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A: Fachverband Atomphysik
A 9: Ultracold atoms I (jointly with Q)
A 9.2: Talk
Tuesday, March 11, 2008, 14:15–14:30, 2F
Bose-Einstein condensation in a periodic potential: A perturbation approach — •Ming-Chiang Chung1, Victor Lopez-Richard2, Carlos Trallero-Giner3, and Andreas Buchleitner4 — 1Max-Planck-Institut für Physik Komplexer Systeme* Noethnitzer Str. 38, D-01187 Dresden, Germany — 2Departamento de Fisica, Universidade Federal de S\~{a}o Carlos, 13.565-905, S\~{a}o Carlos, S\~{a}o Paulo, Brazil — 3Faculty of Physics, Havana University, 10400 Havana, Cuba — 4Quantum Optics and Statistics Institute of Physics Albert-Ludwigs-Universitaet Freiburg Hermann-Herder-Str. 3 D-79104 Freiburg, Germany
Considering the Gross-Pitaevskii equation for Bose-Einstein condensate in a stationary one dimensional optical lattice with period $d$ in reduced coordinates, we are able to formally obtain closed analytical solutions for the order parameter and for the chemical potential. We report solutions for different range of values for the repulsive and the attractive non-linear interactions in the condensate and laser parameters creating the lattice. We have preformed a quantitative analysis with numerical solutions and theoretical estimation of the reported analytical equations allowing the determination of validity ranges of the perturbation approach. This study gives a very useful result establishing the universal range of the non-linear coupling term and lattice parameter values where each solution can be easily implemented.