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Pelka K, Madiot G, Braive R, Xuereb A. Floquet Control of Optomechanical Bistability in Multimode Systems. PHYSICAL REVIEW LETTERS 2022; 129:123603. [PMID: 36179176 DOI: 10.1103/physrevlett.129.123603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/01/2021] [Revised: 04/25/2022] [Accepted: 07/19/2022] [Indexed: 06/16/2023]
Abstract
Cavity optomechanical systems make possible the fine manipulation of mechanical degrees of freedom with light, adding functionality and having broad appeal in photonic technologies. We show that distinct mechanical modes can be exploited with a temporally modulated Floquet drive to steer between distinct steady states induced by changes of cavity radiation pressure. We investigate the additional influence of the thermo-optic nonlinearity on these dynamics and find that it can suppress or amplify the control mechanism in contrast to its often performance-limiting character. Our results provide new techniques for the characterization of thermal properties of optomechanical systems and their control, sensing and computational applications.
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Affiliation(s)
- Karl Pelka
- Department of Physics, University of Malta, Msida MSD 2080, Malta
| | - Guilhem Madiot
- Centre de Nanosciences et de Nanotechnologies, CNRS, Université Paris-Saclay, F-91120 Palaiseau, France
| | - Rémy Braive
- Centre de Nanosciences et de Nanotechnologies, CNRS, Université Paris-Saclay, F-91120 Palaiseau, France
- Université de Paris, F-75006 Paris, France
- Institut Universitaire de France, F-75231 Paris, France
| | - André Xuereb
- Department of Physics, University of Malta, Msida MSD 2080, Malta
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2
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Two-Membrane Cavity Optomechanics: Linear and Non-Linear Dynamics. PHOTONICS 2022. [DOI: 10.3390/photonics9020099] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Abstract
In this paper, we review the linear and non-linear dynamics of an optomechanical system made of a two-membrane etalon in a high-finesse Fabry–Pérot cavity. This two-membrane setup has the capacity to modify on demand the single-photon optomechanical coupling, and in the linearized interaction regime to cool simultaneously two mechanical oscillators. It is a promising platform for realizing cavity optomechanics with multiple resonators. In the non-linear regime, an analytical approach based on slowly varying amplitude equations allows us to derive a consistent and full characterization of the non-linear displacement detection, enabling a truthful detection of membrane displacements much above the usual linear sensing limited by the cavity linewidth. Such a high quality system also shows a pre-synchronization regime.
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3
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Zhang DW, Bin SW, You C, Hu CS. Enhancing the nonlinearity of optomechanical system via multiple mechanical modes. OPTICS EXPRESS 2022; 30:1314-1326. [PMID: 35209294 DOI: 10.1364/oe.446428] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/26/2021] [Accepted: 12/23/2021] [Indexed: 06/14/2023]
Abstract
We theoretically investigate the nonlinear dynamics of an optomechanical system, where the system consists of N identical mechanical oscillators individually coupled to a common cavity field. We find that the optomechanical nonlinearity can be enhanced N times through theoretical analysis and numerical simulation in such a system. This leads to the power thresholds to observe the nonlinear behaviors (bistable, period-doubling, and chaotic dynamics) being reduced to 1/N. In addition, we find that changing the sign (positive or negative) of the coupling strength partly does not affect the threshold of driving power for generating corresponding nonlinear phenomena. Our work may provide a way to engineer optomechanical devices with a lower threshold, which has potential applications in implementing secret information processing and optical sensing.
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4
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Mercadé L, Pelka K, Burgwal R, Xuereb A, Martínez A, Verhagen E. Floquet Phonon Lasing in Multimode Optomechanical Systems. PHYSICAL REVIEW LETTERS 2021; 127:073601. [PMID: 34459652 DOI: 10.1103/physrevlett.127.073601] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/26/2021] [Accepted: 06/15/2021] [Indexed: 06/13/2023]
Abstract
Dynamical radiation pressure effects in cavity optomechanical systems give rise to self-sustained oscillations or 'phonon lasing' behavior, producing stable oscillators up to GHz frequencies in nanoscale devices. Like in photonic lasers, phonon lasing normally occurs in a single mechanical mode. We show here that mode-locked, multimode phonon lasing can be established in a multimode optomechanical system through Floquet dynamics induced by a temporally modulated laser drive. We demonstrate this concept in a suitably engineered silicon photonic nanocavity coupled to multiple GHz-frequency mechanical modes. We find that the long-term frequency stability is significantly improved in the multimode lasing state as a result of the mode locking. These results provide a path toward highly stable ultracompact oscillators, pulsed phonon lasing, coherent waveform synthesis, and emergent many-mode phenomena in oscillator arrays.
