We discuss the dynamic properties of a trapped Bose-condensed gas under variations of the confining field and find analytical scaling solutions for the evolving coherent state (condensate). We further discuss the characteristic features and the depletion of this coherent state.

Bogolyubov-De Gennes equations for the excitations of a Bose condensate in the Thomas-Fermi regime in harmonic traps of any asymmetry and introduce a classification of eigenstates. In the case of cylindrical symmetry we emphasize the presence of an accidental degeneracy in the excitation spectrum at certain values of the projection of orbital angular momentum on the symmetry axis and discuss possible consequences of the degeneracy in the context of new signatures of Bose-Einstein condensation.Comment: 4 pages, LaTeX, other comments are at http://WWW.amolf.nl/departments/quantumgassen/TITLE.HTM

We find scaling solutions for the evolution of a Bose gas in time-dependent anisotropic traps and reveal the phenomenon of stochastization in the evolution of a condensate. In contrast to collisionless gases, the evolution of the thermal gas in the hydrodynamic regime proves to be in many aspects similar to that of the condensate. We emphasize that clear signatures of Bose-Einstein condensation and the effects of the loss of coherence can be found in local correlation properties of the evolving gas through the measurement of the rates of intrinsic or light-induced inelastic collisional processes.

We develop the idea of selectively manipulating the condensate in a trapped Bose-condensed gas, without perturbing the thermal cloud. The idea is based on the possibility to modify the mean field interaction between atoms (scattering length) by nearly resonant incident light or by spatially uniform change of the trapping magnetic field. For the gas in the Thomas-Fermi regime we find analytical scaling solutions for the condensate wavefunction evolving under arbitrary variations of the scattering length a. The change of a from positive to negative induces a global collapse of the condensate, and the final stages of the collapse will be governed by intrinsic decay processes.PACS numbers: 34.20.Cf, 03.75.FiThe discovery of Bose-Einstein condensation (BEC) in trapped clouds of ultra-cold alkali atoms [1-3] opened unique possibilities to investigate collective many-body effects in dilute gases. Isolation of a trapped gas from the environment, provided by a wall-less magnetic confinement, makes this object attractive for studying fundamental problems of the physics of many-body quantum systems, such as relaxation and the loss of coherence in the evolving macroscopic quantum state (condensate).In ongoing experiments [4][5][6][7][8] the condensate is set into motion (for example, undergoes oscillations) by varying the confining field. Scaling theory of coherent evolution (without damping and relaxation) of a Bose condensate in harmonic traps under arbitrary frequency variations has been developed in [9,10]. It is important, however, that variations of the confining potential also cause the evolution of the thermal component of a trapped gas. Moreover, in the hydrodynamic regime the thermal cloud in many aspects evolves similarly to the condensate [9]. For example, the asymmetry of free expansion and eigenfrequencies of small oscillations are almost the same.In this paper we develop the idea of selectively manipulating the condensate, without perturbing the thermal cloud. This is especially important for studying the interaction between the condensate and the thermal component. The idea is based on the possibility to modify the mean field interaction between atoms. At low temperatures the latter is proportional to the scattering length a which, as found in [11], can be changed under the influence of red-detuned nearly resonant light. Another option to modify the scattering length relies on the magnetic field dependence of a, predicted in [12], and assumes spatially uniform variations of the trapping field, without changing the trap frequencies. Since the shape of the condensate wavefunction is predetermined by the interaction between particles, the change of a will cause the evolution of the condensate at constant frequencies of the confining potential. Remarkably, at temperatures T ≫ nŨ (n is the gas density,Ũ = 4πh 2 a/m, and m the atom mass) only the condensate evolution will be pronounced, which resembles the picture of the fourth sound in superfluid helium. In this temperature range the shape of the thermal cloud is...