Optimal coupling of HoW$_{10}$ molecular magnets to superconducting circuits near spin clock transitions

A central goal in quantum technologies is to maximize $G$T$_{2}$, where $G$ stands for the coupling of a qubit to control and readout signals and T$_{2}$ is the qubit's coherence time. This is challenging, as increasing $G$ (e.g. by coupling the qubit more strongly to external stimuli) often leads to deleterious effects on T$_{2}$. Here, we study the coupling of pure and magnetically diluted crystals of HoW$_{10}$ magnetic clusters to microwave superconducting coplanar waveguides. Absorption lines give a broadband picture of the magnetic energy level scheme and, in particular, confirm the existence of level anticrossings at equidistant magnetic fields determined by the combination of crystal field and hyperfine interactions. Such 'spin clock transitions' are known to shield the electronic spins against magnetic field fluctuations. The analysis of the microwave transmission shows that the spin-photon coupling becomes also maximum at these transitions. The results show that engineering spin-clock states of molecular systems offers a promising strategy to combine sizeable spin-photon interactions with a sufficient isolation from unwanted magnetic noise sources.