Scheme for generating maximally entangled atomic states in a spinor Bose–Einstein condensate

We propose a three-step scheme for generating the maximally entangled atomic Greenberger–Horne–Zeilinger (GHZ) states in a spinor Bose–Einstein condensate by using strong classical laser fields to shift atom level and drive single atom Raman transition. Compared with scheme only using single Raman transition [L. You, Phys. Rev. Lett. 90 (2003) 030402], our scheme operates in a fast way, i.e. the time needed to generate the maximally entangled states between atoms with hyperfine spin −1 and 1 is reduced by half. On the other hand, the scheme can be directly used to generate the maximally entangled states between atoms with hyperfine spin 0 and 1.