Nonlinear optomechanical systems with quasi-periodic and chaotic dynamics

Model optomechanical systems with photon-vibration interactions linear, quadratic, and cubic in mechanical displacements are studied under conditions for adiabatic elimination of the photon field. The opportunity of transformation of effective potential describing the dynamics of the mechanical resonator from single-well to double-well is demonstrated. The dynamics of the mechanical resonator is considered in the presence of (i) only linear interaction, (ii) only quadratic interaction, (iii) both linear and quadratic interactions, and (iv) all three interactions, while other parameters of the optomechanical system, the modulation optical field, and the initial conditions remain fixed. Quasiperiodic oscillations of the mechanical resonator in the case (i) are replaced by chaotic ones when the cases (ii) or (iii) are realized. It is interesting that in the presence of all three interactions, the chaotic behavior of the mechanical oscillator becomes quasi-periodic. However, increasing the power of the modulation field again leads to chaos.