Abstract
Coherent manipulation of the qubit is the most essential part of the quantum information processing. In the solid state architecture of the quantum computing using electron spins in quantum dots (QDs)[1], two-qubit operation is relatively easily realized and had been experimentally demonstrated since the accurate control of the spin exchange coupling energy J is straightforward. In contrast, single spin coherent rotation is not easy. Traditionally, spin manipulation is realized by electron spin resonance (ESR), where time-dependent transverse magnetic field of frequency ω close to EZ/h is applied, where EZ is the Zeeman energy by the large external static magnetic field. Selective control of individual spins is hard, but the idea of electric dipole spin resonance (EDSR), which uses oscillating electric field, instead of magnetic field, had been proposed [2,3] and subsequently demonstrated [4,5]. Electron spin dipole itself is independent of the electric field, and the charge (orbital) degree of freedom is efficiently coupled to the electric field. When there are some mechanism to couple the orbital degree with the spin, the spin can be manipulated with electric field, which is called as EDSR. The gradient of the static magnetic field[2] and the spin-orbtit interaction[3] are among these mechanisms. This contribution extends previous theory of EDSR, where the coupling strength e of the effective Hamiltonian,
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