Charge noise induced spin decoherence in a double quantum dot: Effects of a micromagnet

Charge noise is one of the most important error sources for quantum gates in semiconductor systems. We study the decoherence of an electron spin in a double quantum dot in the presence of an inhomogeneous magnetic field. An exact dynamical equation is derived directly from the microscopic Hamiltonian, which allows us to investigate the impact of the non-Markovian properties of the quantized bosonic environment. We show that non-Markovian dynamics could cause a notable correction when measuring spin relaxation time. Our results reduce to the one predicted by the traditional Redfield master equation when Born-Markov approximation is applied. The spin relaxation and dephasing caused by the charge noise is suppressed by certain factors since the noise is indirectly (through the artificial spin-orbit interaction from the micromagnet) coupled to spin. We show these factors strongly depend on the system parameters such as detuning, tunneling strength, field gradients in vertical or horizontal directions. Our results present a systematic approach to study decoherence processes caused by charge noise, particularly for quantum dots in an inhomogeneous magnetic field.