Generation of linear waves in the flow of Bose-Einstein condensate past an obstacle

The theory of linear wave structures generated in Bose-Einstein condensate flow past an obstacle is developed. The shape of wave crests and dependence of amplitude on coordinates far enough from the obstacle are calculated. The results are in good agreement with the results of numerical simulations obtained earlier. The theory gives a qualitative description of experiments with Bose-Einstein condensate flow past an obstacle after condensate's release from a trap.Comment: 11 pages, 3 figures, to be published in Zh. Eksp. Teor. Fi

Three-dimensional vortex dynamics in Bose-Einstein condensates

We simulate in the mean-field limit the effects of rotationally stirring a three-dimensional trapped Bose-Einstein condensate with a Gaussian laser beam. A single vortex cycling regime is found for a range of trap geometries, and is well described as coherent cycling between the ground and the first excited vortex states. The critical angular speed of stirring for vortex formation is quantitatively predicted by a simple model. We report preliminary results for the collisions of vortex lines, in which sections may be exchanged.Comment: 4 pages, 4 figures, REVTeX 3.1; Submitted to Physical Review A (6 March 2000

Critical velocity in cylindrical Bose-Einstein condensates

We describe a dramatic decrease of the critical velocity in elongated cylindrical Bose-Einstein condensates which originates from the non-uniform character of the radial density profile. We discuss this mechanism with respect to recent measurements at MIT.Comment: 3 pages, 2 eps figures, revised according to referee's comment

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

Formation, dynamics and stability of coreless vortex dipoles in phase-separated binary condensates

We study the motion of the Gaussian obstacle potential created by blue detuned laser beam through a phase-separated binary condensate in pancake-shaped traps. For the velocity of the obstacle above a critical velocity, we observe the generation of vortex dipoles in the outer component which can penetrate the inner component. This is equivalent to finite, although small, transport of outer component across the inner component. In the inner component, the same method can lead to the formation of coreless vortex dipoles.Comment: 12 pages, 9 figure

Observation of Superfluid Flow in a Bose-Einstein Condensed Gas

We have studied the hydrodynamic flow in a Bose-Einstein condensate stirred by a macroscopic object, a blue detuned laser beam, using nondestructive {\em in situ} phase contrast imaging. A critical velocity for the onset of a pressure gradient has been observed, and shown to be density dependent. The technique has been compared to a calorimetric method used previously to measure the heating induced by the motion of the laser beam.Comment: 4 pages, 5 figure

Critical velocity for a toroidal Bose-Einstein condensate flowing through a barrier

We consider the setup employed in a recent experiment (Ramanathan et al 2011 Phys. Rev. Lett. 106 130401) devoted to the study of the instability of the superfluid flow of a toroidal Bose-Einstein condensate in presence of a repulsive optical barrier. Using the Gross-Pitaevskii mean-field equation, we observe, consistently with what we found in Piazza et al (2009 Phys. Rev. A 80 021601), that the superflow with one unit of angular momentum becomes unstable at a critical strength of the barrier, and decays through the mechanism of phase slippage performed by pairs of vortex-antivortex lines annihilating. While this picture qualitatively agrees with the experimental findings, the measured critical barrier height is not very well reproduced by the Gross-Pitaevskii equation, indicating that thermal fluctuations can play an important role (Mathey et al 2012 arXiv:1207.0501). As an alternative explanation of the discrepancy, we consider the effect of the finite resolution of the imaging system. At the critical point, the superfluid velocity in the vicinity of the obstacle is always of the order of the sound speed in that region, $v_{\rm barr}=c_{\rm l}$. In particular, in the hydrodynamic regime (not reached in the above experiment), the critical point is determined by applying the Landau criterion inside the barrier region. On the other hand, the Feynman critical velocity $v_{\rm f}$ is much lower than the observed critical velocity. We argue that this is a general feature of the Gross-Pitaevskii equation, where we have $v_{\rm f}=\epsilon\ c_{\rm l}$ with $\epsilon$ being a small parameter of the model. Given these observations, the question still remains open about the nature of the superfluid instability.Comment: Extended versio

Collective excitations of trapped Bose condensates in the energy and time domains

A time-dependent method for calculating the collective excitation frequencies and densities of a trapped, inhomogeneous Bose-Einstein condensate with circulation is presented. The results are compared with time-independent solutions of the Bogoliubov-deGennes equations. The method is based on time-dependent linear-response theory combined with spectral analysis of moments of the excitation modes of interest. The technique is straightforward to apply, is extremely efficient in our implementation with parallel FFT methods, and produces highly accurate results. The method is suitable for general trap geometries, condensate flows and condensates permeated with vortex structures.Comment: 6 pages, 3 figures small typos fixe

Superfluid behaviour of a two-dimensional Bose gas

Two-dimensional (2D) systems play a special role in many-body physics. Because of thermal fluctuations, they cannot undergo a conventional phase transition associated to the breaking of a continuous symmetry. Nevertheless they may exhibit a phase transition to a state with quasi-long range order via the Berezinskii-Kosterlitz-Thouless (BKT) mechanism. A paradigm example is the 2D Bose fluid, such as a liquid helium film, which cannot Bose-condense at non-zero temperature although it becomes superfluid above a critical phase space density. Ultracold atomic gases constitute versatile systems in which the 2D quasi-long range coherence and the microscopic nature of the BKT transition were recently explored. However, a direct observation of superfluidity in terms of frictionless flow is still missing for these systems. Here we probe the superfluidity of a 2D trapped Bose gas with a moving obstacle formed by a micron-sized laser beam. We find a dramatic variation of the response of the fluid, depending on its degree of degeneracy at the obstacle location. In particular we do not observe any significant heating in the central, highly degenerate region if the velocity of the obstacle is below a critical value.Comment: 5 pages, 3 figure