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Affiliation(s)
- Laura Mercadé
- Nanophotonics Technology Center, Universitat Politècnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain
| | - Karl Pelka
- Department of Physics, University of Malta, Msida MSD 2080, Malta
| | - Roel Burgwal
- Department of Applied Physics and Institute of Photonic Integration, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, Netherlands
- Center for Nanophotonics, AMOLF, Science Park 104, 1098 XG Amsterdam, Netherlands
| | - André Xuereb
- Department of Physics, University of Malta, Msida MSD 2080, Malta
| | - Alejandro Martínez
- Nanophotonics Technology Center, Universitat Politècnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain
| | - Ewold Verhagen
- Department of Applied Physics and Institute of Photonic Integration, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, Netherlands
- Center for Nanophotonics, AMOLF, Science Park 104, 1098 XG Amsterdam, Netherlands
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5
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Chen B, Guo Y, Shen H. Spontaneous phase locking of mechanical multimodes in anti-parity-time optomechanics. OPTICS EXPRESS 2020; 28:28762-28772. [PMID: 33114787 DOI: 10.1364/oe.400932] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/24/2020] [Accepted: 09/02/2020] [Indexed: 06/11/2023]
Abstract
We propose a system for observing the spontaneous phase locking of two frequency separate mechanical modes in an anti-parity-time symmetric optomechanical system. In our approach, a common optical cavity mode mediates the coupling between two phonon modes, leading to the phase locking of the coupled mechanical modes to a common frequency in the symmetry unbroken regime. We furthermore observe the change of quantum correlation near the exceptional point. Our results are also directly relevant to numerous other physical platforms, such as atomic ensembles in cavity quantum electrodynamics (QED) systems and spin interaction mediated by collective motional mode in trapped ions.
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6
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Sheng J, Wei X, Yang C, Wu H. Self-Organized Synchronization of Phonon Lasers. PHYSICAL REVIEW LETTERS 2020; 124:053604. [PMID: 32083916 DOI: 10.1103/physrevlett.124.053604] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/19/2019] [Accepted: 01/15/2020] [Indexed: 06/10/2023]
Abstract
Self-organized synchronization is a ubiquitous collective phenomenon, in which each unit adjusts their rhythms to achieve synchrony through mutual interactions. The optomechanical systems, due to their inherently engineerable nonlinearities, provide an ideal platform to study self-organized synchronization. Here, we demonstrate the self-organized synchronization of phonon lasers in a two-membrane-in-the-middle optomechanical system. The probe of each individual membrane enables us to monitor the real-time transient dynamics of synchronization, which reveals that the system enters into the synchronization regime via a torus birth bifurcation line. The phase-locking phenomenon and the transition between in-phase and antiphase regimes are directly observed. Moreover, such a system greatly facilitates the controllable synchronous states, and consequently a phononic memory is realized by tuning the system parameters. This result is an important step towards the future studies of many-body collective behaviors in multiresonator optomechanics with long distances, and might find potential applications in quantum information processing and complex networks.
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Affiliation(s)
- Jiteng Sheng
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
| | - Xinrui Wei
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China
| | - Cheng Yang
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China
| | - Haibin Wu
- State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
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7
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Cao W, Lu X, Meng X, Sun J, Shen H, Xiao Y. Reservoir-Mediated Quantum Correlations in Non-Hermitian Optical System. PHYSICAL REVIEW LETTERS 2020; 124:030401. [PMID: 32031853 DOI: 10.1103/physrevlett.124.030401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/13/2019] [Indexed: 06/10/2023]
Abstract
Recent advances in non-Hermitian physical systems have led to numerous novel optical phenomena and applications. Such systems typically involve gain and loss associated with dissipative coupling to the environment, hence interesting quantum phenomena are often washed out, rendering most realizations classical. Here, in contrast, we propose to employ dissipative coupling to enable quantum correlations. In particular, two distant optical channels are judiciously designed to couple to and exchange information with a common reservoir environment, under an anti-parity-time-symmetric setting of hot but coherent atoms. We realize a non-Hermitian nonlinear phase sensitive parametric process, where atomic motion leads to quantum correlations between two distant light beams in the symmetry-unbroken phase. This Letter starts a new route to exploring the non-Hermitian quantum phenomena by bridging the fields of atomic physics, non-Hermitian optics, quantum information, and reservoir engineering. Potential applications include novel quantum light sources, quantum information processing and sensing, and generalization to correlated many-body systems.
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Affiliation(s)
- Wanxia Cao
- Department of Physics, State Key Laboratory of Surface Physics and Key Laboratory of Micro and Nano Photonic Structures (Ministry of Education), Fudan University, Shanghai 200433, China
| | - Xingda Lu
- Department of Physics, State Key Laboratory of Surface Physics and Key Laboratory of Micro and Nano Photonic Structures (Ministry of Education), Fudan University, Shanghai 200433, China
| | - Xin Meng
- Department of Physics, State Key Laboratory of Surface Physics and Key Laboratory of Micro and Nano Photonic Structures (Ministry of Education), Fudan University, Shanghai 200433, China
| | - Jian Sun
- Department of Physics, State Key Laboratory of Surface Physics and Key Laboratory of Micro and Nano Photonic Structures (Ministry of Education), Fudan University, Shanghai 200433, China
| | - Heng Shen
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - Yanhong Xiao
- Department of Physics, State Key Laboratory of Surface Physics and Key Laboratory of Micro and Nano Photonic Structures (Ministry of Education), Fudan University, Shanghai 200433, China
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan, Shanxi 030006, China
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8
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Luiz GO, Benevides RS, Santos FGS, Espinel YAV, Mayer Alegre TP, Wiederhecker GS. Efficient anchor loss suppression in coupled near-field optomechanical resonators. OPTICS EXPRESS 2017; 25:31347-31361. [PMID: 29245810 DOI: 10.1364/oe.25.031347] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/28/2017] [Accepted: 11/23/2017] [Indexed: 06/07/2023]
Abstract
Elastic dissipation through radiation towards the substrate is a major loss channel in micro- and nanomechanical resonators. Engineering the coupling of these resonators with optical cavities further complicates and constrains the design of low-loss optomechanical devices. In this work we rely on the coherent cancellation of mechanical radiation to demonstrate material and surface absorption limited silicon near-field optomechanical resonators oscillating at tens of MHz. The effectiveness of our dissipation suppression scheme is investigated at room and cryogenic temperatures. While at room temperature we can reach a maximum quality factor of 7.61k (fQ-product of the order of 1011 Hz), at 22 K the quality factor increases to 37k, resulting in a fQ-product of 2 × 1012 Hz.
