Abstract
The electrical control of a spin qubit in a quantum dot relies on spin-orbit coupling (SOC), which could be either intrinsic to the underlying crystal lattice or heterostructure, or extrinsic via, for example, a micro-magnet. In experiments, micromagnets have been used as a synthetic SOC to enable strong coupling of a spin qubit in quantum dots with electric fields. Here we study theoretically the spin relaxation, pure dephasing, spin manipulation, and spin-photon coupling of an electron in a quantum dot due to the synthetic SOC induced spin-orbit mixing. We find qualitative difference in the spin dynamics in the presence of a synthetic SOC compared with the case of the intrinsic SOC. Specifically, spin relaxation due to the synthetic SOC and deformation potential phonon emission (or Johnson noise) shows $B_0^5$ (or $B_0$) dependence with the magnetic field, which is in contrast with the $B_0^7$ (or $B_0^3$) dependence in the case of the intrinsic SOC. Moreover, charge noise induces fast spin dephasing to the first order of the synthetic SOC, which is in sharp contrast with the negligible spin pure dephasing in the case of the intrinsic SOC. These qualitative differences are attributed to the broken time-reversal symmetry ($T$-symmetry) of the synthetic SOC. An SOC with broken $T$-symmetry (such as the synthetic SOC from a micro-magnet) eliminates the ``Van Vleck cancellation'' and causes a finite longitudinal spin-electric coupling that allows the longitudinal coupling between spin and electric field, and in turn allows spin pure dephasing. Finally, through proper choice of magnetic field orientation, the electric-dipole spin resonance via the synthetic SOC can be improved with potential applications in spin-based quantum computing.
Spin-relaxation anisotropy in a nanowire quantum dot with strong spin-orbit coupling
