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

Abstract

The dynamics of a pair of harmonic oscillators represented by three-dimensional fields coupled with a repulsive cubic nonlinearity is investigated through direct simulations of the respective field equations and with the help of the finite-mode Galerkin approximation (GA), which represents the two interacting fields by a superposition of 3+3 harmonic-oscillator p-wave eigenfunctions with orbital and magnetic quantum numbers l=1 and m=1, 0, -1. The system can be implemented in binary Bose-Einstein condensates, demonstrating the potential of the atomic condensates to emulate various complex modes predicted by classical field theories. 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 noncoaxial 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-field equations 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.

(INVITED) Vortex solitons: Old results and new perspectives

“…Lastly, it is relevant to mention the consideration of a binary model with the repulsive cubic nonlinear terms (both intra-and inter-component ones) reported in Ref. [186]. By means of systematic simulations and a semi-analytical approximation based on a finite-mode Galerkin decomposition of the wave functions, nontrivial two-component stationary states and dynamical regimes have been found in that system.…”

Realization of all-optical vortex switching in exciton-polariton condensates

“…The two fundamental states of a vortex represent different rotation directions and can be used to encode binary information for example in vortex-based random access memories [1]. Switching a vortex between its two states is coveted by scientists and the dynamics have been investigated intensively [2][3][4][5][6][7][8]. For example, the manipulation of core magnetization of a vortex in ferromagnetic materials can be achieved by magnetic fields [2][3][4] or by an electrical current through the spin-transfer effect [9,10].…”

Modulational instability of coupled ring waveguides with linear gain and nonlinear loss

“…Even sufficiently complex dynamics of vortices, may be described with relatively high precision 34 , using the so-called Galerkin approximation, i.e. the variational-type ansatz (21) where sum is computed only over a few lowest harmonics.…”