Longitudinal and transverse electric field manipulation of hole spin-orbit qubits in one-dimensional channels

Holes confined in semiconductor nanostructures realize qubits where the quantum mechanical spin is strongly mixed with the quantum orbital angular momentum. The remarkable spin-orbit coupling allows for fast all electrical manipulation of such qubits. We study an idealization of a CMOS device where the hole is strongly confined in one direction (thin film geometry), while it is allowed to move more extensively along a one-dimensional channel. Static electric bias and $ac$ electrical driving are applied by metallic gates arranged along the channel. In quantum devices based on materials with a bulk inversion symmetry, such as silicon or germanium, there exists different possible spin-orbit coupling based mechanisms for qubit manipulation. One of them, the $g$-tensor magnetic resonance ($g$-TMR), relies on the dependence of the effective $g$-factors on the electrical confinement. In this configuration the hole is driven by an $ac$ field parallel to the static electric field and perpendicular to the channel (transverse driving). Another mechanism, which we refer to here as iso-Zeeman electric dipole spin resonance (IZ-EDSR), is due to the Rashba spin-orbit coupling that leads to an effective time-dependent magnetic field experienced by the pseudo-spin oscillating along the quantum channel (longitudinal driving). We compare these two modes of operation and we describe the conditions where the magnitudes of the Rabi frequencies are the largest. Different regimes can be attained by electrical tuning where the coupling to the $ac$ electric field is made either weak or strong...