Stark effect in phosphorus donor dots: electrical control of electron and nuclear spins

Recent experiments have paved the way to build a quantum computer using phosphorus donors in silicon ^[1][2]. The use of electron and nuclear spins as qubits in such a system requires individual qubit control. Here we show that the hyperfine Stark effect, which is the change in hyperfine coupling between electron and nuclear spins due to electric fields, can be used for electrical control of the electron and nuclear spins. For a single donor (1P), the electric field hardly couples the spherical-like ground state wavefunction, resulting in the quadratic stark effect ^[3]. In multi-donor dots, however, the non-spherical bonding and anti-bonding states have finite dipole moments which give rise to a linear Stark effect. For 2P dots, the Stark coefficients of both donors are the same and the maximum values are obtained when the electric field is applied along the donor separation axis. For 3P dots, on the other hand, the Stark coefficients are different for each donor, but the electric field direction can be adjusted to maximize any of them separately. Using the atomistic tight-binding model and effective spin Hamiltonian simulations we show how the 2P and 3P donor dot configurations and electric fields can be engineered for qubit control through Electric Dipole Spin Resonance (EDSR).

[1] S. J. Hile et al., Science Advances 4, 10.1126/sciadv.aaq1459 (2018)

[2] J. J. Pla et al., Nature 496, 334 (2013)

[3] R. Rahman et al., Physical Review Letters 99, 10.1103/physrevlett.99.036403 (2007)