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Acta Physica Sinica

A GENERAL APPROACH TO THE BOSE-EINSTEIN CONDENSATION OF NEUTRAL ATOMS WITH REPELLENT INTERACTION

TAN WEI-HAN, YAN KE-ZHU, 上海大学物理系，上海 201800

Published Jan 1, 1999• 3 citations
Publisher

Abstract

In this paper a general approach to the Bose-Einstein condensation of neutral atoms with repellent interaction is presented.Especially in the case of free atoms (V=0) with repellent interaction,an exact solution for the atom's wave function can be derived,and therefore the calculation of atom's Bose-Einstein condensation is completed.

DOI
10.7498/aps.48.1983

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In this paper a general approach to the Bose-Einstein condensation of neutral atoms with repellent interaction is presented.Especially in the case of free atoms (V=0) with repellent interaction,an exact solution for the atom's wave function can be derived,and therefore the calculation of atom's Bose-Einstein condensation is completed.
Amplifying on a proposal by O'Dell et al. for the realization of Bose-Einstein condensates of neutral atoms with attractive 1∕r1∕r1∕r interaction, we point out that the instance of self-trapping of the condensate, without an external trap potential, is physically best understood by introducing appropriate ``atomic'' units. This reveals a remarkable scaling property: the physics of the condensate depends only on the two parameters N2a∕au{N}^{2}a∕{a}_{u}N2a∕au​ and $\ensuremath{\gamma}∕{N}^{2}$, where NNN is the particle number, aaa the scattering length, au{a}_{u}au​ the ``Bohr'' radius, and $\ensuremath{\gamma}$ the trap frequency in atomic units. We calculate accurate numerical results for self-trapping wave functions and potentials, and for energies, sizes, and peak densities, and compare with previous variational results. We point out the existence of a second solution of the extended Gross-Pitaevskii equation for negative scattering lengths, with and without trapping potential, which is born together with the ground state in a tangent bifurcation. This indicates the existence of an unstable collectively excited state of the condensate for negative scattering lengths.
Bose-Einstein condensation is described in terms of the condensate wave function and the pair-excitation function, the latter being responsible for the existence of phonons. This minimal description in terms of these two functions is generalized to the case with an external potential. For a dilute gas with short-range pairwise repulsive interaction and at very low temperatures when the Bose-Einstein condensation is nearly complete, a partial differential equation is obtained for the condensate wave function and an integro-differential equation for the pair excitation. Experimentally, the external potential is used to trap the atoms, i.e., to keep them together. Since the trap is of macroscopic dimensions, the resulting external potential is often slowly varying. In these cases and when the condensate is in the lowest state, the partial differential equation for the condensate wave function and the integro-differential equation for the pair excitation are solved approximately for the case of a time-independent trap.
This article reviews recent investigations on the phenomenon of Bose-Einstein condensation of dilute gases. Since the experimental observation of quantum degeneracy in atomic gases, the research activity in the field of coherent matter-waves literally exploded. The present topical review aims to give an introduction into the thermodynamics of Bose-Einstein condensation, a general overview over experimental techniques and investigations, and a theoretical foundation for the description of bosonic many-body quantum systems.
The particle distribution in a Bose condensate under the trapping potential and its time evolution after switching off the trapping potential suddenly are calculated. We investigate the problem from the viewpoint of quantum field theory,using a model of self-interacting neutral boson field. Within the approximation of retainng the most dominant term in the Hamiltonian after applying the Bogoliubov replacement, we can calculate analytically the particle distribution as a function of space and time coordinates.
The interaction between two species of atoms in the condensate has been deduced and the trial wave functions that conserve the total spin have been constructed for the states of the ground band. A couple of generalized Gross-Pitaevskii equations have been derived for the spatial wave functions and the energies. The mixture of 23Na^{23}\mathrm{Na}23Na and 87Rb^{87}\mathrm{Rb}87Rb has been calculated as an example. The density of states is found to exhibit a ladder shape.