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The spin resonance of electrons can be coupled to a microwave cavity mode toobtain a photon-magnon hybrid system. These quantum systems are widely studiedfor both fundamental physics and technological quantum applications. In thisarticle, the behavior of a large number of ferrimagnetic spheres coupled to asingle cavity is put under test. We use second-quantization modeling ofharmonic oscillators to theoretically describe our experimental setup andunderstand the influence of several parameters. The magnon-polariton dispersionrelation is used to characterize the system, with a particular focus on thevacuum Rabi mode splitting due to multiple spheres. We combine the resultsobtained with simple hybrid systems to analyze the behavior of a more complexone, and show that it can be devised in such a way to minimize the degrees offreedom needed to completely describe it. By studying single-sphere couplingtwo possible size-effects related to the sample diameter have been identified,while multiple-spheres configurations reveal how to upscale the system. Thischaracterization is useful for the implementation of anaxion-to-electromagnetic field transducer in a ferromagnetic haloscope for darkmatter searches. Our dedicated setup, consisting in ten 2 mm-diameter YIGspheres coupled to a copper microwave cavity, is used for this aim and studiedat mK temperatures. Moreover, we show that novel applications ofoptimally-controlled hybrid systems can be foreseen for setups embedding alarge number of samples.

Coherent coupling between multiple ferrimagnetic spheres and a microwave cavity in the quantum-limit