We theoretically propose and experimentally demonstrate optically tunable nonlinear mechanical damping in a cavity optomechanical system utilizing a partly resolved sideband regime. Optomechanical coupling provides a delayed nonlinear backaction to the mechanical modes, resulting in nonlinear mechanical damping. This optically induced nonlinear damping is observed in the frequency and time domains, and we show using both theory and experiment that it can be tuned via laser detuning. We also observe optically mediated cross-nonlinear damping between two mechanical modes: the amplitude of one mode modulates the damping of the other. The presented results show a fully tunable scheme of nonlinear mechanical damping that will be applicable to various non-trivial systems, governed by nonlinear, nonequilibrium, and non-Hermitian phenomena.

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