Fermi gas by introducing a model based on the zero-temperature spectra of both bosonic collective modes and fermonic single-particle excitations. We calculate the Helmholtz free energy and from it we obtain the entropy, the internal energy and the chemical potential as a function of the temperature. By using these quantities and the Landau's expression for the superfluid density we determine analytically the superfluid fraction, the critical temperature, the first sound velocity and the second sound velocity. We compare our analytical results with other theoretical predictions and experimental data of ultracold atoms and dilute neutron matter.Comment: 7 pages, 6 figures, accepted to publication in Phys. Rev.