Analytical exploration of the optomechanical attractor diagram and of limit cycles

Abstract

We analyse the interplay between mechanical and radiation pressure in an optomechanical cavity system. Our study is based on an analytical evaluation of the infinite Bessel summations involved, which previously had led to a numerical exploration of the so-called attractor diagram. The analytical expressions are then suitable for further asymptotic analysis in opposing regimes of the amplitude, which allows for a characterisation of the diagram in terms of elementary functions. Building on this framework, we investigate the emergence and properties of optomechanical limit cycles beyond the constraints of the resolved sideband approximation. By employing a Fokker-Planck formalism originally developed in the context of laser theory and then used in cavity optomechanics, we describe the quantum regime of these limit cycles, offering a more detailed and unified analytical perspective.

20 pages, 6 figures. v2: More background material given, figures and appendix added. Final, published version

References in corpus (8)

• Quantum Theory of Cavity-Assisted Sideband Cooling of Mechanical Motion
• Theory of ground state cooling of a mechanical oscillator using dynamical back-action
• Resolved Sideband Cooling of a Micromechanical Oscillator
• The optomechanical instability in the quantum regime
• On two-dimensional Bessel functions
• Experimental exploration of the optomechanical attractor diagram and its dynamics
• Discrete time translation symmetry breaking in a Josephson junction laser
• Landau-Zener transition rates of superconducting qubits and absorption spectrum in quantum dots