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9
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Ishibashi K, Kanamoto R. Oscillation collapse in coupled quantum van der Pol oscillators. Phys Rev E 2017; 96:052210. [PMID: 29347706 DOI: 10.1103/physreve.96.052210] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2017] [Indexed: 06/07/2023]
Abstract
The classical self-oscillations can collapse merely due to their mutual couplings. We investigate this oscillation collapse in quantum van der Pol oscillators. For a pair of quantum oscillators, the steady-state mean phonon number is shown to be lower than in the corresponding classical model with a Gaussian white noise that mimics quantum noise. We further show within the mean-field theory that a number of globally coupled oscillators undergo a transition from the synchronized periodic motion to the collective oscillation collapse. A quantum many-body simulation suggests that the increase in the number of oscillators leads to a lower steady-state mean phonon number, bounded below by the mean-field result.
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Affiliation(s)
- Kenta Ishibashi
- Department of Physics, Meiji University, Kawasaki, Kanagawa 214-8571, Japan
| | - Rina Kanamoto
- Department of Physics, Meiji University, Kawasaki, Kanagawa 214-8571, Japan
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10
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Wan LL, Lü XY, Gao JH, Wu Y. Controllable photon and phonon localization in optomechanical Lieb lattices. OPTICS EXPRESS 2017; 25:17364-17374. [PMID: 28789228 DOI: 10.1364/oe.25.017364] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/25/2017] [Accepted: 07/04/2017] [Indexed: 06/07/2023]
Abstract
The Lieb lattice featuring flat band is not only important in strongly-correlated many-body physics, but also can be utilized to inspire new quantum devices. Here we propose an optomechanical Lieb lattice, where the flat-band physics of photon-phonon polaritons is demonstrated. The tunability of the band structure of the optomechanical arrays allows one to obtain an approximate photon or phonon flat band as well as the transition between them. This ultimately leads to the result that the controllable photon or phonon localization could be realized by the path interference effects. This study offers an alternative approach to explore the exotic photon and phonon many-body effects, which has potential applications in the future hybrid-photon-phonon quantum network and engineering new type solid-state quantum devices.
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11
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Seitner MJ, Abdi M, Ridolfo A, Hartmann MJ, Weig EM. Parametric Oscillation, Frequency Mixing, and Injection Locking of Strongly Coupled Nanomechanical Resonator Modes. PHYSICAL REVIEW LETTERS 2017; 118:254301. [PMID: 28696761 DOI: 10.1103/physrevlett.118.254301] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/06/2016] [Indexed: 06/07/2023]
Abstract
We study locking phenomena of two strongly coupled, high quality factor nanomechanical resonator modes to a common parametric drive at a single drive frequency in different parametric driving regimes. By controlled dielectric gradient forces we tune the resonance frequencies of the flexural in-plane and out-of-plane oscillation of the high stress silicon nitride string through their mutual avoided crossing. For the case of the strong common parametric drive signal-idler generation via nondegenerate parametric two-mode oscillation is observed. Broadband frequency tuning of the very narrow linewidth signal and idler resonances is demonstrated. When the resonance frequencies of the signal and idler get closer to each other, partial injection locking, injection pulling, and complete injection locking to half of the drive frequency occurs depending on the pump strength. Furthermore, satellite resonances, symmetrically offset from the signal and idler by their beat note, are observed, which can be attributed to degenerate four-wave mixing in the highly nonlinear mechanical oscillations.
