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Europhysics Letters (EPL)

Expansion of the non-condensed trapped Bose gas in Bose-Einstein condensation

H Wu, E. Arimondo

Published Jul 15, 1998• 14 citations
Publisher

Abstract

The anisotropic density distribution of Bose particles after expansion from a magnetic trap has been taken as an important signature of the formation of Bose-Einstein condensate. In this letter we show that even for a non-condensed trapped gas one can get an anisotropic distribution due to anisotropic collision rates along radial and axial directions. We demonstrate that the mean energies along those directions, different from the energy in the trap, have opposite evolution tendencies with the expansion. This difference is particularly important for the case where a large number of bosons is trapped. We also show that the velocity distribution of the non-condensed gas in the trap, assumed initially isotropic and Gaussian, becomes anisotropic and with linewidth dependent on the expansion direction.

DOI
10.1209/epl/i1998-00332-7

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The anisotropic density distribution of Bose particles after expansion from a magnetic trap has been taken as an important signature of the formation of Bose-Einstein condensate. In this letter we show that even for a non-condensed trapped gas one can get an anisotropic distribution due to anisotropic collision rates along radial and axial directions. We demonstrate that the mean energies along those directions, different from the energy in the trap, have opposite evolution tendencies with the expansion. This difference is particularly important for the case where a large number of bosons is trapped. We also show that the velocity distribution of the non-condensed gas in the trap, assumed initially isotropic and Gaussian, becomes anisotropic and with linewidth dependent on the expansion direction.
We analyze the expansion process of a thermal trapped gas taking place during the detection of Bose-Einstein condensation through an expansion of the condensate. By extending our Monte Carlo method to study this phenomenon, we demonstrate that the velocity distributions of the thermal trapped atoms are anisotropic due to anisotropic explosion of atoms. The radial and axial components of translational temperature are different from the trap temperature and have opposite evolution tendencies with the gas expansion.
The topic of Bose–Einstein condensation in a uniform, non-interacting gas of bosons is treated in most textbooks on statistical mechanics. In the present chapter we discuss the properties of a non-interacting Bose gas in a trap. We shall calculate equilibrium properties of systems in a semi-classical approximation, in which the energy spectrum is treated as a continuum. For this approach to be valid the temperature must be large compared with Δ∊/ k , where Δ∊ denotes the separation between neighbouring energy levels. As is well known, at temperatures below the Bose–Einstein condensation temperature, the lowest-energy state is not properly accounted for if one simply replaces sums by integrals, and it must be included explicitly. The statistical distribution function is discussed in Sec. 2.1, as is the single-particle density of states, which is a key ingredient in the calculations of thermodynamic properties. Calculations of the transition temperature and the fraction of particles in the condensate are described in Sec. 2.2. In Sec. 2.3 the semi-classical distribution function is introduced. From this we obtain the density profile and the velocity distribution of particles, and use these to determine the shape of an anisotropic cloud after free expansion. Thermodynamic properties of Bose gases are calculated as functions of the temperature in Sec. 2.4. Finally, Sec. 2.5 treats corrections to the transition temperature due to a finite particle number.
We investigate the zero-temperature collective excitations of a Bose-condensed atomic gas in anisotropic parabolic traps. The condensate density is determined by solving the Gross-Pitaevskii (GP) equation using a spherical harmonic expansion. The GP eigenfunctions are then used to solve the Bogoliubov equations to obtain the collective excitation frequencies and mode densities. The frequencies of the various modes, classified by their parity and the axial angular momentum quantum number, m, are mapped out as a function of the axial anisotropy. Specific emphasis is placed upon the evolution of these modes from the modes in the limit of an isotropic trap.
We study the expansion of an atomic Fermi gas interacting attractively with a Bose-Einstein condensate. We observe a slower evolution of the radial-to-axial aspect ratio which reveals the importance of the mutual attraction between the two samples during the first phase of the expansion. For large atom numbers, we also observe a bimodal momentum distribution of the Fermi gas, which reflects the spatial distribution of the mixture in trap. This effect allows us to extract important information on the overlap of the two species across the collapse.
We study the expansion of a dilute ultracold sample of fermions initially trapped in an anisotropic harmonic trap. The expansion of the cloud provides valuable information about the state of the system and the role of interactions. In particular, the time evolution of the deformation of the expanding cloud behaves quite differently depending on whether the system is in the normal or in the superfluid phase. For the superfluid phase, we predict an inversion of the deformation of the sample, similar to what happens with Bose-Einstein condensates. Vice versa, in the normal phase, the inversion of the aspect ratio is never achieved, if the mean field interaction is attractive and collisions are negligible.