SU(3) symmetry of spin-1 Bose-Einstein condensate

It is well-known that spin-1 atoms have SU(3) symmetry. In this work, we develop the theory for spin-1 Bose-Einstein condensate (BEC) based on SU(3) Lie group and predict that any spin-1 atom, for instance, Rb-87 can exist in either of two inequivalent fundamental representations of SU(3) namely D(1, 0) or D(0, 1). Furthermore, the SU(3) theoretical treatment results in either ferromagnetic or antiferromagnetic ground states of the spin-1 BEC depending on the sign of a (1,1) - a (0,0), where a (1,1) and a (0,0) are the scattering lengths corresponding to D(1, 1) and D(0, 0) states. We also show that the coherent spin mixing process of spin-1 BEC is due to only the collisions between atoms in the D(1, 0) and D(0, 1) representations.

Automated summary

In this work, the theory for spin-1 Bose-Einstein condensate (BEC) based on SU(3) Lie group is developed, and it is predicted that any spin-1 atom can exist in either of two inequivalent fundamental representations of SU(3). The ground state of the spin-1 BEC can be either ferromagnetic or antiferromagnetic depending on the sign of a (1,1) - a (0,0), and the coherent spin mixing process is due to collisions between atoms in specific representations.