Level attraction is a type of mode hybridization in open systems where instead of forming a hybridization gap, the energy spectrum of two modes coalesce in a region bounded by exceptional points. We demonstrate that this phenomenon can be realized in a Floquet system with memory, which appears in describing linear excitations in a nonlinear driven system with a limit cycle. Linear response of the system in this state is different from its response near thermodynamic equilibrium. We develop a general formalism and provide an example in the context of cavity magnonics, where we show that magnetic excitations in systems driven far from the equilibrium may show level attraction with cavity photons. Our approach works equally well for quantum and semiclassical magnetic dynamics. The theory is formulated so that it can be used in combination with micromagnetic simulations to explore a wide range of experimentally interesting systems.
Excitations that may appear in cavity magnonics experiments are examined with numerical micromagnetics using a recently developed semi-classical cavity magnonics theory. The theory is generally applicable to linear and nonlinear dynamic systems. In this paper, example applications of the theory for magnetic systems are presented where the dynamics is described using numerical micromagnetics for field driven ferromagnets. Examples of large amplitude driving are studied as a function of drive field amplitude and frequency. We comment also on large amplitude dynamics under elliptically polarized driving fields. The main conclusion is that when implemented together with micromagnetics, the theory can be used to describe cavity photon–magnon coupling for a wide variety of linear and nonlinear magnetic dynamics, thereby providing a useful technique for cavity magnonics.
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