Decoherence of electron spin qubit during transfer between two semiconductor quantum dots at low magnetic fields

Abstract

Electron shuttling is one of the current avenues being pursued to scale semiconductor quantum dot-based spin qubits. Adiabatic spin qubit transfer along a chain of tunnel-coupled quantum dots is one of the possible schemes. In this scheme, we theoretically analyze the dephasing of a spin qubit that is adiabatically transferred between two tunnel-coupled quantum dots. We focus on the regime where the Zeeman splitting is lower than the tunnel coupling, such that interdot tunneling with spin flip is absent. We analyze the sources of errors in spin-coherent electron transfer for Si- and GaAs-based quantum dots. In addition to the obvious effect of fluctuations in spin splitting within each dot, leading to finite $T_{2}^{*}$ for the stationary spin qubit, we consider the effects activated by detuning sweeps: failure of charge transfer due to charge noise and phonons, spin relaxation due to the enhancement of spin-orbit mixing at the tunnel-induced anticrossing of states localized in the two dots, and spin dephasing caused by low- and high-frequency noise coupling to the electron's charge. We show that the latter effect is activated by differences in Zeeman splittings between the two dots. Importantly, all the error mechanisms are more dangerous at low tunnel couplings. Our results indicate that away from micromagnets, maximizing the fidelity of coherent transfer aligns with minimizing charge transfer error that was previously considered in J. A. Krzywda and L. Cywi\'nski, Phys. Rev. B 104 075439 (2021). For silicon, we suggest having tunnel coupling fulfilling $ 2t_c \gtrsim 60 \, \mu$eV when one aims to coherently transfer a spin qubit across a $\sim \!10$ $\mu$m long array of $\sim \! 100$ quantum dots with error less than $10^{-3}$.