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Route to chaos in a coupled microresonator system with gain and loss

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Abstract

We consider chaotic dynamics of a system of two coupled ring resonators with a linear gain and a nonlinear absorption. Such a structure can be implemented in various settings including microresonator nanostructures, polariton condensates, optical waveguides or atomic Bose–Einstein condensates of ultra-cold atoms placed in a circular-shaped trap. From the theoretical point of view, this system is attractive due to its modulational instability and rich structure, including various types of spontaneous symmetry breaking, period-doubling bifurcations, eventually leading to chaotic regime. It is described by set of partial differential equations but we show that the so-called Galerkin approximation can explain most of the system characteristics mapping it on the dynamics of few coupled oscillator modes. The main goal of the present study is to investigate various routes to chaos in our non-Hermitian system and to show the correspondence between the continuous operator problem and its discrete representation.

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Acknowledgements

We are grateful to Bruno Eckhardt for interesting discussions. N.V.H. appreciates the hospitality of M.T. during his visit to Warsaw for scientific cooperation. K.B.Z. acknowledges support from the National Science Centre (Poland) through Project FUGA No. 2016/20/S/ST2/00366. J.Z. acknowledges support by PL-Grid Infrastructure and EU Project, the EU H2020-FETPROACT-2014 Project QUIC No. 641122. This research has been also supported by National Science Centre (Poland) under Projects 2016/22/M/ST2/00261 (M.T.) and 2016/21/B/ST2/01086 (J.Z.). N.V.H. was supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 103.01-2017.55.

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Authors and Affiliations

  1. Instytut Fizyki im. Mariana Smoluchowskiego, Uniwersytet Jagielloński, Lojasiewicza 11, 30-348, Kraków, Poland

    Krzysztof Zegadlo & Jakub Zakrzewski

  2. Advanced Institute for Science and Technology, Hanoi University of Science and Technology, Hanoi, Vietnam

    Hung Viet Nguyen

  3. Faculty of Physics, University of Warsaw, ul. Pasteura 5, 02-093, Warsaw, Poland

    Marek Trippenbach

  4. Centro de Física Teórica e Computacional and Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, Edifício C8, 1749-016, Lisboa, Portugal

    Vladimir V. Konotop

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  1. Krzysztof Zegadlo
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  3. Vladimir V. Konotop
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  4. Jakub Zakrzewski
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Correspondence to Hung Viet Nguyen.

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Zegadlo, K., Nguyen, H.V., Konotop, V.V. et al. Route to chaos in a coupled microresonator system with gain and loss. Nonlinear Dyn 97, 559–569 (2019). https://doi.org/10.1007/s11071-019-04997-5

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  • DOI: https://doi.org/10.1007/s11071-019-04997-5

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