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

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

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

Observation of Spin Superfluidity in a Bose Gas Mixture

The spin dynamics of a harmonically trapped Bose-Einstein condensed binary mixture of sodium atoms is experimentally investigated at finite temperature. In the collisional regime the motion of the thermal component is shown to be damped because of spin drag, while the two condensates exhibit a counter flow oscillation without friction, thereby providing direct evidence for spin superfluidity. Results are also reported in the collisionless regime where the spin components of both the condensate and thermal part oscillate without damping, their relative motion being driven by a mean field effect. We also measure the static polarizability of the condensed and thermal parts and we find a large increase of the condensate polarizability with respect to the T=0 value, in agreement with the predictions of theory.Comment: 6 pages, 4 figures + Suppl. Mat. (2 pages, 1 figure

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

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

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

The decay and collisions of dark solitons in superfluid Fermi gases

We study soliton collisions and the decay of solitons into sound in superfluid Fermi gases across the Bose-Einstein condensate to Bardeen-Cooper-Schrieffer (BEC-BCS) crossover by performing numerical simulations of the time-dependent Bogoliubov-de Gennes equations. This decay process occurs when the solitons are accelerated to the bulk pair-breaking speed by an external potential. A similar decay process may occur when solitons are accelerated by an inelastic collision with another soliton. We find that soliton collisions become increasingly inelastic as we move from the BEC to BCS regimes, and the excess energy is converted into sound. We interpret this effect as being due to evolution of Andreev bound states localized within the soliton.Comment: 9 pages, 5 figure

Quantized vortices and collective oscillations of a trapped Bose condensed gas

Using a sum rule approach we calculate the frequency shifts of the quadrupole oscillations of a harmonically trapped Bose gas due to the presence of a quantized vortex. Analytic results are obtained for positive scattering lengths and large N where the shift relative to excitations of opposite angular momentum is found to be proportional to the quantum circulation of the vortex and to decrease as N^{-2/5}. Results are also given for smaller values of N covering the transition between the ideal gas and the Thomas-Fermi limit. For negative scattering lengths we predict a macroscopic instability of the vortex. The splitting of the collective frequencies in toroidal configurations is also discussed.Comment: Rextex, 4 pages, 1 postscript figur

Moment of Inertia and Superfluidity of a Trapped Bose Gas

The temperature dependence of the moment of inertia of a dilute Bose gas confined in a harmonic trap is determined. Deviations from the rigid value, due to the occurrence of Bose-Einstein condensation, reveal the superfluid behaviour of the system. In the noninteracting gas these deviations become important at temperatures of the order of $T_c N^{-1/12}$. The role of interactions is also discussed.Comment: 10 pages, REVTEX, 1 figure attached as postscript fil