Fig. 3: Fano-transparency indicates interference of dispersive and dissipative photon-pressure.

a Schematic of the experimental setting for the observation of photon-pressure induced transparency (PPIT). A strong microwave pump tone (red vertical arrow) with power P_p and frequency \({\omega }_{\mathrm{p}}={\omega }_{0}^{{\prime} }-{\Omega }_{{\mathrm{eff}}}+{\delta }_{{\mathrm{eff}}}\) is sent to the device around the red sideband of the HF cavity. A small VNA probe tone (black vertical arrow) with relative frequency Ω = ω − ω_p scans the HF reflection around \({\omega }_{0}^{{\prime} }\). The beating of the pump and probe tones coherently drives the LF mode with a strength proportional to the dispersive coupling rate \({g}_{\omega }^{{\prime} }\). The resulting LF amplitude in turn induces both a dispersively and a dissipatively generated sideband to the pump tone at ω_p + Ω, which are \(\propto \,{g}_{\omega }^{{\prime} }\) and \(\propto \, {\mathrm{i}}{g}_{\kappa }^{{\prime} }/2\), respectively, and which both interfere with the original probe tone. b HF cavity reflection ∣S₁₁∣ in the presence of a pump tone for three different pump detunings \({\delta }_{{\mathrm{eff}}}={( - {\kappa }_{0}^{{\prime} }/4, 0 ,+ {\kappa }_{0}^{{\prime} }/4)}\) (from top to bottom). Data in left graphs are vs. detuning from HF cavity resonance \(\omega -{\omega }_{0}^{{\prime} }\), and clear PPIT signatures can be identified when \(\omega -{\omega }_{0}^{{\prime} }\approx {\delta }_{{\mathrm{eff}}}\). The smaller graphs on the right show zooms to the transparency resonances (dashed boxes in left graphs) plotted vs. detuning from ω_p + Ω_eff. Symbols are data, lines are fits. The point of PPIT resonance in the zoom for δ_eff ≈ 0 is marked with an orange disk, and the cavity reflection for \({g}_{\omega }^{{\prime} }={g}_{\kappa }^{{\prime} }=0\) is added as dashed purple line in all zooms. c The dataset for δ_eff ≈ 0 in complex representation. Points are data, black line is a theory curve with all parameters from the fit and δ_eff = 0. The cavity resonance traces a large circle anchored at (1, 0), the PPIT signature traces a smaller circle anchored on the resonance point of the bare cavity (purple disk); the resonance point of the PPIT is marked with the orange disk. For \({g}_{\kappa }^{{\prime} }=0\), the PPIT circle would point towards (1, 0) and the dashed line connecting the two resonance points would be the real axis. However, the presence of dissipative coupling leads to a rotation of the PPIT circle around its anchor point by an angle \(\gamma=\arctan (g_\kappa^{\prime} /2{g}_{\omega }^{{\prime} })\). Here, we obtain γ ≈ − 46 ^∘, which corresponds to \({g}_{\kappa }^{{\prime} }/{g}_{\omega }^{{\prime} }\approx -2.1\).