Bao, CG (reprint author), Sun Yat Sen Univ, Sch Phys & Engn, State Key Lab Optoelect Mat & Technol, Guangzhou 510275, Guangdong, Peoples R China.
Based on perturbation theory up to second order, analytical asymptotic expressions for the variation of the population of hyperfine component mu = 0 particles in the ground state of spin-1 condensates against a magnetic field B have been derived. The ranges of B in which the asymptotic expressions are applicable have been clarified via a comparison of the numerical results from the analytical expressions and from a diagonalization of the Hamiltonian in a complete spin space. It was found that, for Rb-87, the two analytical expressions, one for a weak field and the other one for a strong field, together cover the whole range of B from zero to infinity. For Na, the analytical expressions are valid only if B is very weak or sufficiently strong.
National Natural Science Foundation of China (NNSFC) 
; Open Project Program of the State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, China