Transverse vs. longitudinal vs. curvature couplings of spin qubits to superconducting cavity

We consider in detail the origin of the transverse, longitudinal, and curvature couplings of a spin qubit to a superconducting cavity. On the example of single, double, and triple quantum dot spin qubits we use a general framework to show the interrelations between these couplings, and discuss parameter regions, e.g. sweet spots, when transverse (Jaynes-Cummings) coupling can be eliminated, while curvature coupling can be maximized to reach tens of MHz. With the perspective of using curvature couplings for qubit readout or entangling gates, we estimated the dephasing mechanisms, and also discussed possible higher-order effects for these coupling scenarios.