Gate control of a quantum dot single-electron spin through geometric phases: Feynman disentangling method

The use of topological phases for the manipulation of electron spins in GaAs quantum dots is a promising candidate for solid state quantum computation and non-charged based logic devices for projected post-CMOS technology. A single electron can be trapped and its spin can be manipulated by moving the quantum dot adiabatically in a closed loop (Berry effect) through the application of gate potentials. In this paper, we present numerical simulations and analytical expressions for the transition probability of electron spins in single electron devices for a quantum dot. Using analytical and numerical techniques, we calculate the Berry Phase for both non-degenerate and degenerate cases. We show that the spin orbit coupling in III-V type semiconductors will enhance the transition probability of the electron spin over pure Dresselhaus or pure Rashba cases considered separately. Considering these mechanisms separately however, is useful in that an exact solution exists as determined by the Feynman disentangling technique. For the most general cases where the solution of the propagator becomes non-trivial, we carry out the numerical simulations of such propagator.