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Devil's staircase in an optomechanical cavity.

We study self-excited oscillations (SEOs) in an on-fiber optomechanical cavity. While the phase of SEOs randomly diffuses in time when the laser power injected into the cavity is kept constant, phase locking may occur when the laser power is periodically modulated in time. We investigate the dependence of phase locking on the amplitude and frequency of the laser-power modulation. We find that phase locking can be induced with a relatively low modulation amplitude provided that the ratio between the modulation frequency and the frequency of SEOs is tuned close to a rational number of relatively low hierarchy in the Farey tree. To account for the experimental results, a one-dimensional map, which allows evaluating the time evolution of the phase of SEOs, is theoretically derived. By calculating the winding number of the one-dimensional map, the regions of phase locking can be mapped in the plane of modulation amplitude and modulation frequency. Comparison between the theoretical predictions and the experimental findings yields a partial agreement.