Optical rotation of heavy hole spins by non-Abelian geometrical means

A non-Abelian geometric method is proposed for rotating of heavy hole spins in a singly positive charged quantum dot in Voigt geometry. The key ingredient is the delay-dependent non-Abelian geometric phase, which is produced by the nonadiabatic transition between the two degenerate dark states. We demonstrate, by controlling the pump, the Stokes and the driving fields, that the rotations about y and z axes with arbitrary angles can be realized with high fidelity. Fast initialization and heavy hole-spin-state readout are also possible.