Fig. 4: Phase-sensitive and tunable microwave amplification by parametric mechanical driving.
From: Cavity electromechanics with parametric mechanical driving
a Experimental scheme. The cavity is coherently driven on the red sideband ωd = ωc − Ωm. In addition, a small probe tone is swept through the cavity resonance. At the same time, the resonance frequency of the mechanical oscillator is parametrically modulated with 2Ω. b Optomechanically induced transparency (OMIT) without parametric modulation V2Ω = 0. Data are shown in blue, black line is a fit, the dashed box indicates the zoom-in region shown in panel (c). In addition to the data without parametric modulation, we show the highest achieved transmission with parametric driving as orange circles. Close to the mechanical resonance we observe intracavity gain of the probe signal up to ~14 dB and net transmission gain of ~7 dB. The orange line shows a theoretical curve calculated with independently obtained parameters. The schematic in (a) visualizes the amplification mechanism. By the beating of the two cavity tones, energy from the cavity field is converted into mechanical motion, which is amplified by parametric modulation. The hereby increased energy is upconverted back to the probe tone frequency as sideband of the red-detuned drive tone. d The microwave gain is phase-sensitive; it depends on the phase between the parametric modulation and the intracavity amplitude beating. The three data sets (black lines are fits) show the gain for different detunings from ωp − ωd = Ωm (0 Hz, 2π ⋅ 7 Hz and 2π ⋅ 12 Hz). e Probe-tone gain vs. parametric drive voltage for three different red-sideband drive powers. The parametric drive voltage is normalized to its value obtained in Fig. 2 using a resonant drive for amplitude detection. Lines are calculations based on independently extracted parameters. The parametric instability threshold, indicated by dashed vertical lines, is shifted to higher values with increasing red-sideband drive power, partly due to optical damping, partly due to a power-dependent intrinsic mechanical damping rate. The inset shows the extracted threshold voltage vs. effective mechanical linewidth and as dashed line the theoretical prediction. The cooperativity for (b−d) is \({\mathcal{C}}\approx 0.5\) and \({\mathcal{C}}\approx 0.16,0.28,0.5\) for (e).
