Fig. 4
From: Strong negative nonlinear friction from induced two-phonon processes in vibrational systems
Effect of negative nonlinear friction on the resonant response of the plate mode. a The amplitude of forced vibrations a1 versus the driving force frequency ωd1 for Δ = 0 Hz and the driving force amplitudes Fd1 = 0.21 pN (blue) and Fd1 = 0.48 pN (dark blue). The blue line is a fit to the linear regime. The dark blue line is obtained by multiplying the blue line by the drive amplitudes ratio 2.28. Inset: 3D plot of the measured ratio a1/Fd1. b The characteristic width Γpeak of the spectral peak versus drive amplitude for linear friction (black, no sideband pumping), and for positive/negative nonlinear friction (red/blue, pumping at the red-/blue-detuned secondary sideband with Δ = 0 Hz). The solid lines are the theory (Supplementary Note 4). Error bars represent ±1 s.e. c Bistability of forced vibrations due to negative nonlinear friction, Δ = −35 Hz. The driving force amplitude is 0.70 pN. At the bifurcation points ωL and ωH, the amplitude jumps down from the upper branch. Inset: with Δ = −1000 Hz, nonlinear friction is negligible. Mode 1 displays a standard Duffing hysteresis for Fd1 = 3.5 pN (black); at Fd1 = 0.70 pN no hysteresis occurs (gray). d Measured (dots) and calculated stable (solid lines) and unstable (dashed lines) vibration amplitudes for Fd1 = 0.595 pN (green) and 0.980 pN (yellow). Inset: zoom in on the isolated branch
