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Hidden attractors and metamorphoses of basin boundaries in optomechanics

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Abstract

Optomechanical systems are known to exhibit self-sustained limit cycles once driven above the parametric instability point. By increasing the driving in the unresolved sideband limit, they reach chaotic regime through the cascaded period doubling process. Here, we study classical nonlinear dynamics of optomechanical systems operating in the resolved sideband regime (\(\omega _m/\kappa \gg 1\)) having a high mechanical \(Q-\)factor. We combine numerical simulations and analytical calculations to predict new nonlinear phenomena, so far unexplored in optomechanics. In the regime of single optical mode in the cavity, we connect the dynamical multistability to the hidden attractors, i.e., stable periodic state whose basin of attraction does not overlap with the neighbourhood of an unstable equilibrium point. In the regime where more than one optical modes are involved, we show that complex dynamics like metamorphoses of basin boundaries take place. These metamorphoses, which are revealed through the creation (or disappearance) of some new (or old) basin sets, are induced via the increase of the input driving field. Interestingly, we point out also the frequency locking effect which prevents all routes to chaos in the system. However, the locking range shrinks rapidly as the optical linewidth increases. The concept of hidden attractors introduced here provides new opportunities to generate nonclassical states. Moreover, the frequency locking effect can be useful for stable clock oscillations, for metrological applications and to control oscillations in optomechanics.

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The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

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Author notes

  1. Philippe Djorwe

    Present address: Department of Physics, Faculty of Science, The University of Ngaoundere, P.O. Box 454, Ngaoundere, Cameroon

Authors and Affiliations

  1. Department of Physics, Faculty of Science, The University of Ngaoundere, P.O. Box 454, Ngaoundere, Cameroon

    Joseph Yves Effa

  2. Department of Physics, Faculty of Science, The University of Yaounde I, P.O. Box 812, Yaounde, Cameroon

    S. G. Nana Engo

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  1. Philippe Djorwe
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  2. Joseph Yves Effa
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  3. S. G. Nana Engo
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PD contributed to conceptualization, investigation, and writing. JYE contributed to formal analysis and writing. SGNE contributed to supervision, writing, and validation.

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Correspondence to Philippe Djorwe.

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Djorwe, P., Yves Effa, J. & G. Nana Engo, S. Hidden attractors and metamorphoses of basin boundaries in optomechanics. Nonlinear Dyn 111, 5905–5917 (2023). https://doi.org/10.1007/s11071-022-08139-2

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