Detecting spin current fluctuations in quantum magnets via microwave resonators

We theoretically examine spin transport across coupled quantum spin chains that are further coupled to a microwave cavity in series with a transmission line. Spins in the quantum magnet couple inductively to the microwave field and imprint spin transport signatures into the output photon field detected on the transmission line. We first show that in the non-invasive coupling limit the total output photon power is directly proportional to spin current noise at the cavity resonance frequency, and thus that spin current noise is detectable without recourse to destructive techniques. We also discuss the possibility of photon feedback effects on the spin conductivity and noise for the invasive coupling limit.