Landau damping of transverse quadrupole oscillations of an elongated Bose-Einstein condensate

We study the interaction between low-lying transverse collective oscillations and thermal excitations of an elongated Bose-Einstein condensate by means of perturbation theory. We consider a cylindrically trapped condensate and calculate the transverse elementary excitations at zero temperature by solving the linearized Gross-Pitaevskii equations in two dimensions. We use them to calculate the matrix elements between thermal excited states coupled with the quasi-2D collective modes. The Landau damping of transverse collective modes is investigated as a function of temperature. At low temperatures, the damping rate due to the Landau decay mechanism is in agreement with the experimental data for the decay of the transverse quadrupole mode, but it is too small to explain the slow experimental decay of the transverse breathing mode. The reason for this discrepancy is discussed.Comment: 6 pages, LaTeX, 1 figur

Matter wave solitons at finite temperatures

We consider the dynamics of a dark soliton in an elongated harmonically trapped Bose-Einstein condensate. A central question concerns the behavior at finite temperatures, where dissipation arises due to the presence of a thermal cloud. We study this problem using coupled Gross-Pitaevskii and $N$-body simulations, which include the mean field coupling between the condensate and thermal cloud. We find that the soliton decays relatively quickly even at very low temperatures, with the decay rate increasing with rising temperature.Comment: 6 pages, 2 figures, submitted to the Proceedings of QFS '0

Generating vortex rings in Bose-Einstein condensates in the line-source approximation

We present a numerical method for generating vortex rings in Bose-Einstein condensates confined in axially symmetric traps. The vortex ring is generated using the line-source approximation for the vorticity, i.e., the rotational of the superfluid velocity field is different from zero only on a circumference of given radius located on a plane perpendicular to the symmetry axis and coaxial with it. The particle density is obtained by solving a modified Gross-Pitaevskii equation that incorporates the effect of the velocity field. We discuss the appearance of density profiles, the vortex core structure and the vortex nucleation energy, i.e., the energy difference between vortical and ground-state configurations. This is used to present a qualitative description of the vortex dynamics.Comment: Accepted for publication in Phys. Rev.

Nonlinear waves in a cylindrical Bose-Einstein condensate

We present a complete calculation of solitary waves propagating in a steady state with constant velocity v along a cigar-shaped Bose-Einstein trap approximated as infinitely-long cylindrical. For sufficiently weak couplings (densities) the main features of the calculated solitons could be captured by effective one-dimensional (1D) models. However, for stronger couplings of practical interest, the relevant solitary waves are found to be hybrids of quasi-1D solitons and 3D vortex rings. An interesting hierarchy of vortex rings occurs as the effective coupling constant is increased through a sequence of critical values. The energy-momentum dispersion of the above structures is shown to exhibit characteristics similar to a mode proposed sometime ago by Lieb within a strictly 1D model, as well as some rotonlike features.Comment: 10 pages, 12 figure

Breakdown of superfluidity of an atom laser past an obstacle

The 1D flow of a continuous beam of Bose-Einstein condensed atoms in the presence of an obstacle is studied as a function of the beam velocity and of the type of perturbing potential (representing the interaction of the obstacle with the atoms of the beam). We identify the relevant regimes: stationary/time-dependent and superfluid/dissipative; the absence of drag is used as a criterion for superfluidity. There exists a critical velocity below which the flow is superfluid. For attractive obstacles, we show that this critical velocity can reach the value predicted by Landau's approach. For penetrable obstacles, it is shown that superfluidity is recovered at large beam velocity. Finally, enormous differences in drag occur when switching from repulsive to attractive potential.Comment: 15 pages, 6 figure

Adiabatic Output Coupling of a Bose Gas at Finite Temperatures

We develop a general theory of adiabatic output coupling from trapped atomic Bose-Einstein Condensates at finite temperatures. For weak coupling, the output rate from the condensate, and the excited levels in the trap, settles in a time proportional to the inverse of the spectral width of the coupling to the output modes. We discuss the properties of the output atoms in the quasi-steady-state where the population in the trap is not appreciably depleted. We show how the composition of the output beam, containing condensate and thermal component, may be controlled by changing the frequency of the output coupler. This composition determines the first and second order coherence of the output beam. We discuss the changes in the composition of the bose gas left in the trap and show how nonresonant output coupling can stimulate either the evaporation of thermal excitations in the trap or the growth of non-thermal excitations, when pairs of correlated atoms leave the condensate.Comment: 22 pages, 6 Figs. To appear in Physical Review A All the typos from the previous submission have been fixe

Simple method for excitation of a Bose-Einstein condensate

An appropriate, time-dependent modification of the trapping potential may be sufficient to create effectively collective excitations in a cold atom Bose-Einstein condensate. The proposed method is complementary to earlier suggestions and should allow the creation of both dark solitons and vortices.Comment: 8 pages, 7 figures, version accepted for publication in Phys. Rev.

Thermodynamics of an interacting trapped Bose-Einstein gas in the classical field approximation

We present a convenient technique describing the condensate in dynamical equilibrium with the thermal cloud, at temperatures close to the critical one. We show that the whole isolated system may be viewed as a single classical field undergoing nonlinear dynamics leading to a steady state. In our procedure it is the observation process and the finite detection time that allow for splitting the system into the condensate and the thermal cloud.Comment: 4 pages, 4 eps figures, final versio

Generation and evolution of vortex-antivortex pairs in Bose-Einstein condensates

We propose a method for generating and controlling a spatially separated vortex--antivortex pair in a Bose-Einstein condensate trapped in a toroidal potential. Our simulations of the time dependent Gross-Pitaevskii equation show that in toroidal condensates vortex dynamics are different from the dynamics in the homogeneous case. Our numerical results agree well with analytical calculations using the image method. Our proposal offers an effective example of coherent generation and control of vortex dynamics in atomic condensates.Comment: 4 pages, 2 figure

Vortex dynamics in trapped Bose-Einstein condensate

We perform numerical simulations of vortex motion in a trapped Bose-Einstein condensate by solving the two-dimensional Gross-Pitaevskii Equation in the presence of a simple phenomenological model of interaction between the condensate and the finite temperature thermal cloud. At zero temperature, the trajectories of a single, off - centred vortex precessing in the condensate, and of a vortex - antivortex pair orbiting within the trap, excite acoustic emission. At finite temperatures the vortices move to the edge of the condensate and vanish. By fitting the finite -temperature trajectories, we relate the phenomenological damping parameter to the friction coefficients $\alpha$ and $\alpha^{'}$, which are used to describe the interaction between quantised vortices and the normal fluid in superfluid helium.Comment: 16 pages, 18 figures, published in JLT