Observation of Long-Distance Coherence in Critically-Driven Cavity Magnonics*

Developing quantum networks necessitates using a beam of light to coherently administer distant resonators, a process that often encounters the obstacle of dissipation-induced decoherence. Here, we discover a long-distance coherence in cavity magnonics operating in the linear regime. By locally setting the cavity near critical coupling to traveling photons, non-local magnon-photon coherence is established via strong coupling mediated by photons travelling over a 2-meter distance. The coupling strength oscillates anomalously with the photon phase, exhibiting twice the period as conventional photon-mediated couplings. Our work shows the potential of using critical phenomena for harnessing long-distance coherence in networks of distributed systems. The observed anomalous features reveal the tip of an iceberg of photon-mediated coupling in magnetic systems.