Single spin probe of Many-Body Localization

We use an external spin as a dynamical probe of many body localization. The probe spin is coupled to an interacting and disordered environment described by a Heisenberg spin chain in a random field. The spin-chain environment can be tuned between a thermalizing delocalized phase and non-thermalizing localized phase, both in its ground- and high-energy states. We study the decoherence of the probe spin when it couples to the environment prepared in three states: the ground state, the infinite temperature state and a high energy N\'eel state. In the non-thermalizing many body localized regime, the coherence shows scaling behaviour in the disorder strength. The long-time dynamics of the probe spin shows a logarithmic dephasing in analogy with the logarithmic growth of entanglement entropy for a bi-partition of a many-body localized system. In summary, we show that decoherence of the probe spin provides clear signatures of many-body localization.