Bifurcations of nonlinear dynamics in coupled twin spin masers

Abstract

Spin masers are a prototype nonlinear dynamic system. They undergo a bifurcation at a critical amplification factor, transiting into a limit cycle phase characterized by a Larmor precession around the external bias magnetic field, thereby serving as a key frequency reference for precision measurements. Recently, a system of coupled twin spin masers placed in dual bias magnetic fields, involving simultaneously two intrinsic Larmor frequencies, has been studied. Compared with previous spin masers, this setup exhibits new attractors such as quasi-periodic orbits and chaos in addition to the usual limit cycles and the trivial no signal fixed point. The richer dynamic phases imply the existence of bifurcations, whose nature has not been fully analyzed. Here, to shed light on the nature of the bifurcations, we turn to a closely related system and systematically study the various bifurcations therein along different routes in parameter space. We identify the bifurcations as of the types including pitchfork, Hopf, homoclinic bifurcations, and saddle-node bifurcations of cycles. By both analytical and numerical methods, we reveal how various attractors interplay with each other and change their stability. We also quantitatively evaluate the locations where these bifurcations occur by tracking the both stable and even not easily detected unstable limit cycles. These findings deepen our understanding of the underlying mechanisms resulting in the rich dynamic phases in the coupled twin spin masers.