Stability of trapped Bose-Einstein condensates

In three-dimensional trapped Bose-Einstein condensate (BEC), described by the time-dependent Gross-Pitaevskii-Ginzburg equation, we study the effect of initial conditions on stability using a Gaussian variational approach and exact numerical simulations. We also discuss the validity of the criterion for stability suggested by Vakhitov and Kolokolov. The maximum initial chirp (initial focusing defocusing of cloud) that can lead a stable condensate to collapse even before the number of atoms reaches its critical limit is obtained for several specific cases. When we consider two- and three-body nonlinear terms, with negative cubic and positive quintic terms, we have the conditions for the existence of two phases in the condensate. In this case, the magnitude of the oscillations between the two phases are studied considering sufficient large initial chirps. The occurrence of collapse in a BEC with repulsive two-body interaction is also shown to be possible.Comment: 15 pages, 11 figure

Short-Wave Excitations in Non-Local Gross-Pitaevskii Model

It is shown, that a non-local form of the Gross-Pitaevskii equation allows to describe not only the long-wave excitations, but also the short-wave ones in the systems with Bose-condensate. At given parameter values, the excitation spectrum mimics the Landau spectrum of quasi-particle excitations in superfluid Helium with roton minimum. The excitation wavelength, at which the roton minimum exists, is close to the inter-particle interaction range. It is shown, that the existence domain of the spectrum with a roton minimum is reduced, if one accounts for an inter-particle attraction.Comment: 5 pages, 5 figures, UJP style; presented at Bogolyubov Kyiv Conference "Modern Problems of Theoretical and Mathematical Physics", September 15-18, 200

Exact results on the dynamics of multi-component Bose-Einstein condensate

We study the time-evolution of the two dimensional multi-component Bose-Einstein condensate in an external harmonic trap with arbitrary time-dependent frequency. We show analytically that the time-evolution of the total mean-square radius of the wave-packet is determined in terms of the same solvable equation as in the case of a single-component condensate. The dynamics of the total mean-square radius is also the same for the rotating as well as the non-rotating multi-component condensate. We determine the criteria for the collapse of the condensate at a finite time. Generalizing our previous work on a single-component condensate, we show explosion-implosion duality in the multi-component condensate.Comment: Two-column 6 pages, RevTeX, no figures(v1); Added an important reference, version to appear in Physical Review A (v2

Evaluation of turbulent dissipation rate retrievals from Doppler Cloud Radar

Turbulent dissipation rate retrievals from cloud radar Doppler velocity measurements are evaluated using independent, in situ observations in Arctic stratocumulus clouds. In situ validation data sets of dissipation rate are derived using sonic anemometer measurements from a tethered balloon and high frequency pressure variation observations from a research aircraft, both flown in proximity to stationary, ground-based radars. Modest biases are found among the data sets in particularly low- or high-turbulence regimes, but in general the radar-retrieved values correspond well with the in situ measurements. Root mean square differences are typically a factor of 4-6 relative to any given magnitude of dissipation rate. These differences are no larger than those found when comparing dissipation rates computed from tetheredballoon and meteorological tower-mounted sonic anemometer measurements made at spatial distances of a few hundred meters. Temporal lag analyses suggest that approximately half of the observed differences are due to spatial sampling considerations, such that the anticipated radar-based retrieval uncertainty is on the order of a factor of 2-3. Moreover, radar retrievals are clearly able to capture the vertical dissipation rate structure observed by the in situ sensors, while offering substantially more information on the time variability of turbulence profiles. Together these evaluations indicate that radar-based retrievals can, at a minimum, be used to determine the vertical structure of turbulence in Arctic stratocumulus clouds