Impact of $\mathcal{T}$-symmetry on decoherence and control for an electron spin in a synthetic spin-orbit field

Abstract

The electric control of a spin qubit in a quantum dot relies on spin-orbit coupling (SOC). Here, we show that the time-reversal symmetry ($\mathcal{T}$-symmetry) of the intrinsic SOC leads to not only the traditional van Vleck cancellation known for spin relaxation, but also vanishing spin dephasing to the lowest order of SOC, which we term as "longitudinal spin-orbit field cancellation". On the other hand, a micro-magnet used in recent experiments creates a synthetic SOC that breaks $\mathcal{T}$-symmetry, which helps eliminate both the "van Vleck cancellation" and the "longitudinal spin-orbit field cancellation". This modification removes the dependence on the quantization magnetic field of the effective magnetic field $\vec\Omega$ experienced by the spin qubit, and in principle allows a longitudinal component for $\vec\Omega$. Consequently, spin relaxation and dephasing are qualitatively modified \added{compared with the case of the intrinsic SOC}. We further demonstrate that the longitudinal component of $\vec\Omega$ could enable novel schemes for spin coupling and manipulation, with potential applications in semiconductor quantum computing.