We study the steady state motion of a single trapped ion oscillator driven to
the nonlinear regime. Damping is achieved via Doppler laser-cooling. The ion
motion is found to be well described by the Duffing oscillator model with an
additional nonlinear damping term. We demonstrate a unique ability of tuning
both the linear as well as the nonlinear damping coefficients by controlling
the cooling laser parameters. Our observations open a way for the investigation
of nonlinear dynamics on the quantum-to-classical interface as well as
mechanical noise squeezing in laser-cooling dynamics.Comment: 4 pages, 5 figures