Probing many-body localization in a disordered quantum magnet

Quantum states cohere and interfere. Quantum systems composed of many atoms arranged imperfectly rarely display these properties. Here we demonstrate an exception in a disordered quantum magnet that divides itself into nearly isolated subsystems. We probe these coherent clusters of spins by driving the system beyond its linear response regime at a single frequency and measuring the resulting "hole" in the overall linear spectral response. The Fano shape of the hole encodes the incoherent lifetime as well as coherent mixing of the localized excitations. For the disordered Ising magnet, $\mathrm{LiHo_{0.045}Y_{0.955}F_4}$, the quality factor $Q$ for spectral holes can be as high as 100,000. We tune the dynamics of the quantum degrees of freedom by sweeping the Fano mixing parameter $q$ through zero via the amplitude of the ac pump as well as a static external transverse field. The zero-crossing of $q$ is associated with a dissipationless response at the drive frequency, implying that the off-diagonal matrix element for the two-level system also undergoes a zero-crossing. The identification of localized two-level systems in a dense and disordered dipolar-coupled spin system represents a solid state implementation of many-body localization, pushing the search forward for qubits emerging from strongly-interacting, disordered, many-body systems.