  Coherent conversion from microwave to optical wave opens new research avenues
towards long distant quantum network covering quantum communication, computing,
and sensing out of the laboratory. Especially multi-mode enabled system is
essential for practical applications. Here we experimentally demonstrate
coherent multi-mode conversion from the microwave to optical wave via
collective spin excitation in a single crystal yttrium iron garnet (YIG,
Y3Fe5O12) which is strongly coupled to a microwave cavity mode in a
three-dimensional rectangular cavity. Expanding collective spin excitation mode
of our magnon-cavity hybrid system from Kittel to multi magnetostatic modes, we
verify that the size of YIG sphere predominantly plays a crucial role for the
microwave-to-optical multi-mode conversion efficiency at resonant conditions.
We also find that the coupling strength between multi magnetostatic modes and a
cavity mode is manipulated by the position of a YIG inside the cavity. It is
expected to be valuable for designing a magnon hybrid system that can be used
for coherent conversion between microwave and optical photons.
