This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Terence Blésin, Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL) & Center of Quantum Science and Engineering (EPFL);
(2) Wil Kao, Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL) & Center of Quantum Science and Engineering (EPFL);
(3) Anat Siddharth, Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL) & Center of Quantum Science and Engineering (EPFL);
(4) Alaina Attanasio, OxideMEMS lab, Purdue University;
(5) Hao Tian, OxideMEMS lab, Purdue University;
(6) Sunil A. Bhave, OxideMEMS lab, Purdue University;
(7) Tobias J. Kippenberg, Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL) & Center of Quantum Science and Engineering (EPFL).
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Results
Appendix E: Characterization of bidirectional transduction
1. Estimation of cooperavity and singlephoton coupling rate
Given the measured offchip efficiency, the singlephoton coupling rate can be estimated. The offchip efficiency is given by
where ηprobes and ηfiberchip denote the microwave and optical insertion losses, respectively. The onchip efficiency can be written as
The internal efficiency
in the lowcooperativity regime, where the plus and minus signs correspond to the antiStokes and Stokes configurations, respectively. The optical and microwave extraction efficiencies
The singlephoton cooperativity C0 is enhanced by the intracavity photons
where the pump detuning is assumed to be small. The input power in the bus waveguide Pwg is related to the power in the input fiber Pin by the fiberchip coupling efficiency
The offchip efficiency with respect to the microwave probe and optical fiber is thus
2. Estimation of onchip and internal transduction efficiencies
We have achieved η tot = −48 dB at an input pump power of 21 dBm. With the losses quoted in Appendix E 1, the onchip and internal efficiencies can be estimated. For conversion in either directions, the signal goes through the respective input and output ports exactly once, acquiring an attenuation of η probesη fiber−chip = −7 dB. We therefore have η oc = 7.9×10−5 . Knowing the extraction efficiencies ηo = 35% and ηm = 11%, we further obtain η int = 2×10−3 .