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Affiliation(s)
| | - Mehdi Abdi
- Department of Physics, Technische Universität München, 85748 Garching, Germany
- Institute for Theoretical Physics, Ulm University, 89081 Ulm, Germany
| | - Alessandro Ridolfo
- Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra (MIFT), Universita di Messina, 98166 Messina, Italy
| | - Michael J Hartmann
- Institute of Photonics and Quantum Sciences, Heriot-Watt University, EH14 4AS Edinburgh, United Kingdom
| | - Eva M Weig
- Department of Physics, University of Konstanz, 78457 Konstanz, Germany
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12
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Witthaut D, Wimberger S, Burioni R, Timme M. Classical synchronization indicates persistent entanglement in isolated quantum systems. Nat Commun 2017; 8:14829. [PMID: 28401881 PMCID: PMC5394286 DOI: 10.1038/ncomms14829] [Citation(s) in RCA: 52] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2016] [Accepted: 12/16/2017] [Indexed: 11/29/2022] Open
Abstract
Synchronization and entanglement constitute fundamental collective phenomena in multi-unit classical and quantum systems, respectively, both equally implying coordinated system states. Here, we present a direct link for a class of isolated quantum many-body systems, demonstrating that synchronization emerges as an intrinsic system feature. Intriguingly, quantum coherence and entanglement arise persistently through the same transition as synchronization. This direct link between classical and quantum cooperative phenomena may further our understanding of strongly correlated quantum systems and can be readily observed in state-of-the-art experiments, for example, with ultracold atoms. Collective phenomena in many-body systems include synchronization in classical and entanglement in quantum systems. Here the authors study isolated many-body quantum systems and demonstrate that synchronization emerges intrinsically, accompanied by the onset of quantum coherence and persistent entanglement.
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Affiliation(s)
- Dirk Witthaut
- Forschungszentrum Jülich, Institute for Energy and Climate Research (IEK-STE), 52428 Jülich, Germany.,Institute for Theoretical Physics, University of Cologne, Zuelpicher Str. 77, 50937 Köln, Germany.,Network Dynamics, Max Planck Institute for Dynamics and Self-Organization (MPIDS), Am Faßberg, 37077 Göttingen, Germany
| | - Sandro Wimberger
- Dipartimento di Scienze Matematiche, Fisiche ed Informatiche, Universitá di Parma, Via G.P. Usberti 7/a, 43124 Parma, Italy.,INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, Parco Area delle Scienze, 7/A, 43124 Parma, Italy
| | - Raffaella Burioni
- Dipartimento di Scienze Matematiche, Fisiche ed Informatiche, Universitá di Parma, Via G.P. Usberti 7/a, 43124 Parma, Italy.,INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, Parco Area delle Scienze, 7/A, 43124 Parma, Italy
| | - Marc Timme
- Network Dynamics, Max Planck Institute for Dynamics and Self-Organization (MPIDS), Am Faßberg, 37077 Göttingen, Germany.,Department of Physics, University of Darmstadt, 64289 Darmstadt, Germany.,Institute for Theoretical Physics, Technical University of Dresden, 01062 Dresden, Germany
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13
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Gil-Santos E, Labousse M, Baker C, Goetschy A, Hease W, Gomez C, Lemaître A, Leo G, Ciuti C, Favero I. Light-Mediated Cascaded Locking of Multiple Nano-Optomechanical Oscillators. PHYSICAL REVIEW LETTERS 2017; 118:063605. [PMID: 28234503 DOI: 10.1103/physrevlett.118.063605] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/28/2016] [Indexed: 06/06/2023]
Abstract
Collective phenomena emerging from nonlinear interactions between multiple oscillators, such as synchronization and frequency locking, find applications in a wide variety of fields. Optomechanical resonators, which are intrinsically nonlinear, combine the scientific assets of mechanical devices with the possibility of long distance controlled interactions enabled by traveling light. Here we demonstrate light-mediated frequency locking of three distant nano-optomechanical oscillators positioned in a cascaded configuration. The oscillators, integrated on a chip along a common coupling waveguide, are optically driven with a single laser and oscillate at gigahertz frequency. Despite an initial mechanical frequency disorder of hundreds of kilohertz, the guided light locks them all with a clear transition in the optical output. The experimental results are described by Langevin equations, paving the way to scalable cascaded optomechanical configurations.
