Hole spin manipulation in inhomogeneous and non-separable electric fields

The usual models for electrical spin manipulation in semiconductor quantum dots assume a separable confinement potential in the spatial dimensions and/or a homogeneous AC driving field. However, the electric field induced by the gates in quantum dot devices is not fully separable and displays inhomogeneities. We address the electrical manipulation of hole spins in semiconductor heterostructures subject to inhomogeneous vertical electric fields and/or in-plane AC electric fields. We consider Ge quantum dots electrically confined in a Ge/GeSi quantum well as an illustration. We show that the coupling between the vertical and in-plane motions of the hole gives rise to an additional spin-orbit coupling mechanism (beyond the usual linear/cubic in momentum Rashba terms) that modulates the principal axes of the hole gyromagnetic g-matrix. This non-separability mechanism can be of the same order of magnitude as Rashba-type interactions enabling spin manipulation when the magnetic field is applied in the plane of the heterostructure even when the dot is symmetric. More generally, we show that Rabi oscillations in strongly patterned electric fields harness a variety of g-factor modulations. We discuss the implications for the design, modeling and understanding of hole spin qubit devices.