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Zhou X, Ren X, Xiao D, Zhang J, Huang R, Li Z, Sun X, Wu X, Qiu CW, Nori F, Jing H. Higher-order singularities in phase-tracked electromechanical oscillators. Nat Commun 2023; 14:7944. [PMID: 38040766 PMCID: PMC10692225 DOI: 10.1038/s41467-023-43708-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/11/2023] [Accepted: 11/17/2023] [Indexed: 12/03/2023] Open
Abstract
Singularities ubiquitously exist in different fields and play a pivotal role in probing the fundamental laws of physics and developing highly sensitive sensors. Nevertheless, achieving higher-order (≥3) singularities, which exhibit superior performance, typically necessitates meticulous tuning of multiple (≥3) coupled degrees of freedom or additional introduction of nonlinear potential energies. Here we propose theoretically and confirm using mechanics experiments, the existence of an unexplored cusp singularity in the phase-tracked (PhT) steady states of a pair of coherently coupled mechanical modes without the need for multiple (≥3) coupled modes or nonlinear potential energies. By manipulating the PhT singularities in an electrostatically tunable micromechanical system, we demonstrate an enhanced cubic-root response to frequency perturbations. This study introduces a new phase-tracking method for studying interacting systems and sheds new light on building and engineering advanced singular devices with simple and well-controllable elements, with potential applications in precision metrology, portable nonreciprocal devices, and on-chip mechanical computing.
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Affiliation(s)
- Xin Zhou
- College of Intelligence Science and Technology, NUDT, 410073, Changsha, China.
| | - Xingjing Ren
- College of Intelligence Science and Technology, NUDT, 410073, Changsha, China
| | - Dingbang Xiao
- College of Intelligence Science and Technology, NUDT, 410073, Changsha, China
| | - Jianqi Zhang
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy of Precision Measurement Science and Technology, Chinese Academy of Sciences, 430071, Wuhan, China
| | - Ran Huang
- Center for Quantum Computing, Cluster for Pioneering Research, RIKEN, Wako-shi, Saitama, 351-0198, Japan
| | - Zhipeng Li
- Department of Electrical and Computer Engineering, National University of Singapore, Singapore, 117576, Singapore
| | - Xiaopeng Sun
- College of Intelligence Science and Technology, NUDT, 410073, Changsha, China
| | - Xuezhong Wu
- College of Intelligence Science and Technology, NUDT, 410073, Changsha, China.
| | - Cheng-Wei Qiu
- Department of Electrical and Computer Engineering, National University of Singapore, Singapore, 117576, Singapore
| | - Franco Nori
- Center for Quantum Computing, Cluster for Pioneering Research, RIKEN, Wako-shi, Saitama, 351-0198, Japan.
- Department of Physics, University of Michigan, Ann Arbor, MI, 48109-1040, USA.
| | - Hui Jing
- Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, Department of Physics and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, 410081, Changsha, China.
- Academy for Quantum Science and Technology, Zhengzhou University of Light Industry, 450002, Zhengzhou, China.
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Yuksel M, Orhan E, Yanik C, Ari AB, Demir A, Hanay MS. Nonlinear Nanomechanical Mass Spectrometry at the Single-Nanoparticle Level. NANO LETTERS 2019; 19:3583-3589. [PMID: 31117750 DOI: 10.1021/acs.nanolett.9b00546] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/05/2023]
Abstract
Nanoelectromechanical systems (NEMS) have emerged as a promising technology for performing the mass spectrometry of large biomolecules and nanoparticles. As nanoscale objects land on NEMS sensors one by one, they induce resolvable shifts in the resonance frequency of the sensor proportional to their weight. The operational regime of NEMS sensors is often limited by the onset of nonlinearity, beyond which the highly sensitive schemes based on frequency tracking by phase-locked loops cannot be readily used. Here, we develop a measurement architecture with which to operate at the nonlinear regime and measure frequency shifts induced by analytes in a rapid and sensitive manner. We used this architecture to individually characterize the mass of gold nanoparticles and verified the results by performing independent measurements of the same nanoparticles based on linear mass sensing. Once the feasibility of the technique is established, we have obtained the mass spectrum of a 20 nm gold nanoparticle sample by individually recording about 500 single-particle events using two modes working sequentially in the nonlinear regime. The technique obtained here can be used for thin nanomechanical structures that possess a limited dynamic range.
