Hyperfine-mediated spin relaxation in donor-atom qubits in silicon

Abstract

Donor electron spin qubits hosted within nanoscale devices have demonstrated seconds-long relaxation times at magnetic fields suitable for the operation of spin qubits in silicon of B=1.5T. The relaxation rates of these qubits have been shown at milliKelvin temperatures to be mediated by spin-orbit coupling with a B^{5} dependency on magnetic field for B>3T with a transition to a B^{3} dependency at magnetic fields below (B≤3T). This deviation has been observed in many spin qubit systems but is particularly notable in multidonor quantum dot qubits. The reason for this has remained a mystery. In this paper we show that for these multidonor low noise, crystalline qubits this deviation at low magnetic fields can be explained by a hyperfine mediated relaxation mechanism of the electron spin through a quantitative model of the relaxation rates. This model identifies the importance of donor nuclear spin flips which are more apparent in multidonor systems in which the larger numbers of donor nuclei creates stronger confinement potentials and enhanced hyperfine couplings. We show theoretically that with atomic precision engineering of the locations of the donor nuclei in these multidonor quantum dot qubits, and/or nuclear spin control, we can minimize the hyperfine mediated relaxation allowing T_{1} to extend to ∼200 seconds (B=1.5T).