Dynamical instability and dispersion management of an attractive condensate in an optical lattice

We investigate the stability of an attractive Bose-Einstein condensate in a moving 1D optical lattice in the presence of transverse confinement. By means of a Bogoliubov linear stability analysis we find that the system is dynamically unstable for low quasimomenta and becomes stable near the band edge, in a specular fashion with respect to the repulsive case. For low interactions the instability occurs via long wavelength excitations that are not sufficient for spoiling the condensate coherence, producing instead an oscillating density pattern both in real and momentum space. This behaviour is illustrated by simulations for the expansion of the condensate in a moving lattice.Comment: 5 pages, 4 figure

Oscillations of a Bose-Einstein condensate rotating in a harmonic plus quartic trap

We study the normal modes of a two-dimensional rotating Bose-Einstein condensate confined in a quadratic plus quartic trap. Hydrodynamic theory and sum rules are used to derive analytical predictions for the collective frequencies in the limit of high angular velocities, $\Omega$, where the vortex lattice produced by the rotation exhibits an annular structure. We predict a class of excitations with frequency $\sqrt{6} \Omega$ in the rotating frame, irrespective of the mode multipolarity $m$, as well as a class of low energy modes with frequency proportional to $|m|/\Omega$. The predictions are in good agreement with results of numerical simulations based on the 2D Gross-Pitaevskii equation. The same analysis is also carried out at even higher angular velocities, where the system enters the giant vortex regime.Comment: 4 pages, 2 figure

Macroscopic dynamics of a trapped Bose-Einstein condensate in the presence of 1D and 2D optical lattices

The hydrodynamic equations of superfluids for a weakly interacting Bose gas are generalized to include the effects of periodic optical potentials produced by stationary laser beams. The new equations are characterized by a renormalized interaction coupling constant and by an effective mass accounting for the inertia of the system along the laser direction. For large laser intensities the effective mass is directly related to the tunneling rate between two consecutive wells. The predictions for the frequencies of the collective modes of a condensate confined by a magnetic harmonic trap are discussed for both 1D and 2D optical lattices and compared with recent experimental data.Comment: 4 pages, 2 postscript figure

Effects of Disorder in a Dilute Bose Gas

We discuss the effects of a weak random external potential on the properties of the dilute Bose gas at zero temperature. The results recently obtained by Huang and Meng for the depletion of the condensate and of the superfluid density are recovered. Results for the shift of the velocity of sound as well as for its damping due to collisions with the external field are presented. The damping of phonons is calculated also for dense superfluids. (submitted to Phys.Rev.B)Comment: 21 pages, Plain Tex, 2 figures available upon request, preprint UTF 31

Collective oscillations of a trapped Fermi gas near a Feshbach resonance

The frequencies of the collective oscillations of a harmonically trapped Fermi gas interacting with large scattering lengths are calculated at zero temperature using hydrodynamic theory. Different regimes are considered, including the molecular Bose-Einstein condensate and the unitarity limit for collisions. We show that the frequency of the radial compressional mode in an elongated trap exhibits a pronounced non monotonous dependence on the scattering length, reflecting the role of the interactions in the equation of state.Comment: 3 pages, including 1 figur

Temperature-dependent density profiles of trapped boson-fermion mixtures

We present a semiclassical three-fluid model for a Bose-condensed mixture of interacting Bose and Fermi gases confined in harmonic traps at finite temperature. The model is used to characterize the experimentally relevant behaviour of the equilibrium density profile of the fermions with varying composition and temperature across the onset of degeneracy, for coupling strengths relevant to a mixture of $^{39}$K and $^{40}$K atoms.Comment: 9 pages, 2 postscript figures, accepted for publication in Eur. Phys. Jour.

Kinetic energy of a trapped Fermi gas interacting with a Bose-Einstein condensate

We study a confined mixture of bosons and fermions in the regime of quantal degeneracy, with particular attention to the effects of the interactions on the kinetic energy of the fermionic component. We are able to explore a wide region of system parameters by identifying two scaling variables which completely determine its state at low temperature. These are the ratio of the boson-fermion and boson-boson interaction strengths and the ratio of the radii of the two clouds. We find that the effect of the interactions can be sizeable for reasonable choices of the parameters and that its experimental study can be used to infer the sign of the boson-fermion scattering length. The interplay between interactions and thermal effects in the fermionic kinetic energy is also discussed.Comment: REVTEX, 8 pages, 6 figures included. Small corrections to text and figures, accepted for publication in EPJ

Scissors mode and superfluidity of a trapped Bose-Einstein condensed gas

We investigate the oscillation of a dilute atomic gas generated by a sudden rotation of the confining trap (scissors mode). This oscillation reveals the effects of superfluidity exhibited by a Bose-Einstein condensate. The scissors mode is investigated also in a classical gas above T_c in various collisional regimes. The crucial difference with respect to the superfluid case arises from the occurence of low frequency components, which are responsible for the rigid value of the moment of inertia. Different experimental procedures to excite the scissors mode are discussed.Comment: 4 pages, 3 figure