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Liao Z, Shi Z, Sarker MS, Tabata H. Robust QRS detection based on simulated degenerate optical parametric oscillator-assisted neural network. Heliyon 2024; 10:e28903. [PMID: 38576550 PMCID: PMC10990971 DOI: 10.1016/j.heliyon.2024.e28903] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/15/2024] [Revised: 03/22/2024] [Accepted: 03/26/2024] [Indexed: 04/06/2024] Open
Abstract
Accurately detecting the depolarization QRS complex in the ventricles is a fundamental requirement for cardiovascular disease detection using electrocardiography (ECG). In contrast to traditional signal enhancement algorithms, emerging neural network approaches have shown promise for QRS detection because of their generalizability on complex data. However, the inevitable noise present during ECG recording leads to a decrease in the performance of neural networks. To enhance the robustness and performance of neural network-based QRS detectors, we propose a simulated degeneration unit (SDU)-assisted convolutional neural network (CNN). An SDU simulates the physical degeneration process of interfering optical pulses, which can effectively suppress in-band noise. Through comprehensive performance evaluations on three open-source databases, the SDU-enhanced CNN-based approach demonstrated better performance in detecting QRS complexes than other recently reported QRS detectors. Furthermore, real-world noise injection tests indicate that the optimal noise robustness boundary for the CNN equipped with SDU is 167-300% higher than that for the CNN without SDU.
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Affiliation(s)
- Zhiqiang Liao
- Department of Electrical Engineering and Information Systems, Graduate School of Engineering, The University of Tokyo, Tokyo, 113-8656, Japan
- Department of Bioengineering, Graduate School of Engineering, The University of Tokyo, Tokyo, 113-8656, Japan
| | - Zhuozheng Shi
- Department of Bioengineering, Graduate School of Engineering, The University of Tokyo, Tokyo, 113-8656, Japan
- Bioinformatics Interdepartmental Program, University of California Los Angeles, Los Angeles, CA, USA
| | - Md Shamim Sarker
- Department of Electrical Engineering and Information Systems, Graduate School of Engineering, The University of Tokyo, Tokyo, 113-8656, Japan
- Department of Bioengineering, Graduate School of Engineering, The University of Tokyo, Tokyo, 113-8656, Japan
| | - Hitoshi Tabata
- Department of Electrical Engineering and Information Systems, Graduate School of Engineering, The University of Tokyo, Tokyo, 113-8656, Japan
- Department of Bioengineering, Graduate School of Engineering, The University of Tokyo, Tokyo, 113-8656, Japan
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2
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Controls of a superconducting quantum parametron under a strong pump field. Sci Rep 2021; 11:11459. [PMID: 34075132 PMCID: PMC8169783 DOI: 10.1038/s41598-021-90874-4] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2021] [Accepted: 05/17/2021] [Indexed: 11/08/2022] Open
Abstract
Pumped at approximately twice the natural frequency, a Josephson parametric oscillator called parametron or Kerr parametric oscillator shows self-oscillation. Quantum annealing and universal quantum computation using self-oscillating parametrons as qubits were proposed. However, controls of parametrons under the pump field are degraded by unwanted rapidly oscillating terms in the Hamiltonian, which we call non-resonant rapidly oscillating terms (NROTs) coming from the violation of the rotating wave approximation. Therefore, the pump field can be an intrinsic origin of the imperfection of controls of parametrons. Here, we theoretically study the influence of the NROTs on the accuracy of controls of a parametron: a cat-state creation and a single-qubit gate. It is shown that there is a trade-off relationship between the suppression of the nonadiabatic transitions and the validity of the rotating wave approximation in a conventional approach. We also show that the tailored time dependence of the detuning of the pump field can suppress both of the nonadiabatic transitions and the disturbance of the state of the parametron due to the NROTs.
