Coherent microwave-to-optical conversion via six-wave mixing in Rydberg atoms

We present an experimental demonstration of converting a microwave field to an optical field via frequency mixing in a cloud of cold $^{87}$Rb atoms, where the microwave field strongly couples to an electric dipole transition between Rydberg states. We show that the conversion allows the phase information of the microwave field to be coherently transferred to the optical field. With the current energy level scheme and experimental geometry, we achieve a photon conversion efficiency of ~0.3% at low microwave intensities and a broad conversion bandwidth of more than 4 MHz. Theoretical simulations agree well with the experimental data, and indicate that near-unit efficiency is possible in future experiments.