Trapped Bose condensed systems: failure of the Thomas-Fermi approximation in the bulk

Gyula Bene, P. Szépfalusy

Corrections to the Thomas-Fermi-type solution of the Gross-Pitaevskii equation are inevitable in order to get correctly the frequencies of the low lying modes out of the Bogolyubov equations. These corrections are important in the bulk, too, thus the failure of the Thomas-Fermi approximation is not confined to the surface. We discuss this effect quantitatively and consider similar phenomena of spin fluctuations in Bose-Einstein condensed gases in an optical trap.

Mohamed Benarous, H. Chachou-Samet

Nick P. Proukakis

Alexander L. Zubarev, Yeong E. Kim

We present an analytical approximation for nonlinear dynamics of trapped Bose-co ndensed gases. The new approximation is a substantial improvement over the Thomas-Fermi approximation and is shown to be applicable for systems with a rather small number of atoms $N$. The calculated aspect ratios after ballistic expansion are found to be in good agreement with those observed in recent experiments.

Peter Schuck, X. Viñas

Thomas-Fermi theory for Bose-Einstein condensates in inhomogeneous traps is revisited. The phase-space distribution function of the condensate in the Thomas-Fermi limit $(\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\Elzxh}}0)$ is ${f}_{0}(\mathit{R},\mathit{p})\ensuremath{\propto}\ensuremath{\delta}(\ensuremath{\mu}\ensuremath{-}{H}_{\mathrm{cl}})$ where ${H}_{\mathrm{cl}}$ is the classical counterpart of the self-consistent Gross-Pitaevskii Hamiltonian. Starting from this distribution function the Thomas-Fermi kinetic energy is calculated for any number of particles. Good agreement between the Gross-Pitaevskii and Thomas-Fermi kinetic energies is found even for low and intermediate particle numbers N. Application of this Thomas-Fermi theory to the attractive case and to the calculation of the frequencies of the monopole and quadrupole excitations in the sum rule approach yields conclusive results as well. The difference with the usual Thomas-Fermi approach to the Bose-Einstein condensates (large-N limit) is discussed in detail.

Gora V. Shlyapnikov