Simple model for electrical hole spin manipulation in semiconductor quantum dots: Impact of dot material and orientation

We analyze a prototypical particle-in-a-box model for a hole spin qubit. This quantum dot is subjected to static magnetic and electric fields, and to a radio-frequency electric field that drives Rabi oscillations owing to spin-orbit coupling. We derive the equations for the Rabi frequency in a regime where the Rabi oscillations mostly result from the coupling between the qubit states and a single nearby excited state. This regime has been shown to prevail in, e.g., hole spin qubits in thin silicon-on-insulator nanowires. The equations for the Rabi frequency highlight the parameters that control the Rabi oscillations. We show, in particular, that [110]-oriented dots on (001) substrates perform much better than [001]-oriented dots because they take best advantage of the anisotropy of the valence band of the host material. We also conclude that silicon provides the best opportunities for fast Rabi oscillations in this regime despite small spin-orbit coupling.