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Chinese Physics C

Decomposition of the SU (2) Gauge Field and Circulation Condition of the Bose-Einstein Condensate

Li Xi-Guo, Duojie Jia, Gao Yuan

Published Jan 5, 2003• 0 citations
OpenAlex

Abstract

Using decomposition of the SU(2) gauge field in terms of unit vector field, we have discussed circulation condition of the spin-1/2 Bose-Einstein dendensate. For the two-component Bose-Einstein condensate,the SU/(2) symmetry of the internal states leads to a generalization of Mermin-Ho relation as a topological constrain of the superfluid velocity.

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Using decomposition of the SU(2) gauge field in terms of unit vector field, we have discussed circulation condition of the spin-1/2 Bose-Einstein dendensate. For the two-component Bose-Einstein condensate,the SU/(2) symmetry of the internal states leads to a generalization of Mermin-Ho relation as a topological constrain of the superfluid velocity.
The Bose-Einstein condensates of alkali atomic gases are spinor fields with local ``spin-gauge'' symmetry. This symmetry is manifested by a superfluid velocity us{\mathbf{u}}_{s}us​ (or gauge field) generated by the Berry phase of the spin field. In ``static'' traps, us{\mathbf{u}}_{s}us​ splits the degeneracy of the harmonic energy levels, breaks the inversion symmetry of the vortex nucleation frequency ${\mathbf{\ensuremath{\Omega}}}_{c1}$, and can lead to vortex ground states.
The phase separation and vortex states in two-component Bose-Einstein condensate consisting of |F = 1,mf = −1> and |2,1> internal spin states of 87Rb atoms are considered in the framework of Thomas-Fermi approximation. It is shown that in nonrotating system the atoms in the state |1, −1> form a shell about the atoms in the state |2,1>. The critical angular velocity for each state is calculated. These velocities depend drastically on the relative concentrations of the components, the critical angular velocity of the outer component being less than the angular velocity of the inner one. It is shown that the atoms in the |1, −1> state can form a rotating ring about the resting core of the atoms in the state |2,1>. PACS:03.75.Fi; 05.30.Jp; 32.80.Pj. The realization of Bose-Einstein Condensation (BEC) in dilute atomic gases offers new opportunities for studying quantum degenerate fluids [1]. These condensates, which contain thousands of atoms confined to microscale clouds, have similarities to superfluidity and laser,