Rabi oscillations of dissipative structures effected by out-of-phase parametric drives

Dissipative structures are localized, stable patterns that arise due to the intricate balance among dissipation, dispersion, interaction, and external drive. Their creation and manipulation are of great interest in fields as diverse as optics, magnetism, fluids, and the quantum theory. Here, we report on the emergence of Rabi oscillations of these patterns in a dissipative, nonlinear system subject to two localized, out-of-phase, parametric drives. Their period and amplitude are controlled by the drive size and separation, and can be varied over a wide range. We show that this system undergoes a transition similar to the prototypical parity-time ($\mathcal{PT}$) symmetry breaking transition, but in contrast to the usual $\mathcal{PT}$-symmetric models, these oscillations are robust against the drive mismatch. By using a lossy, nonlinear dimer model with out-of-phase drives, we analytically explain some of these findings. Our results demonstrate a new way to robustly balance gain and loss in a globally dissipative medium, and manipulate the dissipative structures.