Bosonic Josephson effect in the Fano-Anderson model

TL;DR

This paper analyzes the dynamics of a Bose-Einstein condensate in a two-reservoir system modeled by the Fano-Anderson model, revealing how the Josephson current depends on the localized mode's energy and identifying regimes with distinct oscillation behaviors.

Contribution

It provides an analytical study of the bosonic Josephson effect in a Fano-Anderson model, highlighting the dependence on on-site energy and identifying different dynamical regimes.

Findings

Josephson current depends on the localized mode's on-site energy.

Two dynamical regimes with distinct oscillation behaviors are identified.

Finite-size simulations confirm analytical results.

Abstract

We investigate the coherent dynamics of a non-interacting Bose-Einstein condensate in a system consisting of two bosonic reservoirs coupled via a spatially localized mode. We describe this system by a two-terminal Fano-Anderson model and investigate analytically the time evolution of observables such as the bosonic Josephson current. In doing so, we find that the Josephson current sensitively depends on the on-site energy of the localized mode. This facilitates to use this setup as a transistor for a Bose-Einstein condensate. We identify two regimes. In one regime, the system exhibits well-behaved long-time dynamics with a slowly oscillating and undamped Josephson current. In a second regime, the Josephson current is a superposition of an extremely weakly damped slow oscillation and an undamped fast oscillation. Our results are confirmed by finite-size simulations.