Chapter

Basics on Bose‐Einstein condensation

D. GuÉry‐Odelin and T. Lahaye

in Ultracold Gases and Quantum Information

Published in print May 2011 | ISBN: 9780199603657
Published online September 2011 | e-ISBN: 9780191729515 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199603657.003.0001

Series: Lecture Notes of the Les Houches Summer School

Basics on Bose‐Einstein condensation

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This chapter introduces basic notions about Bose-Einstein condensates (BECs). One first studies ideal Bose gases, putting an emphasis on the role of the trapping geometry and of the dimensionality. One also introduces the correlation functions characterizing coherence. The second section deals with weakly-interacting BECs, which are described, in a mean-field approach, by the so-called Gross-Pitaevskii equation. This equation is derived and applied to a variety of experimentally relevant situations. The third section deals with beyond-mean-field effects that appear when the interactions are stronger, and introduces in particular the Bogolubov approximation. The last section is devoted to the study of BECs in double-well potentials, a situation inspired from condensed matter systems where beyond-mean-field effects can appear quite easily, and which remains simple enough to be studied theoretically in details.

Keywords: Bose-Einstein condensation; coherent matterwaves; Gross-Pitaevskii equation; Bogolubov approximation; beyond-mean-field effects; double-well potentials; Josephson junction; condensate fragmentation

Chapter.  31567 words.  Illustrated.

Subjects: Mathematical and Statistical Physics

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