Splitting Spin States of Small Spinor Bose Condensates beyond Single-mode Approximation

Duoje Jia, Yan Xu, Zhaoxin Li +2 more

An effective Hamiltionian with level splitting of the collective spin states is derived for a spinor Bose condensate of trapped atoms with hyperfine spin f = 1 beyond the single-mode approximation. The splitting of these spin states arises from quantum polarization between the mf = +1 and mf = -1 spin channels, and is characterized by small magnetization exhibited by the trapped gas. For big ferromagnetic 87 Rb and antiferromagnetic 23 Na Bose gases, the splitting fraction in total energy increases as -N-1 and decreases as N-2 when the atom number N varies, with typical order of 10-6 and 10-4, respectively. In the case of small condensates, the splitting fraction increases as -N-2, with typical order of 10-5~10-6, both for 87 Rb and 23 Na atoms. In both cases of the big and small condensates, the splitting energy is analogous to the anisotropic energy of a magnet, being proportional to the square of the pseudo-magnetization.

XuYan, JiaDuoje, GaoYuan

J. Stenger, S. Inouye, Dan Stamper-Kurn +3 more

Yan Xu, Jia Duo-Je, Zhaoxin Li +4 more

We study the mode deviation effect of a spin-1 Bose-Einstein condensate with large number of atoms in optical trap beyond the single-mode approximation. Based on the effective Hamiltonian with nondegenerate level of the collective spin states, we get the mode deviation factor and explicitly calculate the level splitting energy as function of the atom number N.

Yan Xu, Duoje Jia, Zhaoyang Chen +2 more

The deviation effect of spinor mode from the single-mode for a spin-1 Bose gas of trapped atoms is studied beyond the mean field theory. Based on the effective Hamiltonian with nondegenerated level of the collective spin states, the splitting level of the system energy due to the deviation effect has been calculated. For the large condensates of 87 Rb and 23 Na with atom number N>105, the splitting fraction of the energy, arising from the magnetization exhibited by the trapped Bose gas, is found to have a typical order of (10-4~10-8), decreasing as N-2 for 87 Rb and increasing as -N-2 for 23 Na , respectively.

瞬 内野