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
Tc as functions of the lattice parameters. For typical atom numbers, the critical energy
kBTc, with
kB 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.
We present a method for the effective preparation of a Bose-Einstein condensate (BEC) into the excited bands of an optical lattice via a standing-wave pulse sequence. With our method, the BEC can be prepared in either a single Bloch state in an excited band or a coherent superposition of states in different bands. Our scheme is experimentally demonstrated by preparing a
87Rb BEC into the
d band and the superposition of
s- and
d-band states of a one-dimensional optical lattice, within a few tens of microseconds. We further measure the decay of the BEC in the
d-band state and carry an analytical calculation for the collisional decay of atoms in the excited-band states. Our theoretical and experimental results agree well.
The dynamics of a Bose-Einstein condensate nonadiabatically loaded into a one-dimensional optical lattice is studied by analyzing the phase coherence between sites along the lattice as well as the radial profile of the condensate after a time-of flight. A simple model is proposed that predicts the short-time dephasing as a function of the condensate parameters. In the radial direction, heavily damped oscillations are observed, as well as an increase in the condensate temperature. These findings are interpreted as a rethermalization due to dissipation of the initial condensate excitations into high-lying modes.
We report experimental results on the properties of Bose-Einstein condensates in one-dimensional optical lattices. By accelerating the lattice, we observed Bloch oscillations of the condensate in the lowest band, as well as Landau-Zener (LZ) tunneling into higher bands when the lattice depth was reduced and/or the acceleration of the lattice was increased. The dependence of the LZ tunneling rate on the condensate density was then related to mean-field effects modifying the effective potential acting on the condensate, yielding good agreement with recent theoretical work. We also present several methods for measuring the lattice depth and discuss the effects of the micromotion in the time-orbiting-potential trap on our experimental results.
We study dynamical behaviors of the weakly interacting Bose-Einstein condensate in the one-dimensional optical lattice with an overall double-well potential by solving the time-dependent Gross-Pitaevskii equation. It is observed that the double-well potential dominates the dynamics of such a system even if the lattice depth is several times larger than the height of the double-well potential. This result suggests that the condensate flows without resistance in the periodic lattice just like the case of a single particle moving in periodic potentials. Nevertheless, the effective mass of atoms is increased, which can be experimentally verified since it is connected to the Josephson oscillation frequency. Moreover, the periodic lattice enhances the nonlinearity of the double-well condensate, making the condensate more “self-trapped” in the π -mode self-trapping regime.