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Formation and decay of Bose Einstein condensates in an excited band of a double-well optical lattice



Saurabh Paul, Eite Tiesinga


We study the formation and collision aided decay of an ultra-cold atomic Bose-Einstein condensate in the first excited band of a double-well 2D-optical latt ice with weak harmonic confinement in the perpendicular z direction. This lattice geometry is based on an experiment by Writh. The double well is asymmetric, with the local ground state in the shallow well n early degenerate with the first excited state of the adjacent deep well. We comp are the band structure obtained from a tight-binding model with that obtained numerically using a plane wave basis. We find the tight binding model to be approp riate for the lowest two bands, qualitative for next two bands, and inadequate for even higher excited bands. The band widths of the excited bands are much larger than the harmonic oscillator energy spacing in the z direction. We then study the thermodynamics of a non-interacting Bose gas in the first excited band. We estimate the condensate fraction and critical temperature, Tc, as functions of lattice parameters. For typical atom numbers, the critical energy kTc, with k the Boltzmann constant, is larger than the excited band widths and harmonic oscillator energy. Using conservation of total energy and atom number, we show that the temperature increases after the lattice transformation. Finally, we estimate the time scale for a two-body collision-aided decay of the condensate as a function of lattice parameters. The decay involves two processes, the dominant one in which both colliding atoms decay to the ground band, and the second involving excitation of one atom to a higher band. For this estimate, we have used tight binding wave functions for the lowest four bands, and numerical estim ates for higher bands. The decay rate rapidly increases with lattice depth but stays much smaller than the tunneling rate between the degenerate levels between the deep and shallow wells.
Physical Review A


ultra-cold atoms, optical lattices, quantum gasses, atom-atom scattering


Paul, S. and Tiesinga, E. (2013), Formation and decay of Bose Einstein condensates in an excited band of a double-well optical lattice, Physical Review A, [online],, (Accessed May 27, 2024)


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Created December 11, 2013, Updated October 12, 2021