LAUSR

A slanting magnetic field is usually used to realize a slight hybridization between the spin and the orbital degrees of freedom in a semiconductor quantum dot, such that the spin is manipulable by an external oscillating electric field. Here we show that, the longitudinal slanting field mediates a longitudinal driving term in the electric-dipole spin resonance, such that the spin population inversion exhibits a modulated Rabi oscillation. Fortunately, we can minimize this modulation by increasing the statical magnetic field. The longitudinal slanting field also mediates an interaction between the spin and the $1/f$ charge noise, which causes the spin pure dephasing. Choosing proper spectrum function strength, the spin dephasing time is about $T^{*}_{2}=17$ $\mu$s and the spin echo time is about $T^{\rm echo}_{2}=85$ $\mu$s in a Si quantum dot, in good agreement with experimental observations. We also propose several strategies to alleviate the spin dephasing, such as lowering the experimental temperature, reducing the quantum dot size, engineering the slanting field, and using the dynamical decoupling scheme.