Multiple Quantum Coherence Dynamics of P1 Centers in Diamond

Multiple quantum coherences (MQC) are a form of out-of-time ordered correlator (OTOC) that have been used in nuclear magnetic resonance (NMR) experiments for structure determination and to characterize many-body physics of spin systems. Like all OTOCs, MQC experiments also require reversing the dynamics of a many-body quantum system. Here we use pulse electron paramagnetic resonance to extend MQC techniques to an electron spin system, the substitutional nitrogen or P1 centers in diamond. We demonstrate the use of multiple-pulse Average Hamiltonian techniques to engineer both the forward and reverse evolution of dipolar-coupled P1 to generate a Loschmidt echo. We also use MQC techniques to characterize the growth and decoherence of multispin correlations in the system.