Ground-state properties of an anisotropically trapped alkali gas using Feynman path integration

Abstract

The dilute weakly interacting alkali gas was shown to exhibit the phase transition called Bose-Einstein condensation for the first time in the experiment of Wieman's group in 1995. in this thesis, the ground state properties of the alkali gas trapped in an anisotropic magnetic field are investigated by using the variational method in path integral formalism. The interatomic interaction is approximated by the delta function which is short-range potential. The approximated density matrix is derived. Consequently the ground state energy and wavefunction are obtained. The ground state energy is then compared to the result obtained by the mean field approach both analytically and numerically. The result is shown to equivalent to the variational mean field approach. In addition, a comparison between path integral approach and the numerical mean field approach is shown to give no significant difference. The ground state wavefunction is extracted from the weighting function. Substitute the variational parameters into the expression of wavefunction one can see that the result is close to the numerical method.