1998/10/22 by M. J. Steel, Steel, M. J., Weiping Zhang +1
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Condensed Matter (cond-mat) #FOS: Physical sciences #Nonlinear Photonic Systems #Strong Light-Matter Interactions #cond-mat
paper · pdf · doi:10.48550/arxiv.cond-mat/9810284
9 pages, 7 figures
arxiv created 1998/10/22 · openalex publication_date 1998/10/22 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We consider stationary and propagating solutions for a Bose-Einstein condensate in a periodic optical potential with an additional confining optical or magnetic potential. Using an effective mass approximation we express the condensate wavefunction in terms of slowly-varying envelopes modulating the Bloch modes of the optical lattice. In the limit of a weak nonlinearity, we derive a nonlinear Schrödinger equation for propagation of the envelope function which does not contain the rapid oscillation of the lattice. We then consider the ground state solutions in detail in the regime of weak, moderate and strong nonlinear interactions. We describe the form of solution which is appropriate in each regime, and place careful limits on the validity of each type of solution.