Electrical manipulation of a hole `spin'-orbit qubit in nanowire quantum dot: the nontrivial magnetic field effects

Abstract

Strong 'spin'-orbit coupled one-dimensional hole gas is achievable in a Ge nanowire in the presence of a strong magnetic field. The strong magnetic field lifts the spin-degeneracy in the hole subband dispersions, such that the remaining (spinless) low-energy subband dispersion exhibits strong 'spin'orbit coupling. Recent experimental study in a Ge nanowire hole quantum dot [Froning et al. Nat. Nanotechnol. 16, 308 (2021)] has demonstrated a strong electrical Rabi frequency (∼200 MHz) and a non-vanishing longitudinal g-factor g l so = 1.06. Here, we understand these interesting results in terms of the 'spin'-orbit coupling physics. Using a finite square well to model the quantum dot confining potential, we calculate exactly the level splitting of the 'spin'-orbit qubit and the Rabi frequency in the electric-dipole 'spin' resonance. The 'spin'-orbit coupling modulated longitudinal g-factor g l so is naturally non-vanishing, and has the same order of magnitude as the transverse g t so . Also, both g l so and g t so are magnetic field dependent. Moreover, the 'spin'-orbit coupling has opposite dependence on the longitudinal field and the transverse field, such that the responses of the qubit level splitting and the Rabi frequency to these two fields are totally different.