Four-spin cross relaxation in a hybrid quantum device

Understanding the spin relaxation in superconducting quantum circuit and solid-state spin hybrid systems is of great importance especially for quantum storage purposes. We have studied the longitudinal relaxation for electron spins of substitutional nitrogen (P1) centers in a hybrid quantum device containing a diamond and a superconducting coplanar waveguide resonator. From a series of pump-probe experiments we conclude that the dominated spin relaxation mechanism is a cross-relaxation process induced by a four-spin interaction (four-spin cross relaxation) among different hyperfine split spin transitions. Some features of the four-spin process are discussed based on a set of rate equations. This work provides interesting perspectives in understanding the coherence properties of the hyperfine split spin ensembles in a hybrid quantum system.