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Affiliation(s)
| | | | - Cenk Yanik
- Sabanci University SUNUM Nanotechnology Research Center , 34956 Istanbul , Turkey
| | | | - Alper Demir
- Department of Electrical Engineering , Koc University , 34450 Istanbul , Turkey
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Monga B, Wilson D, Matchen T, Moehlis J. Phase reduction and phase-based optimal control for biological systems: a tutorial. BIOLOGICAL CYBERNETICS 2019; 113:11-46. [PMID: 30203130 DOI: 10.1007/s00422-018-0780-z] [Citation(s) in RCA: 38] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/31/2018] [Accepted: 08/25/2018] [Indexed: 05/20/2023]
Abstract
A powerful technique for the analysis of nonlinear oscillators is the rigorous reduction to phase models, with a single variable describing the phase of the oscillation with respect to some reference state. An analog to phase reduction has recently been proposed for systems with a stable fixed point, and phase reduction for periodic orbits has recently been extended to take into account transverse directions and higher-order terms. This tutorial gives a unified treatment of such phase reduction techniques and illustrates their use through mathematical and biological examples. It also covers the use of phase reduction for designing control algorithms which optimally change properties of the system, such as the phase of the oscillation. The control techniques are illustrated for example neural and cardiac systems.
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Affiliation(s)
- Bharat Monga
- Department of Mechanical Engineering, University of California, Santa Barbara, CA, 93106, USA
| | - Dan Wilson
- Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, TN, 37996, USA
| | - Tim Matchen
- Department of Mechanical Engineering, University of California, Santa Barbara, CA, 93106, USA
| | - Jeff Moehlis
- Department of Mechanical Engineering, University of California, Santa Barbara, CA, 93106, USA.
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Sobreviela G, Riverola M, Torres F, Uranga A, Barniol N. Optimization of the Close-to-Carrier Phase Noise in a CMOS-MEMS Oscillator Using a Phase Tunable Sustaining-Amplifier. IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL 2017; 64:888-897. [PMID: 28207393 DOI: 10.1109/tuffc.2017.2667881] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
In this paper, the phase noise of a 24-MHz complimentary metal-oxide-semiconductor microelectromechanical systems (CMOS-MEMS) oscillator with zero-level vacuum package is studied. We characterize and analyze the nonlinear regime of each one of the modules that compose the oscillator (CMOS sustaining-amplifier and MEMS resonator). As we show, the presented resonator exhibits a high nonlinear behavior. Such a fact is exploited as a mechanism to stabilize the oscillation amplitude, allowing us to maintain the sustaining-amplifier working in the linear regime. Consequently, the nonlinear resonator becomes the main close-to-carrier phase noise source. The sustaining amplifier, which functions as a phase shifter, was developed such that MEMS operation point optimization could be achieved without an increase in circuitry modules. Therefore, the system saves on area and power, and is able to improve the phase noise 26 dBc/Hz (at 1-kHz carrier frequency offset).
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Kenig E, Cross MC. Eliminating 1/f noise in oscillators. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:042901. [PMID: 24827307 DOI: 10.1103/physreve.89.042901] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/01/2013] [Indexed: 06/03/2023]
Abstract
We study 1/f and narrow-bandwidth noise in precision oscillators based on high-quality factor resonators and feedback. The dynamics of such an oscillator are well described by two variables, an amplitude and a phase. In this description we show that low-frequency feedback noise is represented by a single noise vector in phase space. The implication of this is that 1/f and narrow-bandwidth noise can be eliminated by tuning controllable parameters, such as the feedback phase. We present parameter values for which the noise is eliminated and provide specific examples of noise sources for further illustration.
