Asymptotic expressions for the hyperfine populations in the ground state of spin-1 condensates against a magnetic field

Y. M. Liu; Y. Z. He; C. G. Bao

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arXiv · 1509.05687

Asymptotic expressions for the hyperfine populations in the ground state of spin-1 condensates against a magnetic field

Y. M. Liu·Y. Z. He·C. G. Bao

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Abstract

Based on the perturbation theory up to the 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 $B$ has 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 $^{87}$Rb, the two analytical expressions, one for a weak and the other one for a strong field, together cover the whole range of $B$ from 0 to infinite. For Na, the analytical expressions are valid only if $B$ is very weak or sufficiently strong.

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Y. M. Liu, Y. Z. He, C. G. Bao. 2015-09-18. Asymptotic expressions for the hyperfine populations in the ground state of spin-1 condensates against a magnetic field. https://arxiv.org/abs/1509.05687

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