Bose-Einstein condensation in dilute atomic gases

Abstract

The material presented here consists of lecture notes written for a five two-hour sections course given during the 2004 edition of the Brazilian School on Statistical Mechanics. The topics covered are 1. Bose-Einstein condensation of trapped ideal gases; 2. Effective two-body interactions and exact results in the Gross-Pitaevski limit; 3. Atomic structure effects, including "Feshbach resonances" and hybrid condensates; 4. Elementary excitations in the Bogoliubov approximation and beyond; and 5. Splitt traps, interference phenomena and condensate arrays.

Bethe states for the two-site Bose–Hubbard model: A binomial approach

“…After its realization a great deal of progress has taken place both in the theoretical and experimental study of this physical phenomenon [6][7][8][9][10][11][12][13]. A particularly fruitful instrument in relation to ultracold physics are many-body atomic models related to BEC.…”

“…The first experimental verification of the Bose-Einstein condensation (BEC) [1,2,3] occurred after a gap of more than seven decades following its theoretical prediction [4,5]. After its realization a great deal of progress has taken place both in the theoretical and experimental study of this physical phenomenon [6,7,8,9,10,11,12,13]. A particularly fruitful instrument in relation to ultracold physics are many-body atomic models related to BEC.…”