Loading Bose-Einstein-condensed atoms into the ground state of an optical lattice

Abstract

We optimize the turning on of a one-dimensional optical potential, ${V}_{L}(x,t)=S(t){V}_{0}\phantom{\rule{0.2em}{0ex}}{\mathrm{cos}}^{2}(kx)$ to obtain the optimal turn-on function $S(t)$ so as to load a Bose-Einstein condensate into the ground state of the optical lattice of depth ${V}_{0}$. Specifically, we minimize interband excitations at the end of the turn-on of the optical potential at the final ramp time ${t}_{r}$, where $S({t}_{r})=1$, given that $S(0)=0$. Detailed numerical calculations confirm that a simple unit cell model is an excellent approximation when the turn-on time ${t}_{r}$ is long compared with the inverse of the band excitation frequency and short in comparison with nonlinear time $\ensuremath{\hbar}∕\ensuremath{\mu}$ where $\ensuremath{\mu}$ is the chemical potential of the condensate. We demonstrate using the Gross-Pitaevskii equation with an optimal turn-on function $S(t)$ that the ground state of the optical lattice can be loaded with no significant excitation even for times ${t}_{r}$ on the order of the inverse band excitation frequency.