Spin-orbit interactions of two phosphorus donors in silicon

Understanding the form and strength of the spin-orbit interaction is important for spin qubit design. While strong spin-orbit couplings allow us to drive the electron spin qubit electrically, charge noise and phonon also couple to the electron spin and cause decoherence. We show in this work various spin-orbit terms are present depending on the separation direction of the two donors, giving rise to anisotropy in the electron spin relaxation time T₁ in a 2P donor dot qubit. Charge noise causes the electron spin to relax through spin-orbit terms whilst the resulting spin relaxation, together with hyperfine mediated phonon relaxation, explain the measured anisotropy. We show how we can extend the T₁ times ∼ 40 s by minimising the effect of spin-orbit and charge noise and/or by using low magnetic fields (B = 0.75 T) and utilising ramped measurement techniques [1]. Finally, by analysing and modelling the charge noise in the device and obtaining the noise amplitude, we extract the spin-orbit strength which gives the corresponding T₁ times. We find that the H_EB spin-orbit strength of a 2P donor dot is similar to the H_EB spin-orbit strength of a 1P donor dot [2].

[1] D. Keith, Y. Chung, L. Kranz, B. Thorgrimsson, S. K. Gorman, and M. Y. Simmons, Ramped measurement technique for robust high-fidelity spin qubit readout, Science Advances 8, eabq0455 (2022).

[2] B. Weber, Y.-L. Hsueh, T. F. Watson, R. Li, A. R. Hamilton, L. C. Hollenberg, R. Rahman, and M. Y. Simmons, Spin–orbit coupling in silicon for electrons bound to donors, npj Quantum Information 4, 61 (2018).