  We describe a scheme to coherently convert a microwave photon of a
superconducting co-planar waveguide resonator to an optical photon emitted into
a well-defined temporal and spatial mode. The conversion is realized by a cold
atomic ensemble trapped above the surface of the superconducting atom chip,
near the antinode of the microwave cavity. The microwave photon couples to a
strong Rydberg transition of the atoms that are also driven by a pair of laser
fields with appropriate frequencies and wavevectors for an efficient
wave-mixing process. With only few thousand atoms in an ensemble of moderate
density, the microwave photon can be completely converted into an optical
photon emitted with high probability into the phase matched direction and,
e.g., fed into a fiber waveguide. This scheme operates in a free-space
configuration, without requiring strong coupling of the atoms to a resonant
optical cavity.
