Fig. 2: Reflectance of a weak probe with three-photon pumping.
a Measured reflectance spectra ∣r∣2 of the weak probe field (Pp = −161 dBm) as a function of probe frequency ωp (x-axis) and pump power Ppump (y-axis). The pump frequency is ωpump = ω30/3 = 2π × 4.530 GHz. b Numerical simulation of the experiment. The left y-axis is the pump power; the right y-axis is the Rabi frequency Ωpump. We set M = 6 and use the relaxation rates Γn,n−1/2π = nΓ10/2π = 2.264n MHz, where n = 1, 2, …, 5. There are no free fitting parameters for the simulation. c A linecut taken at Ppump = −95 dBm from Supplementary Information Fig. 4, where the two amplified Rabi sidebands cross each other at ωp/2π ≈ 4.739 GHz (indicated by a red arrow in Fig. 2a, b), shows a maximum reflectance 1.402 ± 0.025. The black arrows indicate the width of the reflectance spectrum (Γ/2π ~ 4 MHz). The solid red dots are the experimental data with standard deviation, the solid black curve is the linecut of the numerical simulation from b, and the solid blue curve is the theoretical result without quantum coherence between the amplified Rabi sidebands26. The excess gain (black) is about twice that of the case without quantum interference (blue). The roughly 2% difference between data and theory from 4.72 to 4.73 GHz is most likely due to the gain drift of the HEMT amplifier (see Supplementary Information Fig. 1) measured with the background (reference) reflectance.
