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We report the observation of efficient and low-noise frequency conversion between two microwave modes, mediated by the motion of a mechanical resonator subjected to radiation pressure.
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A finite resolution sideband factor β 1 , 2 = κ 1 , 2 2 / ( 16 Ω m 2 ) \beta_{1,2}=\kappa_{1,2}^{2}/(16\Omega_{m}^{2}) leads to unwanted parametric down conversion of pump photons, and therefore to the amplification of the microwave fields and mechanical motion [ 5 , 21 ] . It adds gain to the frequency conversion and increases the mechanical noise. In the extreme case where C 1 = C 2 ≫ 1 C_{1}=C_{2}\gg 1 , η 1 = η 2 = 1 \eta_{1}=\eta_{2}=1 and κ 1 = κ 2 \kappa_{1}=\kappa_{2} , one can show that both the unwanted power gain and the additional mechanical noise in units of quanta follow approximatively β 1 + β 2 \beta_{1}+\beta_{2} . With β 1 + β 2 ≈ 2 × 10 − 3 \beta_{1}+\beta_{2}\approx 2\times 10^{-3} , these effects are negligible in our device
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