Josephson tunneling between weakly interacting Bose-Einstein condensates

TL;DR

This paper models Josephson tunneling between two Bose-Einstein condensates using Bogoliubov theory, revealing unique finite normal currents at zero temperature and their effects on phase dynamics, with potential experimental applications.

Contribution

It provides a detailed theoretical analysis of Josephson effects in Bose-Einstein condensates, including interaction effects and damping mechanisms, extending previous superconducting models.

Findings

Normal current remains finite at zero temperature.

Normal current causes damping of Josephson oscillations.

Estimates suggest feasible experimental realization with sodium condensates.

Abstract

Based on a tunneling Hamiltonian description, we calculate the Josephson, normal and interference currents between two Bose-Einstein condensates described by the Bogoliubov theory. The dominant Josephson term is of first order in the tunneling with a critical current density proportional to the ground state pressure. In contrast to superconductors, the normal current remains finite at zero temperature. We discuss the dynamics of the relative phase in a semiclassical approximation derived from an exact functional integral approach, which includes the interaction effects at fixed total particle number. It is shown that the normal current leads to a damping of the Josephson oscillations and, at long times, eliminates the macroscopic quantum self trapping predicted by Smerzi et.al. Finally we give estimates for an experimental realization of Josephson tunneling in cold atomic gases, which indicate that coherent transfer of atoms might be realized with a $^{23}$Na condensate.