Quantum limit cycles and the Rayleigh and van der Pol oscillators

Self-oscillating systems, described in classical dynamics as limit cycles, are emerging canonical models for driven dissipative nonequilibrium open quantum systems and key elements technology. We consider a family of that interpolates between the textbook examples Rayleigh van der Pol oscillators follow their transition from to domain, while properly formulating corresponding descriptions. derive an exact analytical solution steady-state simplest these models, applicable any bosonic system—whether mechanical, optical, or otherwise—that is coupled its environment via single-boson double-boson emission absorption. Our generalization arbitrary temperature existing solutions very-low, zero, temperature, often misattributed oscillator. closely explore bifurcation self-oscillations this oscillator, noting changes identifying features uniquely quantum.14 MoreReceived 6 November 2020Accepted 19 January 2021DOI:https://doi.org/10.1103/PhysRevResearch.3.013130Published by American Physical Society under terms Creative Commons Attribution 4.0 International license. Further distribution work must maintain attribution author(s) published article's title, journal citation, DOI.Published SocietyPhysics Subject Headings (PhySH)Research AreasBifurcationsOpen systemsOptomechanicsQuantum fluctuations & noiseQuantum opticsQuantum-to-classical transitionPhysical SystemsMicromechanical nanomechanical oscillatorsTechniquesPhase space dynamicsQuantum master equationQuantum InformationNonlinear DynamicsAtomic, Molecular OpticalCondensed Matter, Materials Applied Physics