Josephson Oscillation and Transition to Self-Trapping for Bose-Einstein-Condensates in a Triple-Well Trap

TL;DR

This paper explores the tunnelling dynamics of Bose-Einstein condensates in a triple-well trap, revealing new oscillation types, self-trapping phenomena, and chaotic regimes as atomic interactions increase.

Contribution

It provides new insights into Josephson oscillations, self-trapping, and chaos in BECs within a triple-well potential, using mean-field analysis and phase space visualization.

Findings

Identification of entangled star structure in eigenenergies

Discovery of new Josephson oscillation types

Observation of chaos during transition to self-trapping

Abstract

We investigate the tunnelling dynamics of Bose-Einstein-Condensates(BECs) in a symmetric as well as in a tilted triple-well trap within the framework of mean-field treatment. The eigenenergies as the functions of the zero-point energy difference between the tilted wells show a striking entangled star structure when the atomic interaction is large. We then achieve insight into the oscillation solutions around the corresponding eigenstates and observe several new types of Josephson oscillations. With increasing the atomic interaction, the Josephson-type oscillation is blocked and the self-trapping solution emerges. The condensates are self-trapped either in one well or in two wells but no scaling-law is observed near transition points. In particular, we find that the transition from the Josephson-type oscillation to the self-trapping is accompanied with some irregular regime where tunnelling dynamics is dominated by chaos. The above analysis is facilitated with the help of the Poicar\'{e} section method that visualizes the motions of BECs in a reduced phase plane.