We investigate the generation of antibunched photon-magnon pairs in a hybrid quantum system that integrates a yttrium iron garnet (YIG) sphere and two microwave cavities. Through a two-mode two-photon drive, strongly correlated photon pairs are initially excited in the two Kerr-nonlinear cavities. One photon mode then coherently couples to the magnon mode in the YIG sphere, enabling the conversion of photon pairs into hybrid photon-magnon pairs, each composed of one photon and one magnon. The introduction of Kerr nonlinearity induces frequency shifts in the energy levels, facilitating a quantum blockade effect. Analysis of the second-order correlation functions for the photon and magnon modes demonstrates not only a conventional blockade induced by energy-level shifts, but also an unconventional blockade arising from destructive quantum interference. The Kerr nonlinearity required to achieve the latter can be weaker. Such strongly correlated photon-magnon pairs exhibit potential applications in quantum networks and quantum information processing.

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• Hybrid quantum systems
• Magnons
• Quantum states of light