Effective Josephson dynamics in resonantly driven Bose-Einstein condensates

TL;DR

This paper demonstrates the orbital Josephson effect in driven Bose-Einstein condensates across various systems, using multiple numerical methods to analyze many-body dynamics and establish the validity of mean-field and few-mode models.

Contribution

It introduces an extended (t,t')-formalism for systematic analysis of long-time dynamics in resonantly driven many-body quantum systems.

Findings

Mean-field and few-mode models accurately describe weak driving regimes.

Identified four dynamical regimes: Rabi, chaos, critical point, self-trapping.

Extended formalism enables systematic long-time dynamics analysis.

Abstract

We show that the orbital Josephson effect appears in a wide range of driven atomic Bose-Einstein condensed systems, including quantum ratchets, double wells and box potentials. We use three separate numerical methods: Gross-Pitaevskii equation, exact diagonalization of the few-mode problem, and the Multi-Configurational Time-Dependent Hartree for Bosons algorithm. We establish the limits of mean-field and few-mode descriptions, demonstrating that they represent the full many-body dynamics to high accuracy in the weak driving limit. Among other quantum measures, we compute the instantaneous particle current and the occupation of natural orbitals. We explore four separate dynamical regimes, the Rabi limit, chaos, the critical point, and self-trapping; a favorable comparison is found even in the regimes of dynamical instabilities or macroscopic quantum self-trapping. Finally, we present an extension of the (t,t')-formalism to general time-periodic equations of motion, which permits a systematic description of the long-time dynamics of resonantly driven many-body systems, including those relevant to the orbital Josephson effect.