Hybridizing collective spin excitations and a cavity with high cooperativity provides a new research subject in the field of cavity quantum electrodynamics and can have potential applications in quantum information. Here we report the quantum control of a single magnon in a macroscopic spin system (i.e., 1 mm-diameter yttrium-iron-garnet sphere) embedded in a microwave cavity. In this hybrid quantum system, an auxiliary superconducting qubit is also embedded in the cavity. Via this microwave cavity, we can implement strong coupling between the magnon and the superconducting qubit. By tuning the qubit frequency via the Autler-Townes effect, we manipulate a single magnon to generate its nonclassical quantum states, including the single-magnon state and its coherent superposition with a vacuum (zero magnon state). We also confirm the deterministic generation of these nonclassical states by Wigner tomography. This experiment offers the first reported deterministic generation of the nonclassical quantum states in a macroscopic spin system. Moreover, we demonstrate the deterministic generation of the macroscopically entangled Bell state between this millimeter-sized spin system and the micrometer-sized superconducting qubit. We develop a joint tomography approach to confirming this deterministic generation of the Bell state, which gives a generation fidelity of about 0.90. This work makes the macroscopic spin system the largest system capable of generating the maximally entangled quantum state and paves a way to explore its promising applications in quantum information.
*This work is supported by the National Key Research and Development Program of China (Grant No. 2022YFA1405200), and the National Natural Science Foundation of China (Grants Nos. 92265202, 11934010, and 12174329).
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