Hierarchical dimensional crossover of an optically-trapped quantum gas with disorder

Abstract

Dimensionality serves as an indispensable ingredient in any attempt to formulate the low-dimensional physics, and studying the dimensional crossover at a fundamental level is challenging. The purpose of this work is to study the hierarchical dimensional crossovers, namely the crossover from three dimensions (3D) to quasi-2D and then to 1D. Our system consists of a 3D Bose-Einstein condensate (BEC) trapped in an anisotropic 2D optical lattice characterized by the lattice depths $V_1$ along the $x$ direction and $V_2$ along the $y$ direction, respectively, where the hierarchical dimensional crossover is controlled via $V_1$ and $V_2$. We analytically derive the ground-state energy, quantum depletion and the superfluid density of the system. Our results demonstrate the 3D-quasi-2D-1D dimensional crossovers in the behavior of quantum fluctuations. Conditions for possible experimental realization of our scenario are also discussed.

Dimensional crossover of a Rabi-coupled two-component Bose–Einstein condensate in an optical lattice

“…With state-of-the-art technology, quasi-1D [6] and quasi-2D [7,8] BECs can be realized by controlling the depth of optical lattices. Along this research line, numerous tight-confinement schemes [9][10][11][12][13][14][15][16][17] have been proposed where BECs can undergo dimensional crossovers directly from 3D to 2D or 1D ( i.e. 3D-2D or 3D-1D crossover).…”