Monte Carlo simulations of Bose-Einstein condensation of trapped atoms - art. no. 013606

We present a Monte Carlo method for the direct simulation of evaporative co oling and the formation of the Bose-Einstein condensate of magnetically tra pped atoms. The motion of the atoms in the trap is treated classically, whi le quantum-mechanical probability is used to describe binary elastic collis ions between bosons. Two implementations of Bose statistics in the frame of a classical Monte Carlo simulation have been developed. The one involves t he evaluation of the number of quantum states in single-atom phase space an d the other makes use of the quantum degeneracy of energy bands. Both techn iques give results compatible with the analytic results for an ideal trappe d Bose gas and with the theory of a weakly interacting Bose gas, as concern s the equilibrium condensate fraction. Our simulation method also makes it possible to study the dynamic formation of the condensate, giving character istic condensation times consistent with the experiments.