Spin evolution of spin-1 Bose-Einstein condensates

TL;DR

This paper derives an exact analytical formula for the spin evolution of spin-1 Bose-Einstein condensates, surpassing mean field theory and aligning well with experimental and numerical results.

Contribution

It provides a general, accurate, and complete analytical description of spin dynamics in spin-1 BECs without approximations.

Findings

Analytical formula matches experimental data qualitatively.

Evolution can be steady over long durations for certain initial states.

Results go beyond mean field theory and previous approximations.

Abstract

An analytical formula is obtained to describe the evolution of the average populations of spin components of spin-1 atomic gases. The formula is derived from the exact time-dependent solution of the Hamiltonian $H_{S}=c mathbf{S}^{2}$ without using approximation. Therefore it goes beyond the mean field theory and provides a general, accurate, and complete description for the whole process of non-dissipative evolution starting from various initial states. The numerical results directly given by the formula coincide qualitatively well with existing experimental data, and also with other theoretical results from solving dynamic differential equations. For some special cases of initial state, instead of undergoing strong oscillation as found previously, the evolution is found to go on very steadily in a very long duration.