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Affiliation(s)
- Eyal Kenig
- Department of Physics, California Institute of Technology, Pasadena, California 91125, USA
| | - M C Cross
- Department of Physics, California Institute of Technology, Pasadena, California 91125, USA
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Kenig E, Cross MC, Moehlis J, Wiesenfeld K. Phase noise of oscillators with unsaturated amplifiers. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:062922. [PMID: 24483546 DOI: 10.1103/physreve.88.062922] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/09/2013] [Indexed: 06/03/2023]
Abstract
We study the role of amplifier saturation in eliminating feedback noise in self-sustained oscillators. We extend previous works that use a saturated amplifier to quench fluctuations in the feedback magnitude, while simultaneously tuning the oscillator to an operating point at which the resonator nonlinearity cancels fluctuations in the feedback phase. We consider a generalized model which features an amplitude-dependent amplifier gain function. This allows us to determine the total oscillator phase noise in realistic configurations due to noise in both quadratures of the feedback, and to show that it is not necessary to drive the resonator to large oscillation amplitudes in order to eliminate noise in the phase of the feedback.
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Affiliation(s)
- Eyal Kenig
- Department of Physics, California Institute of Technology, Pasadena, California 91125, USA
| | - M C Cross
- Department of Physics, California Institute of Technology, Pasadena, California 91125, USA
| | - Jeff Moehlis
- Department of Mechanical Engineering, University of California, Santa Barbara, California 93106, USA
| | - Kurt Wiesenfeld
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
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Villanueva LG, Kenig E, Karabalin RB, Matheny MH, Lifshitz R, Cross MC, Roukes ML. Surpassing fundamental limits of oscillators using nonlinear resonators. PHYSICAL REVIEW LETTERS 2013; 110:177208. [PMID: 23679770 PMCID: PMC3839326 DOI: 10.1103/physrevlett.110.177208] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/19/2012] [Revised: 12/11/2012] [Indexed: 05/22/2023]
Abstract
In its most basic form an oscillator consists of a resonator driven on resonance, through feedback, to create a periodic signal sustained by a static energy source. The generation of a stable frequency, the basic function of oscillators, is typically achieved by increasing the amplitude of motion of the resonator while remaining within its linear, harmonic regime. Contrary to this conventional paradigm, in this Letter we show that by operating the oscillator at special points in the resonator's anharmonic regime we can overcome fundamental limitations of oscillator performance due to thermodynamic noise as well as practical limitations due to noise from the sustaining circuit. We develop a comprehensive model that accounts for the major contributions to the phase noise of the nonlinear oscillator. Using a nanoelectromechanical system based oscillator, we experimentally verify the existence of a special region in the operational parameter space that enables suppressing the most significant contributions to the oscillator's phase noise, as predicted by our model.
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Affiliation(s)
- L. G. Villanueva
- Kavli Nanoscience Institute, California Institute of Technology, Pasadena, California 91125, USA
| | - E. Kenig
- Kavli Nanoscience Institute, California Institute of Technology, Pasadena, California 91125, USA
| | - R. B. Karabalin
- Kavli Nanoscience Institute, California Institute of Technology, Pasadena, California 91125, USA
| | - M. H. Matheny
- Kavli Nanoscience Institute, California Institute of Technology, Pasadena, California 91125, USA
| | - Ron Lifshitz
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, 69978 Tel Aviv, Israel
| | - M. C. Cross
- Kavli Nanoscience Institute, California Institute of Technology, Pasadena, California 91125, USA
| | - M. L. Roukes
- Kavli Nanoscience Institute, California Institute of Technology, Pasadena, California 91125, USA
- Corresponding author.
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