Shape dependence and anisotropic finite-size scaling of the phase coherence of three-dimensional Bose-Einstein-condensed gases

We investigate the equilibrium phase-coherence properties of Bose-condensed particle systems, focusing on their shape dependence and finite-size scaling (FSS). We consider three-dimensional (3D) homogeneous systems confined to anisotropic L×L×La boxes, below the Bose-Einstein-condensate (BEC) transition temperature Tc. We show that the phase correlations develop peculiar anisotropic FSS for any T<Tc, in the large-L limit keeping the ratio λ≡La/L2 and the particle density fixed. This phenomenon is effectively described by the 3D spin-wave theory. Its universality is confirmed by quantum Monte Carlo simulations of the 3D Bose-Hubbard model in the BEC phase. The phase-coherence correlations of very elongated BEC systems, λ→, are characterized by the coherence length ξa∼Atρs/T, where At is the transverse area and ρs is the superfluid density.