Condensed Matter Physics, 2013, vol. 16, No. 2, 23002:116
DOI:10.5488/CMP.16.23002
arXiv:1307.1990
Title:
Selfconsistent approach for Bosecondensed atoms in optical lattices
Author(s):

V.I. Yukalov
(Bogolubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, Russia)

Bose atoms in optical lattices are considered at low temperatures
and weak interactions, when BoseEinstein condensate is formed. A
selfconsistent approach, based on the use of a representative
statistical ensemble, is employed, guaranteeing a gapless spectrum
of collective excitations and the validity of conservation laws. In
order to show that the approach is applicable to both weak and tight
binding, the problem is treated in the Bloch as well as in the
Wannier representations. Both these ways result in similar
expressions that are compared for the selfconsistent
HartreeFockBogolubov approximation. A convenient general formula
for the superfluid fraction of atoms in an optical lattice is
derived.
Key words:
BoseEinstein condensate, representative ensemble,
optical lattices, Bloch representation, Wannier representation, superfluidity
PACS:
03.75.Hh, 03.75.Nt, 05.30.Ch, 05.30.Jp, 05.70.Ce
