Collision Dynamics of Bose-Einstein Condensates

TL;DR

This paper investigates the complex collision behaviors of Bose-Einstein condensates using coupled Gross-Pitaevskii equations, revealing regimes of transmission, reflection, and transient dynamics influenced by inter-particle interactions.

Contribution

It introduces a detailed analysis of collision regimes in Bose-Einstein condensates based on a one-dimensional model, highlighting the effects of interaction strength on dynamics.

Findings

Large and small inter-particle repulsions lead to periodic transmission or reflection.

Intermediate interactions cause extended transient dynamics and density fracturing.

Non-trivial collision behaviors depend on non-linear interactions and are potentially observable.

Abstract

We study the collision dynamics of two Bose-Einstein condensates with their dynamical wave functions modeled by a set of coupled, time-dependent Gross-Pitaevskii equations. Beginning with an effective one-dimensional system, we identify regimes characterized by the relationship between inter- and intra-atomic interactions and the initial configuration of the system, akin to the equilibrium phase diagram of two interacting Bose condensates. We consider a dynamical setup in which two wave packets are initially at rest with a small separation about the center of an asymmetric harmonic trap. Upon release, we observe a rapid approach to dynamical equilibrium in the limits of very large and very small inter-particle repulsion, characterized by periodic transmission or reflection of the condensates as distinguishable units, whereas the intermediate, critical regime is characterized by extended transient dynamics, density fracturing, and dynamical mixing. We therefore have reason to believe that non-trivial behavior may exist during the collisions of Bose-Einstein condensates as a result of their non-linear interactions, and these effects may be observable in a suitable laboratory environment.