  We study the phase controlled transmission properties in a compound system
consisting of a 3D copper cavity and an yttrium iron garnet (YIG) sphere. By
tuning the relative phase of the magnon pumping and cavity probe tones,
constructive and destructive interferences occur periodically, which strongly
modify both the cavity field transmission spectra and the group delay of light.
Moreover, the tunable amplitude ratio between pump-probe tones allows us to
further improve the signal absorption or amplification, accompanied by either
significantly enhanced optical advance or delay. Both the phase and
amplitude-ratio can be used to realize in-situ tunable and switchable fast-slow
light. The tunable phase and amplitude-ratio lead to the zero reflection of the
transmitted light and an abrupt fast-slow light transition. Our results confirm
that direct magnon pumping through the coupling loops provides a versatile
route to achieve controllable signal transmission, storage, and communication,
which can be further expanded to the quantum regime, realizing coherent-state
processing or quantum-limited precise measurements.