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Affiliation(s)
- E Gil-Santos
- Matériaux et Phénomènes Quantiques, Université Paris Diderot, CNRS UMR 7162 Sorbonne Paris Cité, 75013 Paris, France
| | - M Labousse
- Matériaux et Phénomènes Quantiques, Université Paris Diderot, CNRS UMR 7162 Sorbonne Paris Cité, 75013 Paris, France
| | - C Baker
- Matériaux et Phénomènes Quantiques, Université Paris Diderot, CNRS UMR 7162 Sorbonne Paris Cité, 75013 Paris, France
| | - A Goetschy
- Matériaux et Phénomènes Quantiques, Université Paris Diderot, CNRS UMR 7162 Sorbonne Paris Cité, 75013 Paris, France
- Institut Langevin, ESPCI Paris, CNRS UMR 7587, PSL Research University, 75005 Paris, France
| | - W Hease
- Matériaux et Phénomènes Quantiques, Université Paris Diderot, CNRS UMR 7162 Sorbonne Paris Cité, 75013 Paris, France
- Institut Langevin, ESPCI Paris, CNRS UMR 7587, PSL Research University, 75005 Paris, France
| | - C Gomez
- Centre de Nanosciences et de Nanotechnologies, CNRS, Université Paris Sud, Université Paris-Saclay, C2N-Marcoussis, 91460 Marcoussis, France
| | - A Lemaître
- Centre de Nanosciences et de Nanotechnologies, CNRS, Université Paris Sud, Université Paris-Saclay, C2N-Marcoussis, 91460 Marcoussis, France
| | - G Leo
- Matériaux et Phénomènes Quantiques, Université Paris Diderot, CNRS UMR 7162 Sorbonne Paris Cité, 75013 Paris, France
| | - C Ciuti
- Matériaux et Phénomènes Quantiques, Université Paris Diderot, CNRS UMR 7162 Sorbonne Paris Cité, 75013 Paris, France
| | - I Favero
- Matériaux et Phénomènes Quantiques, Université Paris Diderot, CNRS UMR 7162 Sorbonne Paris Cité, 75013 Paris, France
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14
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Li T, Bao TY, Zhang YL, Zou CL, Zou XB, Guo GC. Long-distance synchronization of unidirectionally cascaded optomechanical systems. OPTICS EXPRESS 2016; 24:12336-12348. [PMID: 27410149 DOI: 10.1364/oe.24.012336] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Synchronization is of great scientific interest due to the abundant applications in a wide range of systems. We propose an all-optical scheme to achieve the controllable long-distance synchronization of two dissimilar optomechanical systems, which are unidirectionally coupled through a fiber with light. Synchronization, unsynchronization, and the dependence of the synchronization on driving laser strength and intrinsic frequency mismatch are studied based on the numerical simulation. Taking the fiber attenuation into account, we show that two optomechanical resonators can be unidirectionally synchronized over a distance of tens of kilometers. We also analyze the unidirectional synchronization of three optomechanical systems, demonstrating the scalability of our scheme.
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15
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Zhang M, Shah S, Cardenas J, Lipson M. Synchronization and Phase Noise Reduction in Micromechanical Oscillator Arrays Coupled through Light. PHYSICAL REVIEW LETTERS 2015; 115:163902. [PMID: 26550878 DOI: 10.1103/physrevlett.115.163902] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/19/2015] [Indexed: 06/05/2023]
Abstract
Synchronization of many coupled oscillators is widely found in nature and has the potential to revolutionize timing technologies. Here, we demonstrate synchronization in arrays of silicon nitride micromechanical oscillators coupled in an all-to-all configuration purely through an optical radiation field. We show that the phase noise of the synchronized oscillators can be improved by almost 10 dB below the phase noise limit for each individual oscillator. These results open a practical route towards synchronized oscillator networks.
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Affiliation(s)
- Mian Zhang
- School of Electrical and Computer Engineering, Cornell University, Ithaca, New York 14853, USA
| | - Shreyas Shah
- School of Electrical and Computer Engineering, Cornell University, Ithaca, New York 14853, USA
| | - Jaime Cardenas
- School of Electrical and Computer Engineering, Cornell University, Ithaca, New York 14853, USA
| | - Michal Lipson
- School of Electrical and Computer Engineering, Cornell University, Ithaca, New York 14853, USA
- Kavli Institute at Cornell for Nanoscale Science, Ithaca, New York 14853, USA
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16
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Lauter R, Brendel C, Habraken SJM, Marquardt F. Pattern phase diagram for two-dimensional arrays of coupled limit-cycle oscillators. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:012902. [PMID: 26274242 DOI: 10.1103/physreve.92.012902] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/12/2015] [Indexed: 06/04/2023]
Abstract
Arrays of coupled limit-cycle oscillators represent a paradigmatic example for studying synchronization and pattern formation. We find that the full dynamical equations for the phase dynamics of a limit-cycle oscillator array go beyond previously studied Kuramoto-type equations. We analyze the evolution of the phase field in a two-dimensional array and obtain a "phase diagram" for the resulting stationary and nonstationary patterns. Our results are of direct relevance in the context of currently emerging experiments on nano- and optomechanical oscillator arrays, as well as for any array of coupled limit-cycle oscillators that have undergone a Hopf bifurcation. The possible observation in optomechanical arrays is discussed briefly.
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Affiliation(s)
- Roland Lauter
- Institut für Theoretische Physik II, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstr. 7, 91058 Erlangen, Germany
- Max Planck Institute for the Science of Light, Günther-Scharowsky-Straße 1/Bau 24, 91058 Erlangen, Germany
| | - Christian Brendel
- Institut für Theoretische Physik II, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstr. 7, 91058 Erlangen, Germany
| | - Steven J M Habraken
- Institut für Theoretische Physik II, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstr. 7, 91058 Erlangen, Germany
| | - Florian Marquardt
- Institut für Theoretische Physik II, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstr. 7, 91058 Erlangen, Germany
- Max Planck Institute for the Science of Light, Günther-Scharowsky-Straße 1/Bau 24, 91058 Erlangen, Germany
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17
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Cudmore P, Holmes CA. Phase and amplitude dynamics of nonlinearly coupled oscillators. CHAOS (WOODBURY, N.Y.) 2015; 25:023110. [PMID: 25725646 DOI: 10.1063/1.4908604] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
This paper addresses the amplitude and phase dynamics of a large system of nonlinearly coupled, non-identical damped harmonic oscillators, which is based on recent research in coupled oscillation in optomechanics. Our goal is to investigate the existence and stability of collective behaviour which occurs due to a play-off between the distribution of individual oscillator frequency and the type of nonlinear coupling. We show that this system exhibits synchronisation, where all oscillators are rotating at the same rate, and that in the synchronised state the system has a regular structure related to the distribution of the frequencies of the individual oscillators. Using a geometric description, we show how changes in the non-linear coupling function can cause pitchfork and saddle-node bifurcations which create or destroy stable and unstable synchronised solutions. We apply these results to show how in-phase and anti-phase solutions are created in a system with a bi-modal distribution of frequencies.
