Josephson Oscillation and Nonlinear Self-Trapping in Quasi-one-dimensional Quantum Liquid

In this article, we study the two-mode method to analyze the Josephson oscillation for a trapped binary Bose-Einstein condensate while taking into account the beyond mean-field and three body interactions. For this purpose, we use the archetypal model of double well potential and study the Josephson oscillation and self-trapping phases in quasi-one dimension. Additionally, our analysis provides quantitative discussion on the effect of asymmetry and dimension. We further corroborate our findings with Bogoliubov quasi-particle method and notice regions of instabilities and roton like mode.

💡 Research Summary

This paper presents a comprehensive theoretical study of Josephson oscillations (JO) and nonlinear self‑trapping (ST) in a quasi‑one‑dimensional (Q1D) binary Bose‑Einstein condensate (BEC) confined in a double‑well potential, explicitly incorporating beyond‑mean‑field (BMF) corrections and three‑body (3B) interactions. The authors begin by motivating the work through the recent experimental realization of quantum liquids—droplet states stabilized by a delicate balance between attractive mean‑field (MF) interactions and repulsive Lee‑Huang‑Yang (LHY) quantum fluctuations. They argue that such systems provide an ideal platform to explore macroscopic quantum tunnelling phenomena, especially Josephson dynamics, where nonlinearities play a decisive role.

The model is built on a dimensionless extended Gross‑Pitaevskii equation (GPE): i∂ₜψ =