Soliton dynamics of an atomic spinor condensate on a Ring Lattice

TL;DR

This paper investigates the complex soliton dynamics of ultra-cold atomic spinor condensates on a ring lattice, revealing a novel internal Josephson effect, resonance states, and transitions to chaos driven by interaction strength.

Contribution

It introduces a new understanding of soliton behavior and resonance phenomena in spinor condensates on a ring lattice, highlighting the onset of chaos and phase transitions.

Findings

Identification of a novel spatio-temporal internal Josephson effect.

Observation of resonance states with integer frequency ratios.

Detection of chaos onset and phase transition in spinor condensate dynamics.

Abstract

We study the dynamics of macroscopically-coherent matter waves of an ultra-cold atomic spin-one or spinor condensate on a ring lattice of six sites and demonstrate a novel type of spatio-temporal internal Josephson effect. Using a discrete solitary mode of uncoupled spin components as an initial condition, the time evolution of this many-body system is found to be characterized by two dominant frequencies leading to quasiperiodic dynamics at various sites. The dynamics of spatially-averaged and spin-averaged degrees of freedom, however, is periodic enabling an unique identification of the two frequencies. By increasing the spin-dependent atom-atom interaction strength we observe a resonance state, where the ratio of the two frequencies is a characteristic integer multiple and the spin-and-spatial degrees of freedom oscillate in "unison". Crucially, this resonant state is found to signal the onset to chaotic dynamics characterized by a broad band spectrum. In a ferromagnetic spinor condensate with attractive spin-dependent interactions, the resonance is accompanied by a transition from oscillatory- to rotational-type dynamics as the time evolution of the relative phase of the matter wave of the individual spin projections changes from bounded to unbounded.