Staircase mechanical energy growth in optomechanical systems of median mechanical frequencies

Owing to the radiation-force-induced nonlinearity, cavity optomechanical systems (COMS) exhibit dynamical phenomena such as back-action induced oscillation, chaos, mechanical amplitude locking, and anomalous stabilization, which occur under different driving conditions and different system parameters. We here identify a previously unknown dynamical pattern of staircase evolution for the energy of mechanical resonator, when a COMS with neither very large nor very small built-in mechanical frequency is driven by a two-tone field, which satisfies a condition that the frequency difference of the two tones matches the built-in mechanical frequency. The properties of this phenomenon are analyzed for the different system parameters due to fabrication such as mechanical frequencies and quality factors, as well as under the varied driving conditions such as unequal drive tone powers and mismatched drive tone difference from the mechanical frequency. Some special features, such as an emergent bifurcation due to the tone power difference, together with the totally different responses of the system to the drive tone mismatches of opposite signs, are discovered to exist only in this type of COMS with median mechanical frequencies. This work fills a gap in the study of the dynamics of COMS under two-tone drives. In the aspect of applications, the rapid increase of mechanical energy exhibited in the phenomenon promises phonon laser generation, and the sensitive dynamical response to the drive tone mismatches offers a potential approach to high-precision sensing.