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

TL;DR

This paper develops an optimal control method to load a Bose-Einstein condensate into the ground state of an optical lattice with minimal excitations, using numerical simulations based on the Gross-Pitaevskii equation.

Contribution

It introduces a specific optimal turn-on function for the optical potential that minimizes interband excitations during loading.

Findings

Optimal turn-on function reduces excitations significantly.

Simple unit cell model is effective for long ramp times.

Ground state loading is achievable with minimal excitations.

Abstract

We optimize the turning on of a one-dimensional optical potential, V_L(x,t) = S(t) V_0 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 \hbar/\mu where \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 very little excitation even for times t_r on the order of the inverse band excitation frequency.