  Coherent conversion of microwave and optical photons in the single-quantum
level can significantly expand our ability to process signals in various
fields. Efficient up-conversion of a feeble signal in the microwave domain to
the optical domain will lead to quantum-noise-limited microwave amplifiers.
Coherent exchange between optical photons and microwave photons will also be a
stepping stone to realize long-distance quantum communication. Here we
demonstrate bidirectional and coherent conversion between microwave and light
using collective spin excitations in a ferromagnet. The converter consists of
two harmonic oscillator modes, a microwave cavity mode and a magnetostatic mode
called Kittel mode, where microwave photons and magnons in the respective modes
are strongly coupled and hybridized. An itinerant microwave field and a
travelling optical field can be coupled through the hybrid system, where the
microwave field is coupled to the hybrid system through the cavity mode, while
the optical field addresses the hybrid system through the Kittel mode via
Faraday and inverse Faraday effects. The conversion efficiency is theoretically
analyzed and experimentally evaluated. The possible schemes for improving the
efficiency are also discussed.
