Quantum Monte Carlo study of the three- to one-dimensional crossover for a trapped Bose gas

We investigate the crossover from three to one dimension in a Bose gas confined in highly anisotropic traps. By using quantum Monte Carlo techniques, we solve the many-body Schr\"odinger equation for the ground state and obtain exact results for the energy per particle and the mean square radii of the cloud in the transverse and longitudinal direction. Results are compared with the predictions of mean-field theory obtained from the Gross-Pitaevskii equation and with the one-dimensional Lieb-Liniger equation of state. We explicitly prove the occurrence of important beyond mean-field effects, including the appearance of Fermi-like properties as the system enters the Tonks gas regime.