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Sarkar P, Bhattacharjee JK. Nonlinear parametric oscillator: A tool for probing quantum fluctuations. Phys Rev E 2020; 102:052204. [PMID: 33327191 DOI: 10.1103/physreve.102.052204] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/16/2020] [Accepted: 10/15/2020] [Indexed: 06/12/2023]
Abstract
Nanomechanical oscillators have, over the last few years, started probing regimes where quantum fluctuations are important. Here we consider a nonlinear parametric oscillator in the quantum domain. We show that in the classical subharmonic resonance zone, the quantum fluctuations are finite but greatly magnified depending on the strength of the nonlinear coupling. This should make such oscillators useful in probing quantum fluctuations.
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Affiliation(s)
- Prasun Sarkar
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata-700 032, India
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4
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Wang Z, Navarrete-Benlloch C, Cai Z. Pattern Formation and Exotic Order in Driven-Dissipative Bose-Hubbard Systems. PHYSICAL REVIEW LETTERS 2020; 125:115301. [PMID: 32975958 DOI: 10.1103/physrevlett.125.115301] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/18/2020] [Accepted: 08/17/2020] [Indexed: 06/11/2023]
Abstract
Modern experimental platforms such as superconducting circuit arrays call for the exploration of bosonic tight-binding models in unconventional situations with no counterpart in real materials. Here we investigate one such situation in which excitations are driven and damped by pairs, leading to pattern formation and exotic bosonic states emerging from a nonequilibrium quantum many-body system. Focusing on a two-dimensional driven-dissipative Bose-Hubbard model, we find that its steady states are characterized by the condensation of bosons around momenta lying on a "Bose surface," a bosonic analog of the Fermi surface in solid-state systems. The interplay between instabilities generated by the driving, the nonlinear dissipative mode coupling, and the underlying lattice effect allows the system to equilibrate into an exotic superfluid state of bosons condensed on a closed ring in momentum space instead of discrete points. Such an unconventional state with a spatially uniform density distribution goes beyond the traditional scope of pattern formation and thus has no counterpart in the classical literature. In addition, it is a state connected to several open problems in modern condensed-matter physics. Here we provide the means to stabilize it, opening the way to its experimental study. Moreover, we also provide a concrete experimental implementation of our model in currently available superconducting circuit arrays. We also investigate the relaxation spectrum around the condensate, which shows a characteristic purely diffusive behavior.
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Affiliation(s)
- Zijian Wang
- Wilczek Quantum Center, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
- Zhiyuan College, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Carlos Navarrete-Benlloch
- Wilczek Quantum Center, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Zi Cai
- Wilczek Quantum Center, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
- Key Laboratory of Artificial Structures and Quantum Control, Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
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5
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Hamerly R, Inagaki T, McMahon PL, Venturelli D, Marandi A, Onodera T, Ng E, Langrock C, Inaba K, Honjo T, Enbutsu K, Umeki T, Kasahara R, Utsunomiya S, Kako S, Kawarabayashi KI, Byer RL, Fejer MM, Mabuchi H, Englund D, Rieffel E, Takesue H, Yamamoto Y. Experimental investigation of performance differences between coherent Ising machines and a quantum annealer. SCIENCE ADVANCES 2019; 5:eaau0823. [PMID: 31139743 PMCID: PMC6534389 DOI: 10.1126/sciadv.aau0823] [Citation(s) in RCA: 42] [Impact Index Per Article: 8.4] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/04/2018] [Accepted: 04/17/2019] [Indexed: 05/05/2023]
Abstract
Physical annealing systems provide heuristic approaches to solving combinatorial optimization problems. Here, we benchmark two types of annealing machines-a quantum annealer built by D-Wave Systems and measurement-feedback coherent Ising machines (CIMs) based on optical parametric oscillators-on two problem classes, the Sherrington-Kirkpatrick (SK) model and MAX-CUT. The D-Wave quantum annealer outperforms the CIMs on MAX-CUT on cubic graphs. On denser problems, however, we observe an exponential penalty for the quantum annealer [exp(-αDW N 2)] relative to CIMs [exp(-αCIM N)] for fixed anneal times, both on the SK model and on 50% edge density MAX-CUT. This leads to a several orders of magnitude time-to-solution difference for instances with over 50 vertices. An optimal-annealing time analysis is also consistent with a substantial projected performance difference. The difference in performance between the sparsely connected D-Wave machine and the fully-connected CIMs provides strong experimental support for efforts to increase the connectivity of quantum annealers.
