  We show that cold Rydberg gases enable an efficient six-wave mixing process
where terahertz or microwave fields are coherently converted into optical
fields and vice versa. This process is made possible by the long lifetime of
Rydberg states, the strong coupling of millimeter waves to Rydberg transitions
and by a quantum interference effect related to electromagnetically induced
transparency (EIT). Our frequency conversion scheme applies to a broad spectrum
of millimeter waves due to the abundance of transitions within the Rydberg
manifold, and we discuss two possible implementations based on focussed
terahertz beams and millimeter wave fields confined by a waveguide,
respectively. We analyse a realistic example for the interconversion of
terahertz and optical fields in rubidium atoms and find that the conversion
efficiency can in principle exceed 90\%.
