Fig. 3: Saturation and noise properties of the amplification process (Figures 2a and 3 were measured in different cooldowns with the same sample).

Solid dots represent experimental data with standard deviation; solid red curves show the results of numerical simulations. We set the pump frequency to a fixed value of ω₃₀/6π = 4.530 GHz, and the pump power to P_pump = −96.5 dBm. a Measured reflectance ∣r∣² as a function of probe power P_p (bottom x-axis) at the point where we observed the maximum power amplification (1.405 ± 0.072) at weak probe power. The top x-axis shows the Rabi frequency Ω_p. b At the maximum amplification point, the pump field induces a population inversion between the states \(\left\vert {D}_{3},F\right\rangle \leftrightarrow \left\vert {D}_{4},F+1\right\rangle\) [label (i)] and \(\left\vert {D}_{4},F\right\rangle \leftrightarrow \left\vert {D}_{5},F+1\right\rangle\) [label (ii)]. This population inversion leads to the spontaneous emission of photons, as depicted in the measured spectrum in red on the left y-axis as a function of frequency ω. The spectrum reveals the characteristic emission profile corresponding to these states. The noise temperature, crucial for amplifier operation, is shown in blue on the right y-axis. The arrows indicate the width of the spectrum (Γ/2π ~ 4 MHz).