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Affiliation(s)
- Ryan Hamerly
- Research Laboratory of Electronics, Massachusetts Institute of Technology, 50 Vassar Street, Cambridge, MA 02139, USA
- National Institute of Informatics, Hitotsubashi 2-1-2, Chiyoda-ku, Tokyo 101-8403, Japan
- Corresponding author. (R.H.); (T.I.); (P.L.M.)
| | - Takahiro Inagaki
- NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi, Kanagawa 243-0198, Japan
- Corresponding author. (R.H.); (T.I.); (P.L.M.)
| | - Peter L. McMahon
- National Institute of Informatics, Hitotsubashi 2-1-2, Chiyoda-ku, Tokyo 101-8403, Japan
- E. L. Ginzton Laboratory, Stanford University, Stanford, CA 94305, USA
- School of Applied and Engineering Physics, Cornell University, Ithaca, NY 14853, USA
- Corresponding author. (R.H.); (T.I.); (P.L.M.)
| | - Davide Venturelli
- NASA Ames Research Center Quantum Artificial Intelligence Laboratory (QuAIL), Mail Stop 269-1, Moffett Field, CA 94035, USA
- USRA Research Institute for Advanced Computer Science (RIACS), 615 National Avenue, Mountain View, CA 94035, USA
| | - Alireza Marandi
- E. L. Ginzton Laboratory, Stanford University, Stanford, CA 94305, USA
- California Institute of Technology, Pasadena, CA 91125, USA
| | - Tatsuhiro Onodera
- E. L. Ginzton Laboratory, Stanford University, Stanford, CA 94305, USA
| | - Edwin Ng
- E. L. Ginzton Laboratory, Stanford University, Stanford, CA 94305, USA
| | - Carsten Langrock
- E. L. Ginzton Laboratory, Stanford University, Stanford, CA 94305, USA
| | - Kensuke Inaba
- NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi, Kanagawa 243-0198, Japan
| | - Toshimori Honjo
- NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi, Kanagawa 243-0198, Japan
| | - Koji Enbutsu
- NTT Device Technology Laboratories, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi, Kanagawa 243-0198, Japan
| | - Takeshi Umeki
- NTT Device Technology Laboratories, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi, Kanagawa 243-0198, Japan
| | - Ryoichi Kasahara
- NTT Device Technology Laboratories, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi, Kanagawa 243-0198, Japan
| | - Shoko Utsunomiya
- National Institute of Informatics, Hitotsubashi 2-1-2, Chiyoda-ku, Tokyo 101-8403, Japan
| | - Satoshi Kako
- National Institute of Informatics, Hitotsubashi 2-1-2, Chiyoda-ku, Tokyo 101-8403, Japan
| | - Ken-ichi Kawarabayashi
- National Institute of Informatics, Hitotsubashi 2-1-2, Chiyoda-ku, Tokyo 101-8403, Japan
| | - Robert L. Byer
- E. L. Ginzton Laboratory, Stanford University, Stanford, CA 94305, USA
| | - Martin M. Fejer
- E. L. Ginzton Laboratory, Stanford University, Stanford, CA 94305, USA
| | - Hideo Mabuchi
- E. L. Ginzton Laboratory, Stanford University, Stanford, CA 94305, USA
| | - Dirk Englund
- Research Laboratory of Electronics, Massachusetts Institute of Technology, 50 Vassar Street, Cambridge, MA 02139, USA
| | - Eleanor Rieffel
- NASA Ames Research Center Quantum Artificial Intelligence Laboratory (QuAIL), Mail Stop 269-1, Moffett Field, CA 94035, USA
| | - Hiroki Takesue
- NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato Wakamiya, Atsugi, Kanagawa 243-0198, Japan
| | - Yoshihisa Yamamoto
- E. L. Ginzton Laboratory, Stanford University, Stanford, CA 94305, USA
- ImPACT Program, Japan Science and Technology Agency, Gobancho 7, Chiyoda-ku, Tokyo 102-0076, Japan
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6
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Foss-Feig M, Niroula P, Young JT, Hafezi M, Gorshkov AV, Wilson RM, Maghrebi MF. Emergent equilibrium in many-body optical bistability. PHYSICAL REVIEW. A 2017; 95:10.1103/PhysRevA.95.043826. [PMID: 31093586 PMCID: PMC6513354 DOI: 10.1103/physreva.95.043826] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Many-body systems constructed of quantum-optical building blocks can now be realized in experimental platforms ranging from exciton-polariton fluids to ultracold Rydberg gases, establishing a fascinating interface between traditional many-body physics and the driven-dissipative, nonequilibrium setting of cavity QED. At this interface, the standard techniques and intuitions of both fields are called into question, obscuring issues as fundamental as the role of fluctuations, dimensionality, and symmetry on the nature of collective behavior and phase transitions. Here, we study the driven-dissipative