Abstract
Motivated by the recent realization of a $^{52}$Cr Bose-Einstein condensate, we consider the phase diagram of a general spin-three condensate as a function of its scattering lengths. We classify each phase according to its ``reciprocal spinor,'' using a method developed in a previous work. We show that such a classification can be naturally extended to describe the vortices for a spinor condensate by using the topological theory of defects. To illustrate, we systematically describe the types of vortex excitations for each phase of the spin-three condensate.
Highlights
We classify each phase according to its reciprocal spinor, using a method developed in a previous work
Spin rotations which leave this set of points invariant will take a spinor A␣ into itself modulo an overall phase which can be computed through geometrical considerations
The last column gives the number of conjugacy classes of 1 for each spin state, which gives the number of possible vortex excitations
Summary
We systematically describe the types of vortex excitations for each phase of the spin-three condensate. In addition to having such rich phase diagrams, spinor condenstates in general and the 52Cr condensate in particular will have intriguing topological excitations. Spin rotations which leave this set of points invariant will take a spinor A␣ into itself modulo an overall phase which can be computed through geometrical considerations.
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