Josephson oscillation and induced collapse in an attractive Bose-Einstein condensate

TL;DR

This study uses the Gross-Pitaevskii equation to analyze Josephson oscillations in an attractive Bose-Einstein condensate within an optical lattice, revealing frequency independence from atom number and interaction type, and identifying conditions leading to collapse.

Contribution

It provides a detailed theoretical analysis of Josephson oscillations in attractive BECs, highlighting the effects of optical lattice parameters and predicting collapse conditions.

Findings

Josephson frequency is independent of atom number and interaction type.

Frequency decreases with increasing lattice strength at fixed wavelength.

Collapse occurs when laser wavelength exceeds 2000 nm for attractive BECs.

Abstract

Using the axially-symmetric time-dependent Gross-Pitaevskii equation we study the Josephson oscillation of an attractive Bose-Einstein condensate (BEC) in a one-dimensional periodic optical-lattice potential. We find that the Josephson frequency is virtually independent of the number of atoms in the BEC and of the inter-atomic interaction (attractive or repulsive). We study the dependence of Josephson frequency on the laser wave length and the strength of the optical-lattice potential. For a fixed laser wave length (795 nm), the Josephson frequency decreases with increasing strength as found in the experiment of Cataliotti {\it et al.} [Science {\bf 293}, 843 (2001)]. For a fixed strength, the Josephson frequency remains essentially unchanged for a reasonable variation of laser wave length around 800 nm. However, for a fixed strength, the Josephson oscillation is disrupted with the increase of laser wave length beyond 2000 nm leading to a collapse of a sufficiently attractive BEC. These features of Josephson oscillation can be tested experimentally with present set ups.