Bose-Hubbard model, a minimal description of numerous atomic, optical, and solid-state systems in which particle loss is countered by coherent driving. Despite being a lattice version of optical bistability, a foundational and patently nonequilibrium model of cavity QED, the steady state possesses an emergent equilibrium description in terms of a classical Ising model. We establish this picture by making new connections between traditional techniques from many-body physics (functional integrals) and quantum optics (the system-size expansion). To lowest order in a controlled expansion-organized around the experimentally relevant limit of weak interactions-the full quantum dynamics reduces to nonequilibrium Langevin equations, which support a phase transition described by model A of the Hohenberg-Halperin classification. Numerical simulations of the Langevin equations corroborate this picture, revealing that canonical behavior associated with the Ising model manifests readily in simple experimental observables.
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Affiliation(s)
- M Foss-Feig
- United States Army Research Laboratory, Adelphi, Maryland 20783, USA
- Joint Quantum Institute, NIST and University of Maryland, College Park, Maryland 20742, USA
- Joint Center for Quantum Information and Computer Science, NIST and University of Maryland, College Park, Maryland 20742, USA
| | - P Niroula
- Joint Quantum Institute, NIST and University of Maryland, College Park, Maryland 20742, USA
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - J T Young
- Joint Quantum Institute, NIST and University of Maryland, College Park, Maryland 20742, USA
| | - M Hafezi
- Joint Quantum Institute, NIST and University of Maryland, College Park, Maryland 20742, USA
- Department of Electrical and Computer Engineering and Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742, USA
| | - A V Gorshkov
- Joint Quantum Institute, NIST and University of Maryland, College Park, Maryland 20742, USA
- Joint Center for Quantum Information and Computer Science, NIST and University of Maryland, College Park, Maryland 20742, USA
| | - R M Wilson
- Department of Physics, United States Naval Academy, Annapolis, Maryland 21402, USA
| | - M F Maghrebi
- Joint Quantum Institute, NIST and University of Maryland, College Park, Maryland 20742, USA
- Joint Center for Quantum Information and Computer Science, NIST and University of Maryland, College Park, Maryland 20742, USA
- Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
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7
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Computational Principle and Performance Evaluation of Coherent Ising Machine Based on Degenerate Optical Parametric Oscillator Network. ENTROPY 2016. [DOI: 10.3390/e18040151] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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8
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Wilson RM, Mahmud KW, Hu A, Gorshkov AV, Hafezi M, Foss-Feig M. Collective phases of strongly interacting cavity photons. PHYSICAL REVIEW. A 2016; 94:10.1103/PhysRevA.94.033801. [PMID: 31098434 PMCID: PMC6515917 DOI: 10.1103/physreva.94.033801] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
We study a coupled array of coherently driven photonic cavities, which maps onto a driven-dissipative XY spin- 1 2 model with ferromagnetic couplings in the limit of strong optical nonlinearities. Using a site-decoupled mean-field approximation, we identify steady-state phases with canted antiferromagnetic order, in addition to limit cycle phases, where oscillatory dynamics persist indefinitely. We also identify collective bistable phases, where the system supports two steady states among spatially uniform, antiferromagnetic, and limit cycle phases. We compare these mean-field results to exact quantum trajectory simulations for finite one-dimensional arrays. The exact results exhibit short-range antiferromagnetic order for parameters that have significant overlap with the mean-field phase diagram. In the mean-field bistable regime, the exact quantum dynamics exhibits real-time collective switching between macroscopically distinguishable states. We present a clear physical picture for this dynamics and establish a simple relationship between the switching times and properties of the quantum Liouvillian.
