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Science in China. Series G, Physics, mechanics & astronomy/Science in China. Series G, Physics, Mechanics & Astronomy

Critical temperature and condensed fraction of Bose-Einstein condensation in optical lattices

Yu Xue-Cai, Xue Huang, Yutang Ye

Published Apr 1, 2007• 0 citations
Publisher
DOI
10.1007/s11433-007-0017-y

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We propose a model that includes itinerant and localized states to study Bose–Einstein condensation of ultracold atoms in optical lattices (Bose–Anderson model). It is found that the original itinerant and localized states intermix to give rise to a new energy band structure with two quasiparticle energy bands. We have computed the critical temperature Tc of the Bose–Einstein condensation of the quasiparticles in the Bose–Anderson model using our newly developed numerical algorithm and found that Tc increases as na3 (the number density times the lattice constant cubed) increases according to the power law Tc≈18.93(na3)0.59 nK for na3<0.125 and according to the linear relation Tc≈8.75+10.53na3 nK for 1.25<na3<12.5 for the given model parameters. With the self-consistent equations for the condensation fractions obtained within the Bogoliubov mean-field approximation, the effects of the on-site repulsion U on the quasiparticle condensation are investigated. We have found that, for values up to several times the zeroth-order critical temperature, U enhances the zeroth-order condensation fraction at intermediate temperatures and effectively raises the critical temperature, while it slightly suppresses the zeroth-order condensation fraction at very low temperatures.

Modern Physics Letters B•Sep 20, 2005•0 citations
Critical temperature and condensate fraction of Bose-Einstein condensation in the optical lattice are studied.The results show that the critical temperature in optical lattices can be characterized with an equivalent critical temperature in a single lattice,which provide a fast evaluation of critical temperature and condensate fraction of Bose-Einstein condensation confined with pure optical trap.Critical temperature can be estimated with an equivalent critical temperature.It is predicted that critical temperature is proportional to q in q number lattices for superfluid state and should be equal to that in a single lattic for Mott insulate state.Required potential depth or Rabi frequency and maximum atom number in the lattices both for superfluid state and Mott state are presented based on views of thermal mechanical statistics.
We propose a model that includes itinerant and localized states to study Bose–Einstein condensation of ultracold atoms in optical lattices (Bose–Anderson model). It is found that the original itinerant and localized states intermix to give rise to a new energy band structure with two quasiparticle energy bands. We have computed the critical temperature Tc of the Bose–Einstein condensation of the quasiparticles in the Bose–Anderson model using our newly developed numerical algorithm and found that Tc increases as na3 (the number density times the lattice constant cubed) increases according to the power law Tc≈18.93(na3)0.59 nK for na3<0.125 and according to the linear relation Tc≈8.75+10.53na3 nK for 1.25<na3<12.5 for the given model parameters. With the self-consistent equations for the condensation fractions obtained within the Bogoliubov mean-field approximation, the effects of the on-site repulsion U on the quasiparticle condensation are investigated. We have found that, for values up to several times the zeroth-order critical temperature, U enhances the zeroth-order condensation fraction at intermediate temperatures and effectively raises the critical temperature, while it slightly suppresses the zeroth-order condensation fraction at very low temperatures.