Systematic vector solitary waves from their linear limits in one-dimensional $n$-component Bose-Einstein condensates

Abstract

We systematically construct a series of vector solitary waves in harmonically trapped one-dimensional three-, four-, and five-component Bose-Einstein condensates. These stationary states are continued in chemical potentials from the analytically tractable low-density linear limit of respective states, as independent linear quantum harmonic oscillator states, to the high-density nonlinear Thomas-Fermi regime. A systematic interpolation procedure is proposed to achieve this sequential continuation via a trajectory in the multi-dimensional space of the chemical potentials. The Bogolyubov-de Gennes (BdG) spectra analysis shows that all of the states considered herein can be fully stabilized in suitable chemical potential intervals in the Thomas-Fermi regime. Finally, we present some typical SU (n)-rotation-induced and driving-induced dynamics. This method can be extended to higher dimensions and shows significant promise for finding a wide range of solitary waves ahead.

Controlled engineering of a vortex-bright soliton dynamics using a constant driving force

“…First, the work should be studied in the Manakov setting. From the robust nature of the VB soliton and also the recent extension of the DB AC oscillation to Manakov systems [32], it is expected that the VB AC dynamics presented herein should well exist at the more experimentally relevant Manakov interactions. Indeed, our preliminary results show that the dynamics can be readily realized to the Manakov interactions, and the constant interaction energy feature appears to be quite generic in a homogeneous trap without requiring the total density is approximately uniform.…”

“…This significantly simplifies the theoretical analysis as the interaction energy is conserved to an excellent approximation. The dynamics, however, is not limited to this particular choice of interactions [32].…”

“…Our numerical setup includes identifying numerically exact stationary states using the finite element method for a spatial discretization and the Newton's method towards convergence, conducting the Bogolyubov-de Gennes stability analysis, and finally integrating the dynamics using the regular fourth-order Runge-Kutta method. Our VB soliton is numerically continued in a controlled manner from its underlying linear limit in a harmonic potential [32]. In this setting, the linear limit is a vortex state (|10 + i|01 )/ √ 2 coupled with the ground state |00 with chemical potentials 2 and 1, respectively, where |n x n y is a linear oscillator state in Cartesian coordinates.…”

“…It was recently demonstrated that the trapped bright soliton provides an excellent opportunity for engineering the dynam- * Electronic address: wenlongcmp@scu.edu.cn ics of a vector soliton by driving the bright soliton using a constant driving force [31,32]. Naturally, engineering soliton dynamics is of enormous interest, and previous works have already paid much attention to guiding or driving solitons with time-varying potentials, particularly optical lattices and impurity potentials [33][34][35].…”