Spinor Bose Condensates in Optical Traps

In an optical trap, the ground state of spin-1 Bosons such as 23Na, 39K, and 87Rb can be either a ferromagnetic or a “polar” state, depending on the scattering lengths in different angular momentum channel. The collective modes of these states have very different spin character and spatial distributions. While ordinary vortices are stable in the polar state, only those with unit circulation are stable in the ferromagnetic state. The ferromagnetic state also has coreless (or Skyrmion) vortices like those of superfluid 3He-A. Two months ago, the MIT group has succeeded in trapping a Na Bose condensate by purely optical means [1]. This experiment has opened up a new direction in the study of confined dilute atomic gases. In conventional magnetic traps, the spins of the alkali atoms are frozen. As a result, even though the alkali atoms carry spins, they behave like scalar particles. In contrast, the spin of the alkali atoms are essentially free in an optical trap. The spinor nature of alkali Bose condensate can therefore be manifested [2]. Because of the wide range of hyperfine spins of the alkali Bosons and Fermions, the optical trap has provided great opportunities to study dilute quantum gases of atoms with large spins. The purpose of this paper is to point out the general properties of the spinor Bose condensates. As we shall see, they possess a whole host of quantum phenomena absent in scalar condensates. These include changes in ground state structures with interaction parameters, vector and quadrupolar spin wave modes, topological and energetic instability of doubly quantized singular vortices, and the existence of coreless (or Skyrmion) vortices. All these results are simple consequences of the effective low energy Hamiltonian of the