Geometric Phase Associated with Spinor Rotations

Apoorva G. Wagh, Veer Chand Rakhecha

Jae-yoon Choi, Seji Kang, Sang Won Seo +2 more

For a spin-carrying particle moving in a spatially varying magnetic field, effective electromagnetic forces can arise due to the geometric phase associated with adiabatic spin rotation of the particle. We report the observation of a geometric Hall effect in a spinor Bose-Einstein condensate with a skyrmion spin texture. Under translational oscillations of the spin texture, the condensate resonantly develops a circular motion in a harmonic trap, demonstrating the existence of an effective Lorentz force. When the condensate circulates, quantized vortices are nucleated in the boundary region of the condensate and the vortex number increases over 100 without significant heating. We attribute the vortex nucleation to the shearing effect of the effective Lorentz force from the inhomogeneous effective magnetic field.

张晓燕, 胡连

Jae-yoon Choi, Seji Kang, Sang Won Seo +2 more

For a spin-carrying particle moving in a spatially varying magnetic field, effective electromagnetic forces can arise due to the geometric phase associated with adiabatic spin rotation of the particle. We report the observation of a geometric Hall effect in a spinor Bose-Einstein condensate with a Skyrmion spin texture. Under translational oscillations of the spin texture, the condensate resonantly develops a circular motion in a harmonic trap, demonstrating the existence of an effective Lorentz force. When the condensate circulates, quantized vortices are nucleated in the boundary region of the condensate and the vortex number increases over 100 without significant heating. We attribute the vortex nucleation to the shearing effect of the effective Lorentz force from the inhomogeneous effective magnetic field.

Mirjana Božić

Apoorva G. Wagh, Veer Chand Rakhecha

We examine spinor evolutions in a general time-dependent magnetic field B. We derive a condition the B variation must satisfy in order that the effective field direction ${\mathbf{r}\mathbf{\^{}}}_{\mathrm{B}}^{\ensuremath{'}}$ for a frame rotating with B becomes stationary in that frame. This condition is both sufficient and necessary for B to bring about a spinor evolution which exactly maintains a fixed angle between the spin and B. The adiabatic evolution used by Berry is just a special case, albeit only approximate, of these fixed-angle evolutions. To the other extreme of the fixed-angle evolutions, the nontrivial parallel transportation occurs, which is exact, necessarily nonadiabatic, and yields a pure geometric phase. Hence an experiment aimed at observing the geometric phase should seek to effect not an adiabatic evolution but a parallel transportation.