Influence of the particle number on the spin dynamics of ultracold atoms

TL;DR

This paper investigates how the number of particles affects the quantum spin dynamics of ultracold spin-1 atoms, revealing slow convergence to mean-field behavior and highlighting significant quantum corrections in small systems relevant for experiments.

Contribution

It provides a detailed analysis of particle number effects on spin dynamics, especially near energy degeneracies, and discusses implications for experiments with few-atom systems.

Findings

Convergence to mean-field dynamics is slow near energy degeneracies.

Quantum corrections are significant in few-atom regimes.

Spin dynamics exhibit beat notes at large magnetic fields.

Abstract

We study the dependency of the quantum spin dynamics on the particle number in a system of ultracold spin-1 atoms within the single-spatial-mode approximation. We find, for all strengths of the spin-dependent interaction, convergence towards the mean-field dynamics in the thermodynamic limit. The convergence is, however, particularly slow when the spin-changing collisional energy and the quadratic Zeeman energy are equal, i.e. deviations between quantum and mean-field spin dynamics may be extremely large under these conditions. Our estimates show, that quantum corrections to the mean-field dynamics may play a relevant role in experiments with spinor Bose-Einstein condensates. This is especially the case in the regime of few atoms, which may be accessible in optical lattices. Here, spin dynamics is modulated by a beat note at large magnetic fields due to the significant influence of correlated many-body spin states.