  Recent quantum technologies have established precise quantum control of
various microscopic systems using electromagnetic waves. Interfaces based on
cryogenic cavity electro-optic systems are particularly promising, due to the
direct interaction between microwave and optical fields in the quantum regime.
Quantum optical control of superconducting microwave circuits has been
precluded so far due to the weak electro-optical coupling as well as
quasi-particles induced by the pump laser. Here we report the coherent control
of a superconducting microwave cavity using laser pulses in a multimode
electro-optical device at millikelvin temperature with near-unity
cooperativity. Both the stationary and instantaneous responses of the microwave
and optical modes comply with the coherent electro-optical interaction, and
reveal only minuscule amount of excess back-action with an unanticipated time
delay. Our demonstration enables wide ranges of applications beyond quantum
transductions, from squeezing and quantum non-demolition measurements of
microwave fields, to entanglement generation and hybrid quantum networks.
