Phase control of magnomechanically induced transparency in a closed-loop three-cavity array

In this paper, we propose a scheme to generate the phase control of magnomechanically induced transparency (MMIT) in a three-cavity system, into one cavity of which a yttrium iron garnet (YIG) sphere is placed. When two microwave cascade cavities are extended to a coupled three-cavity array, the single window MMIT is changed into a multi-window MMIT structure due to the existence of multiple quantum interference channels. Interestingly, when the three cavities are linked end-to-end forming a closed-loop structure, the phase control of MMIT is achievable, providing an additional degree to control MMIT. In addition, the phase-dependent slow light effects are also discussed briefly. The present system may find potential applications in solid-state quantum information processing.