Cooperativity Requirements for Microwave-to-Optical Single-Photon Transduction

Linking a superconducting circuit to an optical fibre requires converting a microwave photon into an optical photon. In an electro-optic or optomechanical converter the efficiency is set by two cooperativities, one on each side of the device, and by how well they are matched. This study computes the quantities that follow from stated assumptions for a bidirectional converter with internal efficiency formula stated in the text, external coupling 0.9 on each side, and a thermal occupation of 0.1 microwave photons, using the relations set out in the Methods. The headline results are eta at C 10 10 = 0.907, eta external at C 10 10 = 0.7347, eta at C 10 100 = 0.3246, eta at C 1 1 = 0.4444, eta at C 100 100 = 0.9901. The central question is stated as follows: What conversion efficiency and added noise follow for cooperativity pairs from below unity to one hundred, and how much efficiency is lost when the two cooperativities differ by a factor of ten? The answer obtained here is conditional on the assumptions listed in the paper and in the deposited calculation; changing an assumption changes the numbers in the way the sensitivity discussion describes. Reported conversion efficiencies span many orders of magnitude, from very small values in early devices to tens of percent in the most advanced, with added noise often the stricter criterion. The work is a computation, not a laboratory measurement, and it is labelled accordingly. Where the computed result is unfavourable to the device or effect under study, that outcome is reported in the same terms as a favourable one, because a bound that only appears when it is welcome is not a bound at all. All numerical statements in this abstract are reproduced by the deposited script from the stated inputs.