Effects of disorder on quantum fluctuations and superfluid density of a Bose-Einstein condensate in a two-dimensional optical lattice

TL;DR

This study analyzes how weak disorder and a 2D optical lattice influence quantum fluctuations and superfluid density in a Bose-Einstein condensate, revealing a 3D to 1D crossover and a specific normal fluid density behavior.

Contribution

It provides analytical expressions for ground state energy and quantum depletion considering disorder and lattice effects in BECs, highlighting a crossover and normal fluid density behavior.

Findings

Lattice induces a 3D to 1D crossover in quantum fluctuations despite disorder.

Disorder and lattice together cause the normal fluid density to approach 4/3 of quantum depletion.

Analytical expressions for ground state energy and quantum depletion are derived.

Abstract

We investigate a Bose-Einstein condensate trapped in a 2D optical lattice in the presence of weak disorder within the framework of the Bogoliubov theory. In particular, we analyze the combined effects of disorder and an optical lattice on quantum fluctuations and superfluid density of the BEC system. Accordingly, the analytical expressions of the ground state energy and quantum depletion of the system are obtained. Our results show that the lattice still induces a characteristic 3D to 1D crossover in the behavior of quantum fluctuations, despite the presence of weak disorder. Furthermore, we use the linear response theory to calculate the normal fluid density of the condensate induced by disorder. Our results in the 3D regime show that the combined presence of disorder and lattice induce a normal fluid density that asymptotically approaches 4/3 of the corresponding condensate depletion. Conditions for possible experimental realization of our scenario are also proposed.