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Strong `spin'-orbit coupled one-dimensional hole gas is achievable in a Genanowire in the presence of a strong magnetic field. The strong magnetic fieldlifts the two-fold degeneracy in the hole subband dispersions, so that theeffective low-energy subband dispersion exhibits strong `spin'-orbit coupling.Here, we study the electrical `spin' manipulation in a Ge nanowire quantum dotfor both the lowest and second lowest hole subband dispersions. Using a finitesquare well to model the quantum dot confining potential, we calculate exactlythe level splitting of the `spin'-orbit qubit and the Rabi frequency in theelectric-dipole `spin' resonance. The `spin'-orbit coupling modulatedlongitudinal $g$-factor $g_{\rm so}$ is not only non-vanishing but alsomagnetic field dependent. Moreover, the `spin'-orbit couplings of the lowestand second lowest subband dispersions have opposite magnetic dependences, sothat the results for these two subband dispersions are totally different.

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