Dynamics in multiple-well Bose-Einstein condensates

TL;DR

This paper investigates the complex dynamics of three-dimensional Bose-Einstein condensates in a four-well ring trap, using a multimode model and phase space analysis to identify stability regimes and validate findings with numerical simulations.

Contribution

It introduces a reduced two-mode Hamiltonian approach for analyzing BEC dynamics in a symmetric four-well potential, linking stability analysis with numerical simulations.

Findings

Identification of periodic orbits in different regimes

Regions of stability and instability in phase space

Validation of two-mode models with Gross-Pitaevskii simulations

Abstract

We study the dynamics of three-dimensional weakly linked Bose-Einstein condensates using a multimode model with an effective interaction parameter. The system is confined by a ring-shaped four-well trapping potential. By constructing a two-mode Hamiltonian in a reduced highly symmetric phase space, we examine the periodic orbits and calculate their time periods both in the self-trapping and Josephson regimes. The dynamics in the vicinity of the reduced phase space is investigated by means of a Floquet multiplier analysis, finding regions of different linear stability and analyzing their implications on the exact dynamics. The numerical exploration in an extended region of the phase space demonstrates that two-mode tools can also be useful for performing a partition of the space in different regimes. Comparisons with Gross-Pitaevskii simulations confirm these findings and emphasize the importance of properly determining the effective on-site interaction parameter governing the multimode dynamics.