We consider a spin circuit-QED device where a superconducting microwave resonator is capacitively coupled to a single hole confined in a semiconductor quantum dot. Thanks to the strong spin-orbit coupling intrinsic to valence-band states, the gyromagnetic $\mathtt{g}$ matrix of the hole can be modulated electrically. This modulation couples the photons in the resonator to the hole spin. We show that the applied gate voltages and the magnetic-field orientation enable a versatile control of the spin-photon interaction, whose character can be switched from fully transverse to fully longitudinal. The longitudinal coupling is actually maximal when the transverse one vanishes and vice versa. This “reciprocal sweetness” results from geometrical properties of the $\mathtt{g}$ matrix and protects the spin against dephasing or relaxation. We estimate coupling rates reaching $\sim 10\mathrm{MHz}$ in realistic settings and discuss potential circuit-QED applications harnessing either the transverse or the longitudinal spin-photon interaction. Furthermore, we demonstrate that the $\mathtt{g}$-matrix curvature can be used to achieve parametric longitudinal coupling with enhanced coherence.

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• Circuit quantum electrodynamics
• Quantum information architectures & platforms
• Quantum interconnects
• Quantum dots
• Superconducting qubits