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

First and second sound in cylindrically trapped gases

We investigate the propagation of density and temperature waves in a cylindrically trapped gas with radial harmonic confinement. Starting from two-fluid hydrodynamic theory we derive effective 1D equations for the chemical potential and the temperature which explicitly account for the effects of viscosity and thermal conductivity. Differently from quantum fluids confined by rigid walls, the harmonic confinement allows for the propagation of both first and second sound in the long wave length limit. We provide quantitative predictions for the two sound velocities of a superfluid Fermi gas at unitarity. For shorter wave-lengths we discover a new surprising class of excitations continuously spread over a finite interval of frequencies. This results in a non-dissipative damping in the response function which is analytically calculated in the limiting case of a classical ideal gas.Comment: 4 pages, 2 figures. Published version in Phys. Rev. Let

Equilibrium and dynamics of a trapped superfluid Fermi gas with unequal masses

Interacting Fermi gases with equal populations but unequal masses are investigated at zero temperature using local density approximation and the hydrodynamic theory of superfluids in the presence of harmonic trapping. We derive the conditions of energetic stability of the superfluid configuration with respect to phase separation and the frequencies of the collective oscillations in terms of the mass ratio and the trapping frequencies of the two components. We discuss the behavior of the gas after the trapping potential of a single component is switched off and show that, near a Feshbach resonance, the released component can still remain trapped due to many-body interaction effects. Explicit predictions are presented for a mixture of $^6$Li and $^{40}$K with resonant interaction.Comment: 4 pages, 2 figure

Collective Excitations of a "Gravitationally" Self-Bound Bose Gas

We investigate the collective excitations of an atomic Bose-Einstein condensate in the self-binding regime produced by electromagnetically induced ``gravity'' (1/r attraction). Analytical expressions for the frequencies of the monopole and quadrupole modes are obtained at zero temperature, using the sum-rule approach, and compared with the exact results available in the Thomas-Fermi limit. The low-energy dynamics of such condensates is shown to be dominated by the effective ``plasma'' frequency. An analog of the Jeans gravitational instability is analyzed.Comment: 4 pages, 1 eps figur

Equation of state and collective frequencies of a trapped Fermi gas along the BEC-unitarity crossover

We show that the study of the collective oscillations in a harmonic trap provides a very sensitive test of the equation of state of a Fermi gas near a Feshbach resonance. Using a scaling approach, whose high accuracy is proven by comparison with exact hydrodynamic solutions, the frequencies of the lowest compressional modes are calculated at T=0 in terms of a dimensionless parameter characterizing the equation of state. The predictions for the collective frequencies, obtained from the equations of state of mean field BCS theory and of recent Monte-Carlo calculations, are discussed in detail.Comment: 4 pages, 3 figure

Umklapp collisions and center of mass oscillation of a trapped Fermi gas

Starting from the the Boltzmann equation, we study the center of mass oscillation of a harmonically trapped normal Fermi gas in the presence of a one-dimensional periodic potential. We show that for values of the the Fermi energy above the first Bloch band the center of mass motion is strongly damped in the collisional regime due to umklapp processes. This should be contrasted with the behaviour of a superfluid where one instead expects the occurrence of persistent Josephson-like oscillations.Comment: 11 pages, 3 figures, corrected typo

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

The dynamics of dark solitons in a trapped superfluid Fermi gas

We study soliton oscillations in a trapped superfluid Fermi gas across the Bose-Einstein condensate to Bardeen-Cooper-Schrieffer (BEC-BCS) crossover. We derive an exact equation relating the phase jump across the soliton to its energy, and hence obtain an expression for the soliton period. Our analytic approach is supported by simulations of the time-dependent Bogoliubov-de Gennes equations, which show that the period dramatically increases as the soliton becomes shallower on the BCS side of the resonance. Finally, we propose an experimental protocol to test our predictions.Comment: 5 pages, 4 figure