Abstract

The bifurcations or transitions of the classical nonlinear systems with finite degrees of freedom exhibit some dynamical behaviors that are similar to those in the phase transitions of many-body systems. A dynamical type of them in the form of a sudden transition of the amplitudes between two harmonic oscillations, which are stable under periodically driving force, is not so common to see. We show that a sudden transition of this type can be realized in a system of coupling a microresonator that supports a mechanical vibration to another microresonator, and the system was experimentally demonstrated as a phonon laser. If the pump laser power or the intercavity coupling strength is adjusted to a critical value, the cavity field patterns will suddenly change, together with a jump of the stabilized mechanical amplitude. Such transition can be applied to a precise measurement of the optomechanical coupling constant, which is hard to measure due to its proportion to a tiny zero-point mechanical fluctuation amplitude.