We present a scheme for rapidly loading a Bose-Einstein condensate into a single Bloch state of a weak optical lattice at a quasimomentum of $q=\ensuremath{\Elzxh}k.$ Rabi cycling of the Bose-Einstein condensate between momentum states is modified by a phase shift applied to the lattice. By appropriately choosing the magnitude and timing of the phase shift, we demonstrate nearly perfect loading of the lattice ground state, the signature of which is an abrupt halt to the Rabi cycling.
We optimize the turning on of a one-dimensional optical potential,
VL(x,t)=S(t)V0cos2(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
V0. Specifically, we minimize interband excitations at the end of the turn-on of the optical potential at the final ramp time
tr, where
S(tr)=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
tr 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
tr on the order of the inverse band excitation frequency.
By loading Bose-Einstein condensates into a three dimensional optical lattice potential we are able to demonstrate several new intriguing regimes in the physics of ultracold atoms. For example by changing the lattice potential depth we have been able to induce a quantum phase transition from a superfluid to a Mott insulating ground state of the system. Furthermore, by rapidly isolating the different potential wells from each other the collapse and revival of the matter wave field of a Bose-Einstein condensate has been observed. 1