Step-by-step dimensional crossover of an optically-trapped quantum gas with disorder

Abstract

Dimensionality serves as an indispensable ingredient to any attempt of formulating the lowdimensional physics, and studying dimensional crossover on a fundamental level is challenging. The purpose of this work is to study the step-by-step dimensional crossover from three-dimension (3D) to quasi-2D and then 1D. Our model system consists of a 3D Bose-Einstein condensate (BEC) trapped in an anisotropic 2D optical lattice characterized by the lattice depths of V1 along x-direction and V2 along y-direction respectively. The gradually dimensional crossover is controlled by the continuous increase of V1 and V2. Then we analyze the combined effects of dimensionality and disorder on both equilibrium and non-equilibrium quantum fluctuations of the model system. Accordingly, the analytical expressions of the ground-state energy, quantum depletion and superfluid density of the system are obtained. Our results show that the step-by-step dimensional crossover induces a characteristic 3D to quasi-2D and 1D step-by crossover in the behavior of quantum fluctuations. Conditions for possible experimental realization of our scenario are also discussed.