  We establish the emergence of chaotic motion in optomechanical systems. Chaos
appears at negative detuning for experimentally accessible values of the pump
power and other system parameters. We describe the sequence of period doubling
bifurcations that leads to chaos, and state the experimentally observable
signatures in the optical spectrum. In addition to the semi-classical dynamics
we analyze the possibility of chaotic motion in the quantum regime. We find
that quantum mechanics protects the optomechanical system against irregular
dynamics, such that simple periodic orbits reappear and replace the classically
chaotic motion. In this way observation of the dynamical signatures makes it
possible to pin down the crossover from quantum to classical mechanics.