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Affiliation(s)
- P Cudmore
- School of Mathematical and Physical Sciences, The University of Queensland, St Lucia QLD 4072, Australia
| | - C A Holmes
- School of Mathematical and Physical Sciences, The University of Queensland, St Lucia QLD 4072, Australia
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18
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Xu M, Tieri DA, Fine EC, Thompson JK, Holland MJ. Synchronization of two ensembles of atoms. PHYSICAL REVIEW LETTERS 2014; 113:154101. [PMID: 25375711 DOI: 10.1103/physrevlett.113.154101] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/22/2013] [Indexed: 06/04/2023]
Abstract
We propose a system for observing the correlated phase dynamics of two mesoscopic ensembles of atoms through their collective coupling to an optical cavity. We find a dynamical quantum phase transition induced by pump noise and cavity output coupling. The spectral properties of the superradiant light emitted from the cavity show that at a critical pump rate the system undergoes a transition from the behavior of two independent oscillators to the phase locking that is the signature of quantum synchronization.
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Affiliation(s)
- Minghui Xu
- JILA, National Institute of Standards and Technology and Department of Physics, University of Colorado, Boulder, Colorado 80309-0440, USA
| | - D A Tieri
- JILA, National Institute of Standards and Technology and Department of Physics, University of Colorado, Boulder, Colorado 80309-0440, USA
| | - E C Fine
- JILA, National Institute of Standards and Technology and Department of Physics, University of Colorado, Boulder, Colorado 80309-0440, USA
| | - James K Thompson
- JILA, National Institute of Standards and Technology and Department of Physics, University of Colorado, Boulder, Colorado 80309-0440, USA
| | - M J Holland
- JILA, National Institute of Standards and Technology and Department of Physics, University of Colorado, Boulder, Colorado 80309-0440, USA
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19
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León Aveleyra G, Holmes CA, Milburn GJ. Synchronization in a mechanical resonator array coupled quadratically to a common electromagnetic field mode. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:062912. [PMID: 25019856 DOI: 10.1103/physreve.89.062912] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/10/2013] [Indexed: 06/03/2023]
Abstract
Optomechanical systems are based on the nonlinear coupling between the electromagnetic (EM) field in a resonator and one or more bulk mechanical resonators such that the frequency of the EM field resonator depends on the displacement coordinates of each of the mechanical resonators. In this paper we consider the case of multiple mechanical resonators interacting with a common field for which the frequency of the EM resonance is tuned to depend quadratically (to lowest order) on the displacement of the resonators. By using the method of amplitude equations around a critical point, it is shown that groups of near-identical bulk mechanical resonators with low driving fail to synchronize unless their natural frequencies are identical, in which case the resulting system can exhibit multistability.
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Affiliation(s)
- G León Aveleyra
- School of Mathematical and Physical Sciences, The University of Queensland, St. Lucia, Queensland 4072, Australia
| | - C A Holmes
- School of Mathematical and Physical Sciences, The University of Queensland, St. Lucia, Queensland 4072, Australia
| | - G J Milburn
- School of Mathematical and Physical Sciences, The University of Queensland, St. Lucia, Queensland 4072, Australia
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20
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Mahboob I, Mounaix M, Nishiguchi K, Fujiwara A, Yamaguchi H. A multimode electromechanical parametric resonator array. Sci Rep 2014; 4:4448. [PMID: 24658349 PMCID: PMC3963032 DOI: 10.1038/srep04448] [Citation(s) in RCA: 50] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2014] [Accepted: 03/07/2014] [Indexed: 11/09/2022] Open
Abstract
Electromechanical resonators have emerged as a versatile platform in which detectors with unprecedented sensitivities and quantum mechanics in a macroscopic context can be developed. These schemes invariably utilise a single resonator but increasingly the concept of an array of electromechanical resonators is promising a wealth of new possibilities. In spite of this, experimental realisations of such arrays have remained scarce due to the formidable challenges involved in their fabrication. In a variation to this approach, we identify 75 harmonic vibration modes in a single electromechanical resonator of which 7 can also be parametrically excited. The parametrically resonating modes exhibit vibrations with only 2 oscillation phases which are used to build a binary information array. We exploit this array to execute a mechanical byte memory, a shift-register and a controlled-NOT gate thus vividly illustrating the availability and functionality of an electromechanical resonator array by simply utilising higher order vibration modes.
