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Chinese Physics C

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

Xi Li

Published Jan 1, 2003• 1 citation
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.
I use a time-dependent Lagrangian formalism and a variational trial function to study the dynamics of a two-component vortex in a spin-orbit coupled Bose-Einstein condensate (BEC). For a single-component BEC, various experiments have validated this theoretical approach, for example a thermal quench that yields a quantized vortex in roughly 25% of trials. To be definite, I assume the specific spin-orbit form used in recent NIST experiments, which introduces a spatial asymmetry because of the external Raman laser beams. I here generalize this formalism to include a two-component order parameter that has quantized circulation in each component but not necessarily with the same circulation. For example a singly quantized vortex in just one component yields a BEC analog of the half-quantum vortex familiar in 3^33He-A and in ppp-wave chiral superconductors. This and other unusual two-component vortices have both periodic trajectories and unbounded trajectories that leave the condensate, depending on the initial conditions. The optimized phase of the order parameter induces a term in the particle current that cancels the contribution from the vector potential, leaving pure circulating current around the vortex.