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Affiliation(s)
- Ryan M Wilson
- Department of Physics, The United States Naval Academy, Annapolis, Maryland 21402, USA
- Kavli Institute of Theoretical Physics, Santa Barbara, California 93106, USA
| | - Khan W Mahmud
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Anzi Hu
- Department of Physics, American University, Washington, DC 20016, USA
| | - Alexey V Gorshkov
- Kavli Institute of Theoretical Physics, Santa Barbara, California 93106, USA
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Mohammad Hafezi
- Kavli Institute of Theoretical Physics, Santa Barbara, California 93106, USA
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
- Department of Electrical Engineering and Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742, USA
| | - Michael Foss-Feig
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
- United States Army Research Laboratory, Adelphi, Maryland 20783, USA
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9
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Navarrete-Benlloch C, Roldán E, Chang Y, Shi T. Regularized linearization for quantum nonlinear optical cavities: application to degenerate optical parametric oscillators. OPTICS EXPRESS 2014; 22:24010-24023. [PMID: 25321977 DOI: 10.1364/oe.22.024010] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Nonlinear optical cavities are crucial both in classical and quantum optics; in particular, nowadays optical parametric oscillators are one of the most versatile and tunable sources of coherent light, as well as the sources of the highest quality quantum-correlated light in the continuous variable regime. Being nonlinear systems, they can be driven through critical points in which a solution ceases to exist in favour of a new one, and it is close to these points where quantum correlations are the strongest. The simplest description of such systems consists in writing the quantum fields as the classical part plus some quantum fluctuations, linearizing then the dynamical equations with respect to the latter; however, such an approach breaks down close to critical points, where it provides unphysical predictions such as infinite photon numbers. On the other hand, techniques going beyond the simple linear description become too complicated especially regarding the evaluation of two-time correlators, which are of major importance to compute observables outside the cavity. In this article we provide a regularized linear description of nonlinear cavities, that is, a linearization procedure yielding physical results, taking the degenerate optical parametric oscillator as the guiding example. The method, which we call self-consistent linearization, is shown to be equivalent to a general Gaussian ansatz for the state of the system, and we compare its predictions with those obtained with available exact (or quasi-exact) methods. Apart from its operational value, we believe that our work is valuable also from a fundamental point of view, especially in connection to the question of how far linearized or Gaussian theories can be pushed to describe nonlinear dissipative systems which have access to non-Gaussian states.
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10
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Barth I, Friedland L. Quantum phenomena in a chirped parametric anharmonic oscillator. PHYSICAL REVIEW LETTERS 2014; 113:040403. [PMID: 25105601 DOI: 10.1103/physrevlett.113.040403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/19/2014] [Indexed: 06/03/2023]
Abstract
Parametric ladder climbing and the quantum saturation of the threshold for the classical parametric autoresonance due to the zero point fluctuations at low temperatures are discussed. The probability for capture into the chirped parametric resonance is found by solving the Schrödinger equation in the energy basis and the associated resonant phase-space dynamics is illustrated via the Wigner distribution. The numerical threshold for capture into the resonance is compared with the classical and quantum theories in different parameter regimes.
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Affiliation(s)
- I Barth
- Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - L Friedland
- Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel
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11
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Peano V, Marthaler M, Dykman MI. Sharp tunneling peaks in a parametric oscillator: quantum resonances missing in the rotating wave approximation. PHYSICAL REVIEW LETTERS 2012; 109:090401. [PMID: 23002813 DOI: 10.1103/physrevlett.109.090401] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/21/2012] [Indexed: 06/01/2023]
Abstract
We describe a new mechanism of tunneling between period-two vibrational states of a weakly nonlinear, parametrically modulated oscillator. The tunneling results from resonant transitions induced by the fast oscillating terms conventionally disregarded in the rotating wave approximation (RWA). The tunneling amplitude displays resonant peaks as a function of the modulation frequency; near the maxima it is exponentially larger than the RWA tunneling amplitude.
