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

We study the formation and collision-aided decay of an ultracold atomic Bose-Einstein condensate in the first excited band of a double-well two-dimensional optical lattice with weak harmonic confinement in the perpendicular z direction. This lattice geometry is based on an experiment by Wirth et al. [Nat. Phys. 7, 147 (2010)]. The double well is asymmetric, with the local ground state in the shallow well nearly degenerate with the first excited state of the adjacent deep well. We compare 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 in quantitative agreement for the lowest two bands, in qualitative agreement for the next two bands, and inadequate for even higher excited bands. The bandwidths of the excited bands are much larger than the harmonic-oscillator energy spacing in the z direction. We then study the thermodynamics of a noninteracting Bose gas in the first excited band. We estimate the condensate fraction and critical temperature T-c as functions of the lattice parameters. For typical atom numbers, the critical energy k(B)T(c), with k(B) the Boltzmann constant, is larger than the excited bandwidths 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 the 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 estimates for higher bands. The decay rate rapidly increases with lattice depth, but close to the critical temperature, it stays smaller than the tunneling rate between the s and p orbitals in adjacent wells.