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

TL;DR

This paper studies how the shape and size of three-dimensional Bose-Einstein condensates affect phase coherence, revealing anisotropic finite-size scaling behaviors described by spin-wave theory and confirmed by quantum Monte Carlo simulations.

Contribution

It introduces the concept of shape-dependent anisotropic finite-size scaling in 3D BECs and validates the universality of these effects through simulations.

Findings

Anisotropic finite-size scaling occurs for any temperature below T_c.

The phenomena are effectively described by 3D spin-wave theory.

Coherence length in elongated BECs scales with superfluid density and temperature.

Abstract

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 x L x L_a boxes, below the BEC transition temperature $T_c$. We show that the phase correlations develop peculiar anisotropic FSS for any $T<T_c$, in the large-$L$ limit keeping the ratio \lambda = L_a/L^2 fixed. This phenomenon is effectively described by the 3D spin-wave (SW) theory. Its universality is confirmed by quantum Monte Carlo simulations of the 3D Bose-Hubbard model in the BEC phase. The phase-coherence properties of very elongated BEC systems, \lambda>>1, are characterized by a coherence length \xi_a \sim A_t \rho_s/T where A_t is the transverse area and \rho_s is the superfluid density.