Dynamics of spinor Bose-Einstein condensates close to spin-spatial resonances

TL;DR

This paper introduces a coupled-channel framework to analyze the complex dynamics of spinor Bose-Einstein condensates near spin-spatial resonances, highlighting the importance of beyond-Bogoliubov effects.

Contribution

The authors develop an efficient coupled-channel approach that captures long-time dynamics and resonance phenomena in spinor BECs, extending beyond standard Bogoliubov theory.

Findings

Resonant excitations classified into particle-hole and non-particle-hole types.

Beyond-quadratic-order terms are crucial near resonances for accurate dynamics.

Framework benchmarks well against 1D Gross-Pitaevskii simulations.

Abstract

We develop a coupled-channel framework to describe the dynamics of spinor Bose-Einstein condensates (BECs), with particular emphasis on the behavior near resonances between spin dynamics and spatial excitations. Taking advantage of the disparity between the spin-dependent and spin-independent scattering lengths in typical spinor BECs, the Bogoliubov modes of the spin-independent part of the full system Hamiltonian provide an efficient set of basis functions for describing the system dynamics in a coupled-channel framework. For quadratic Zeeman shifts far from any resonance, the system can be described by a single spatial wavefunction during the spin dynamics, i.e., the so-called single-mode approximation holds. By tuning the quadratic Zeeman shift, we find resonant excitations of the Bogoliubov modes, which can be classified into two categories: those with particle-hole correlations and those without particle-hole correlations. We show that the beyond-quadratic-order terms that are neglected in standard Bogoliubov theories become increasingly important for capturing the long-time dynamics of the system near resonances. The coupled-channel framework is benchmarked against results from 1D Gross-Pitaevskii equation simulations. The framework developed in this work not only provides a numerically efficient tool for describing spinor BEC dynamics governed by different length scales, but also provides a clean physical interpretation of resonance phenomena in spinor BECs. Applications of this approach to other systems and extensions to the beyond-mean-field regime are also discussed.