Dynamics of dipoles and vortices in nonlinearly-coupled three-dimensional harmonic oscillators

TL;DR

This paper investigates the complex dynamics of coupled three-dimensional matter-wave oscillators, revealing stable vortex and dipole formations, and periodic angular momentum exchanges through simulations and a finite-mode approximation.

Contribution

It introduces a finite-mode Galerkin approximation to accurately predict ground states and dynamical regimes of coupled 3D harmonic oscillators with nonlinear interactions.

Findings

GA accurately predicts degenerate ground states with dipoles and vortices.

Stable dynamical regimes involve periodic exchange of angular momentum.

Simulations agree well with GA, confirming the model's effectiveness.

Abstract

The dynamics of a pair of three-dimensional matter-wave harmonic oscillators (HOs) coupled by a repulsive cubic nonlinearity is investigated through direct simulations of the respective GrossPitaevskii equations (GPEs) and with the help of the finite-mode Galerkin approximation (GA),which represents the two interacting wave functions by a superposition of 3 + 3 HO p -wave eigenfunctions with orbital and magnetic quantum numbers l = 1 and m = 1; 0; 1. First, the GA very accurately predicts a broadly degenerate set of the system's ground states in the p -wave manifold, in the form of complexes built of a dipole coaxial with another dipole or vortex, as well as complexes built of mutually orthogonal dipoles. Next, pairs of non-coaxial vortices and/or dipoles, including pairs of mutually perpendicular vortices, develop remarkably stable dynamical regimes, which feature periodic exchange of the angular momentum and periodic switching between dipoles and vortices. For a moderately strong nonlinearity, simulations of the coupled GPEs agree very well with results produced by the GA, demonstrating that the dynamics is accurately spanned by the set of six modes limited to l = 1.