In contrast to the commonly used qubit resonator transverse coupling via the σxy-degree of freedom, longitudinal coupling through σz presents a tantalizing alternative: it does not hybridize the modes, eliminating Purcell decay, and it enables quantum-non-demolishing qubit readout independent of the qubit-resonator frequency detuning. Here, we demonstrate longitudinal coupling between a {Cr7Ni} molecular spin qubit ensemble and the kinetic inductance of a granular aluminum superconducting microwave resonator. The inherent frequency-independence of this coupling allows for the utilization of a 7.8 GHz readout resonator to measure the full {Cr7Ni} magnetization curve spanning 0-600 mT, corresponding to a spin frequency range of fspin=0-15 GHz. For 2 GHz detuning from the readout resonator, we measure a 1/e spin relaxation time τ=0.38 s, limited by phonon decay to the substrate. Based on these results, we propose a path towards longitudinal coupling of single spins to a superconducting fluxonium qubit.
@article{arxiv.2502.07605,
title = {Kinetic inductance coupling for circuit QED with spins},
author = {S. Günzler and D. Rieger and M. Spiecker and T. Koch and G. A. Timco and R. E. P. Winpenny and I. M. Pop and W. Wernsdorfer},
journal= {arXiv preprint arXiv:2502.07605},
year = {2025}
}