Fig. 4

Scaling up the optomechanical single-photon coupling rate with the applied in-plane magnetic field. a Representation of the applied magnetic field components to the SQUID loop. During the experiment, the cavity flux responsivity was fixed at two different values by adjusting the flux bias point \({\Phi }_{{\rm{b}}}\). In addition to this constant parameter, the in-plane magnetic field \({B}_{| | }\) was swept from \(1\) to \(10\) mT in steps of \(1\) mT. The transmission \(| {S}_{21}|\) depending on the normalized bias flux is shown in (b) for \({B}_{| | }=1\) mT (black: \(0\) dB, white: \(-30\) dB). The two different set-points represented as orange dashed and red dotted lines, respectively, correspond to a flux responsivity of \(\sim 17\) MHz\(/{\Phi }_{0}\) and \(\sim {\!}60\) MHz\(/{\Phi }_{0}\). Posterior to tuning the cavity to the desired working point, an OMIT experiment was performed and the single-photon coupling rate of the system was extracted. The experimental procedure was repeated in increasing steps of \(1\) mT of in-plane field. The resulting single-photon coupling rates \({g}_{0}\) are shown in (c) as squares. The dashed and dotted lines show theoretical lines and the gray areas consider uncertainties in the flux responsivity of \(10 \%\) and a possible in-plane field offset of \(\pm {\!}0.5\) mT. Error bars consider \(10 \%\) uncertainty in the extracted values, cf. Supplementary Note 6