We present numerical studies of Bose-Einstein condensates in an optical box trap. The box trap is modeled by using Gaussian-wall or hard-wall trapping potentials along the boundary of the box to mimic a recent experimental setup. In order to study a quasi-one-dimensional system, the Gaussian walls are separated differently along the axial and radial directions. Furthermore, the two-body interaction is described by a hard-sphere potential, whose radius equals the
s-wave scattering length. Using a finite-temperature path integral Monte Carlo method, we have calculated the density profiles of the system as a function of the temperature, the strength of the two-body interaction, and the number of particles. Our numerical results show clearly the Tonks-gas--like behavior in the strong interaction limit. In addition, we have compared our numerical data with the experimental data and theoretical results, and found that our simulation data agree with them quantitatively.
We present a Monte Carlo method for the direct simulation of evaporative cooling and the formation of the Bose-Einstein condensate of magnetically trapped atoms. The motion of the atoms in the trap is treated classically, while quantum-mechanical probability is used to describe binary elastic collisions between bosons. Two implementations of Bose statistics in the frame of a classical Monte Carlo simulation have been developed. The one involves the evaluation of the number of quantum states in single-atom phase space and the other makes use of the quantum degeneracy of energy bands. Both techniques give results compatible with the analytic results for an ideal trapped Bose gas and with the theory of a weakly interacting Bose gas, as concerns the equilibrium condensate fraction. Our simulation method also makes it possible to study the dynamic formation of the condensate, giving characteristic condensation times consistent with the experiments.