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Affiliation(s)
- I. Mahboob
- NTT Basic Research Laboratories, NTT Corporation, Atsugi-shi, Kanagawa 243-0198, Japan
| | - M. Mounaix
- NTT Basic Research Laboratories, NTT Corporation, Atsugi-shi, Kanagawa 243-0198, Japan
| | - K. Nishiguchi
- NTT Basic Research Laboratories, NTT Corporation, Atsugi-shi, Kanagawa 243-0198, Japan
| | - A. Fujiwara
- NTT Basic Research Laboratories, NTT Corporation, Atsugi-shi, Kanagawa 243-0198, Japan
| | - H. Yamaguchi
- NTT Basic Research Laboratories, NTT Corporation, Atsugi-shi, Kanagawa 243-0198, Japan
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21
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Gieseler J, Spasenović M, Novotny L, Quidant R. Nonlinear mode coupling and synchronization of a vacuum-trapped nanoparticle. PHYSICAL REVIEW LETTERS 2014; 112:103603. [PMID: 24679293 DOI: 10.1103/physrevlett.112.103603] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/12/2013] [Indexed: 06/03/2023]
Abstract
We study the dynamics of a laser-trapped nanoparticle in high vacuum. Using parametric coupling to an external excitation source, the linewidth of the nanoparticle's oscillation can be reduced by three orders of magnitude. We show that the oscillation of the nanoparticle and the excitation source are synchronized, exhibiting a well-defined phase relationship. Furthermore, the external source can be used to controllably drive the nanoparticle into the nonlinear regime, thereby generating strong coupling between the different translational modes of the nanoparticle. Our work contributes to the understanding of the nonlinear dynamics of levitated nanoparticles in high vacuum and paves the way for studies of pattern formation, chaos, and stochastic resonance.
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Affiliation(s)
- Jan Gieseler
- ICFO-Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain
| | - Marko Spasenović
- ICFO-Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain and Institut of Physics, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia
| | - Lukas Novotny
- Photonics Laboratory, ETH Zürich, 8093 Zürich, Switzerland
| | - Romain Quidant
- ICFO-Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain and ICREA-Institució Catalana de Recerca i Estudis Avançats, 08010 Barcelona, Spain
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22
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Matheny MH, Grau M, Villanueva LG, Karabalin RB, Cross MC, Roukes ML. Phase synchronization of two anharmonic nanomechanical oscillators. PHYSICAL REVIEW LETTERS 2014; 112:014101. [PMID: 24483899 DOI: 10.1103/physrevlett.112.014101] [Citation(s) in RCA: 63] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/06/2013] [Indexed: 06/03/2023]
Abstract
We investigate the synchronization of oscillators based on anharmonic nanoelectromechanical resonators. Our experimental implementation allows unprecedented observation and control of parameters governing the dynamics of synchronization. We find close quantitative agreement between experimental data and theory describing reactively coupled Duffing resonators with fully saturated feedback gain. In the synchronized state we demonstrate a significant reduction in the phase noise of the oscillators, which is key for sensor and clock applications. Our work establishes that oscillator networks constructed from nanomechanical resonators form an ideal laboratory to study synchronization--given their high-quality factors, small footprint, and ease of cointegration with modern electronic signal processing technologies.
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Affiliation(s)
- Matthew H Matheny
- Kavli Nanoscience Institute and Departments of Physics, Applied Physics, and Bioengineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Matt Grau
- Kavli Nanoscience Institute and Departments of Physics, Applied Physics, and Bioengineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Luis G Villanueva
- Kavli Nanoscience Institute and Departments of Physics, Applied Physics, and Bioengineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Rassul B Karabalin
- Kavli Nanoscience Institute and Departments of Physics, Applied Physics, and Bioengineering, California Institute of Technology, Pasadena, California 91125, USA
| | - M C Cross
- Kavli Nanoscience Institute and Departments of Physics, Applied Physics, and Bioengineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Michael L Roukes
- Kavli Nanoscience Institute and Departments of Physics, Applied Physics, and Bioengineering, California Institute of Technology, Pasadena, California 91125, USA
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23
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Bagheri M, Poot M, Fan L, Marquardt F, Tang HX. Photonic cavity synchronization of nanomechanical oscillators. PHYSICAL REVIEW LETTERS 2013; 111:213902. [PMID: 24313490 DOI: 10.1103/physrevlett.111.213902] [Citation(s) in RCA: 51] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2013] [Revised: 10/08/2013] [Indexed: 06/02/2023]
Abstract
Synchronization in oscillatory systems is a frequent natural phenomenon and is becoming an important concept in modern physics. Nanomechanical resonators are ideal systems for studying synchronization due to their controllable oscillation properties and engineerable nonlinearities. Here we demonstrate synchronization of two nanomechanical oscillators via a photonic resonator, enabling optomechanical synchronization between mechanically isolated nanomechanical resonators. Optical backaction gives rise to both reactive and dissipative coupling of the mechanical resonators, leading to coherent oscillation and mutual locking of resonators with dynamics beyond the widely accepted phase oscillator (Kuramoto) model. In addition to the phase difference between the oscillators, also their amplitudes are coupled, resulting in the emergence of sidebands around the synchronized carrier signal.