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Affiliation(s)
- V Peano
- Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
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12
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Holmes CA, Meaney CP, Milburn GJ. Synchronization of many nanomechanical resonators coupled via a common cavity field. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:066203. [PMID: 23005192 DOI: 10.1103/physreve.85.066203] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/03/2011] [Indexed: 06/01/2023]
Abstract
Using amplitude equations, we show that groups of identical nanomechanical resonators, interacting with a common mode of a cavity microwave field, synchronize to form a single mechanical mode which couples to the cavity with a strength dependent on the squared sum of the individual mechanical-microwave couplings. Classically this system is dominated by periodic behavior which, when analyzed using amplitude equations, can be shown to exhibit multistability. In contrast, groups of sufficiently dissimilar nanomechanical oscillators may lose synchronization and oscillate out of phase at significantly higher amplitudes. Further, the method by which synchronization is lost resembles that for large amplitude forcing which is not of the Kuramoto form.
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Affiliation(s)
- C A Holmes
- Centre for Engineered Quantum Systems, School of Mathematical and Physical Sciences, The University of Queensland, St. Lucia, Queensland 4072, Australia
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13
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Deuar P, Drummond PD. First-principles quantum dynamics in interacting Bose gases II: stochastic gauges. ACTA ACUST UNITED AC 2006. [DOI: 10.1088/0305-4470/39/11/011] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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14
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Klimov AB, Espinoza P. Classical evolution of quantum fluctuations in spin-like systems: squeezing and entanglement. ACTA ACUST UNITED AC 2005. [DOI: 10.1088/1464-4266/7/6/004] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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15
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Etchegoin P. Self-tunnelling oscillations in non-linear quantum mechanics and the electron-transfer problem. Chem Phys 2004. [DOI: 10.1016/j.chemphys.2003.10.025] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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16
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Mertens CJ, Kennedy TA. Nonequilibrium Green-function theory of quantum-optical correlations. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1996; 53:3497-3513. [PMID: 9913293 DOI: 10.1103/physreva.53.3497] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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17
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Kinsler P. Testing quantum mechanics using third-order correlations. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1996; 53:2000-2008. [PMID: 9913101 DOI: 10.1103/physreva.53.2000] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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18
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Kinsler P, Drummond PD. Critical fluctuations in the quantum parametric oscillator. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1995; 52:783-790. [PMID: 9912302 DOI: 10.1103/physreva.52.783] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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19
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Yeon KH, Kim HJ, Um CI, George TF, Pandey LN. Wave function in the invariant representation and squeezed-state function of the time-dependent harmonic oscillator. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1994; 50:1035-1039. [PMID: 9910989 DOI: 10.1103/physreva.50.1035] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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20
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Kinsler P, Fernée M, Drummond PD. Limits to squeezing and phase information in the parametric amplifier. PHYSICAL REVIEW A 1993; 48:3310-3320. [PMID: 9909987 DOI: 10.1103/physreva.48.3310] [Citation(s) in RCA: 46] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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21
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Mertens CJ, Kennedy TA, Swain S. Many-body quantum theory of the optical parametric oscillator. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1993; 48:2374-2385. [PMID: 9909862 DOI: 10.1103/physreva.48.2374] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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22
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de Oliveira FAM. s-order nondiagonal quasiprobabilities. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1992; 45:5104-5112. [PMID: 9907597 DOI: 10.1103/physreva.45.5104] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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de Oliveira FAM. s-order positive quasiprobabilities: Nonlinear dynamics without divergences. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1992; 45:3350-3353. [PMID: 9907376 DOI: 10.1103/physreva.45.3350] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Kinsler P, Drummond PD. Comment on "Langevin equation for the squeezing of light by means of a parametric oscillator". PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1991; 44:7848-7850. [PMID: 9905927 DOI: 10.1103/physreva.44.7848] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Mortimer IK, Risken H. Eigenvalues for the quantum parametric oscillator in the overdamped regime. PHYSICAL REVIEW. A, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 1991; 44:617-627. [PMID: 9905712 DOI: 10.1103/physreva.44.617] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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