Steady states and oscillation modes of two driven dissipative oscillators with non-Hermitian coupling

Abstract

We analyze the dynamics of two harmonic oscillators with nonlinear, non-Hermitian coupling between them. Specifically, we consider a synthetic antiferromagnet composed of two ferromagnetic layers with antiferromagnetic interactions between the two layers, leading to the emergence of two oscillation modes of the combined system. We analyze the response of this system to external driving fields. We determine the allowed steady states under various driving conditions. We then analyze the dynamics of small deviations away from the different steady states, which reveals the normal modes that can be probed using spectroscopic techniques in experiment. As expected, the nonlinear system exhibits multistability, in which multiple steady states can exist for the same driving conditions. We find that the dynamical response can be drastically different depending on which one of the two modes is driven and on the strength of the driving. Specifically, we can obtain level-repulsion or level-attraction patterns in the spectrum. In addition to the rich variety of spectra, we find that some steady states exhibit normal modes that contain multiple frequencies. Our results explain recent experiments on synthetic antiferromagnets and provide guidance for designing experiments that can explore previously unseen phenomena in these systems.