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Affiliation(s)
- Mahmood Bagheri
- Department of Electrical Engineering, Yale University, New Haven, Connecticut 06511, USA
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24
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Manzano G, Galve F, Giorgi GL, Hernández-García E, Zambrini R. Synchronization, quantum correlations and entanglement in oscillator networks. Sci Rep 2013; 3:1439. [PMID: 23486526 PMCID: PMC3596799 DOI: 10.1038/srep01439] [Citation(s) in RCA: 110] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/10/2013] [Accepted: 02/18/2013] [Indexed: 11/25/2022] Open
Abstract
Synchronization is one of the paradigmatic phenomena in the study of complex systems. It has been explored theoretically and experimentally mostly to understand natural phenomena, but also in view of technological applications. Although several mechanisms and conditions for synchronous behavior in spatially extended systems and networks have been identified, the emergence of this phenomenon has been largely unexplored in quantum systems until very recently. Here we discuss synchronization in quantum networks of different harmonic oscillators relaxing towards a stationary state, being essential the form of dissipation. By local tuning of one of the oscillators, we establish the conditions for synchronous dynamics, in the whole network or in a motif. Beyond the classical regime we show that synchronization between (even unlinked) nodes witnesses the presence of quantum correlations and entanglement. Furthermore, synchronization and entanglement can be induced between two different oscillators if properly linked to a random network.
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Affiliation(s)
- Gonzalo Manzano
- Institute for Cross Disciplinary Physics and Complex Systems, IFISC (CSIC-UIB), Palma de Mallorca, Spain
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25
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Ludwig M, Marquardt F. Quantum many-body dynamics in optomechanical arrays. PHYSICAL REVIEW LETTERS 2013; 111:073603. [PMID: 23992065 DOI: 10.1103/physrevlett.111.073603] [Citation(s) in RCA: 58] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/01/2012] [Revised: 05/30/2013] [Indexed: 06/02/2023]
Abstract
We study the nonlinear driven dissipative quantum dynamics of an array of optomechanical systems. At each site of such an array, a localized mechanical mode interacts with a laser-driven cavity mode via radiation pressure, and both photons and phonons can hop between neighboring sites. The competition between coherent interaction and dissipation gives rise to a rich phase diagram characterizing the optical and mechanical many-body states. For weak intercellular coupling, the mechanical motion at different sites is incoherent due to the influence of quantum noise. When increasing the coupling strength, however, we observe a transition towards a regime of phase-coherent mechanical oscillations. We employ a Gutzwiller ansatz as well as semiclassical Langevin equations on finite lattices, and we propose a realistic experimental implementation in optomechanical crystals.
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Affiliation(s)
- Max Ludwig
- Institute for Theoretical Physics, Universität Erlangen-Nürnberg, Erlangen, Germany.
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26
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Botari T, Leonel ED. One-dimensional Fermi accelerator model with moving wall described by a nonlinear van der Pol oscillator. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:012904. [PMID: 23410401 DOI: 10.1103/physreve.87.012904] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/18/2012] [Indexed: 06/01/2023]
Abstract
A modification of the one-dimensional Fermi accelerator model is considered in this work. The dynamics of a classical particle of mass m, confined to bounce elastically between two rigid walls where one is described by a nonlinear van der Pol type oscillator while the other one is fixed, working as a reinjection mechanism of the particle for a next collision, is carefully made by the use of a two-dimensional nonlinear mapping. Two cases are considered: (i) the situation where the particle has mass negligible as compared to the mass of the moving wall and does not affect the motion of it; and (ii) the case where collisions of the particle do affect the movement of the moving wall. For case (i) the phase space is of mixed type leading us to observe a scaling of the average velocity as a function of the parameter (χ) controlling the nonlinearity of the moving wall. For large χ, a diffusion on the velocity is observed leading to the conclusion that Fermi acceleration is taking place. On the other hand, for case (ii), the motion of the moving wall is affected by collisions with the particle. However, due to the properties of the van der Pol oscillator, the moving wall relaxes again to a limit cycle. Such kind of motion absorbs part of the energy of the particle leading to a suppression of the unlimited energy gain as observed in case (i). The phase space shows a set of attractors of different periods whose basin of attraction has a complicated organization.
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Affiliation(s)
- Tiago Botari
- Departamento de Física-UNESP-Univ Estadual Paulista, Av. 24A 1515, 13506-900 Rio Claro, SP, Brazil
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27
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Zhang M, Wiederhecker GS, Manipatruni S, Barnard A, McEuen P, Lipson M. Synchronization of micromechanical oscillators using light. PHYSICAL REVIEW LETTERS 2012; 109:233906. [PMID: 23368207 DOI: 10.1103/physrevlett.109.233906] [Citation(s) in RCA: 111] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/24/2012] [Indexed: 06/01/2023]
Abstract
Synchronization, the emergence of spontaneous order in coupled systems, is of fundamental importance in both physical and biological systems. We demonstrate the synchronization of two dissimilar silicon nitride micromechanical oscillators, that are spaced apart by a few hundred nanometers and are coupled through an optical cavity radiation field. The tunability of the optical coupling between the oscillators enables one to externally control the dynamics and switch between coupled and individual oscillation states. These results pave a path toward reconfigurable synchronized oscillator networks.
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Affiliation(s)
- Mian Zhang
- School of Electrical and Computer Engineering, Cornell University, Ithaca, New York 14853, USA
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