Efficient microwave-to-optical frequency conversion (MOC) is crucial for applications such as radiometry, electrometry, quantum microwave illumination and quantum networks. Rydberg atoms provide a unique platform for realizing free-space MOC, promising wide-bandwidth, scalable, and flexible quantum interfaces. Here, we develop a theoretical framework to evaluate the system conversion efficiency, accounting for the mismatch between microwave and optical wavelengths comparing with the atomic ensemble size. Our analysis reveals that the conversion efficiency is fundamentally limited by the focusing of the free-space microwave field, with an upper bound of about 3/16 for diffraction-limited focusing. We propose using a microwave near-field antenna to overcome this limit. Our work provides a foundation for assessing and optimizing free-space MOC, paving the way for a variety of applications based on free-space MOC.
In this paper, we propose a scheme for frequency conversion between optical photons and microwave photons in non-Markovian environments using both magnetic and mechanical excitations as intermediate media. When the frequencies of optical photons, magnons, phonons, and microwave photons resonance, the conversion efficiency can be made close to reach 98.76
% by adjusting the defined complex cooperativities, while in the case of Markovian, the conversion efficiency is 90.44
%. By controlling the environmental spectral widths, the efficiency of frequency conversion exhibits a transition from Markovian regimes to non-Markovian regimes. This transformation simultaneously improves frequency conversion efficiency and conversion bandwidth, which is due to the excitation backflow generated by the interaction between the system and the non-Markovian environments. In the case, when the optical pump power in the non-Markovian regimes are of a large order of magnitude, the conversion bandwidth can be increased, but at the cost of reduced conversion efficiency. Our scheme improves the frequency conversion efficiency and bandwidth between optical photons and microwave photons, breaking the limitations of frequency conversion in Markovian environments and providing a new approach for long-distance quantum communication research of other non-Markovian quantum systems in quantum optics.