Optically trapped quasi-two-dimensional Bose gases in random environment: quantum fluctuations and superfluid density

TL;DR

This paper analyzes how disorder affects quantum fluctuations and superfluid density in a quasi-2D Bose gas confined by an optical lattice, providing analytical insights into the system's ground state and superfluid properties.

Contribution

It offers an analytical expression for the ground state energy and superfluid density of a 2D Bose gas in a random potential, highlighting disorder effects in low-dimensional quantum gases.

Findings

Disorder induces a characteristic $1/\ln(1/n_{2D}a_{2D}^2)$ dependence of quantum depletion and normal fluid density.

The ratio of normal fluid density to quantum depletion increases to 2, indicating enhanced superfluid suppression in 2D.

Analytical conditions for experimental realization are proposed.

Abstract

We investigate a dilute Bose gas confined in a tight one-dimensional (1D) optical lattice plus a superimposed random potential at zero temperature. Accordingly, the ground state energy, quantum depletion and superfluid density are calculated. The presence of the lattice introduces a crossover to the quasi-2D regime, where we analyze asymptotically the 2D behavior of the system, particularly the effects of disorder. We thereby offer an analytical expression for the ground state energy of a purely 2D Bose gas in a random potential. The obtained disorder-induced normal fluid density $n_n$ and quantum depletion $n_d$ both exhibit a characteristic $1/\ln\left(1/n_{2D}a_{2D}^{2}\right)$ dependence. Their ratio $n_n/n_d$ increases to $2$ compared to the familiar $4/3$ in lattice-free 3D geometry, signifying a more pronounced contrast between superfluidity and Bose-Einstein condensation in low dimensions. Conditions for possible experimental realization of our scenario are also proposed.