Subharmonic Entrainment of Kerr Breather Solitons

We predict subharmonic entrainment of breather-soliton oscillations to a periodic perturbation at the round-trip time ${T}_{R}$ in Kerr-nonlinear optical resonators; an integer ratio ${T}_{b}/{T}_{R}=N\ensuremath{\gg}1$ results for breathing period ${T}_{b}$. Rigid entrainment is observed with intermediate finesse ($\mathcal{F}\ensuremath{\sim}30--40$) for $N$ up to 20, and we propose a way to realize higher entrainment ratios at higher finesse. This nontrivial synchronization across the widely separated timescales of the photon lifetime and round-trip time points to a new direction for research in this field and may find application, for example, in the measurement of a pulse train repetition rate that is electronically inaccessible.