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Gely MF, Sanz Mora A, Yanai S, van der Spek R, Bothner D, Steele GA. Apparent nonlinear damping triggered by quantum fluctuations. Nat Commun 2023; 14:7566. [PMID: 37990020 PMCID: PMC10663546 DOI: 10.1038/s41467-023-43128-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: 03/26/2021] [Accepted: 11/01/2023] [Indexed: 11/23/2023] Open
Abstract
Nonlinear damping, the change in damping rate with the amplitude of oscillations plays an important role in many electrical, mechanical and even biological oscillators. In novel technologies such as carbon nanotubes, graphene membranes or superconducting resonators, the origin of nonlinear damping is sometimes unclear. This presents a problem, as the damping rate is a key figure of merit in the application of these systems to extremely precise sensors or quantum computers. Through measurements of a superconducting resonator, we show that from the interplay of quantum fluctuations and the nonlinearity of a Josephson junction emerges a power-dependence in the resonator response which closely resembles nonlinear damping. The phenomenon can be understood and visualized through the flow of quasi-probability in phase space where it reveals itself as dephasing. Crucially, the effect is not restricted to superconducting circuits: we expect that quantum fluctuations or other sources of noise give rise to apparent nonlinear damping in systems with a similar conservative nonlinearity, such as nano-mechanical oscillators or even macroscopic systems.
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Affiliation(s)
- Mario F Gely
- Kavli Institute of NanoScience, Delft University of Technology, PO Box 5046, 2600 GA, Delft, The Netherlands.
- Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford, OX1 3PU, UK.
| | - Adrián Sanz Mora
- Kavli Institute of NanoScience, Delft University of Technology, PO Box 5046, 2600 GA, Delft, The Netherlands
| | - Shun Yanai
- Kavli Institute of NanoScience, Delft University of Technology, PO Box 5046, 2600 GA, Delft, The Netherlands
- Institute for Quantum Computing, University of Waterloo, 200 University Avenue West, Waterloo, ON, N2L 3G1, Canada
- Department of Physics and Astronomy, University of Waterloo, 200 University Avenue West, Waterloo, ON, N2L 3G1, Canada
| | - Rik van der Spek
- Kavli Institute of NanoScience, Delft University of Technology, PO Box 5046, 2600 GA, Delft, The Netherlands
| | - Daniel Bothner
- Kavli Institute of NanoScience, Delft University of Technology, PO Box 5046, 2600 GA, Delft, The Netherlands
- Physikalisches Institut, Center for Quantum Science (CQ) and LISA+, University of Tübingen, Auf der Morgenstelle 14, 72076, Tübingen, Germany
| | - Gary A Steele
- Kavli Institute of NanoScience, Delft University of Technology, PO Box 5046, 2600 GA, Delft, The Netherlands
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Wang M, Perez-Morelo DJ, Lopez D, Aksyuk VA. Persistent Nonlinear Phase-Locking and Nonmonotonic Energy Dissipation in Micromechanical Resonators. PHYSICAL REVIEW. X 2022; 12:10.1103/physrevx.12.041025. [PMID: 38680940 PMCID: PMC11047221 DOI: 10.1103/physrevx.12.041025] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Indexed: 05/01/2024]
Abstract
Many nonlinear systems are described by eigenmodes with amplitude-dependent frequencies, interacting strongly whenever the frequencies become commensurate at internal resonances. Fast energy exchange via the resonances holds the key to rich dynamical behavior, such as time-varying relaxation rates and signatures of nonergodicity in thermal equilibrium, revealed in the recent experimental and theoretical studies of micro- and nanomechanical resonators. However, a universal yet intuitive physical description for these diverse and sometimes contradictory experimental observations remains elusive. Here we experimentally reveal persistent nonlinear phase-locked states occurring at internal resonances and demonstrate that they are essential for understanding the transient dynamics of nonlinear systems with coupled eigenmodes. The measured dynamics of a fully observable micromechanical resonator system are quantitatively described by the lower-frequency mode entering, maintaining, and exiting a persistent phase-locked period-tripling state generated by the nonlinear driving force exerted by the higher-frequency mode. This model describes the observed phase-locked coherence times, the direction and magnitude of the energy exchange, and the resulting nonmonotonic mode energy evolution. Depending on the initial relative phase, the system selects distinct relaxation pathways, either entering or bypassing the locked state. The described persistent phase locking is not limited to particular frequency fractions or types of nonlinearities and may advance nonlinear resonator systems engineering across physical domains, including photonics as well as nanomechanics.
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Affiliation(s)
- Mingkang Wang
- Microsystems and Nanotechnology Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
- Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742, USA
| | - Diego J. Perez-Morelo
- Microsystems and Nanotechnology Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
- Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20742, USA
| | - Daniel Lopez
- Microsystems and Nanotechnology Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
- Materials Research Institute, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Vladimir A. Aksyuk
- Microsystems and Nanotechnology Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
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Keşkekler A, Shoshani O, Lee M, van der Zant HSJ, Steeneken PG, Alijani F. Tuning nonlinear damping in graphene nanoresonators by parametric-direct internal resonance. Nat Commun 2021; 12:1099. [PMID: 33597524 PMCID: PMC7889630 DOI: 10.1038/s41467-021-21334-w] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/08/2020] [Accepted: 01/18/2021] [Indexed: 11/09/2022] Open
Abstract
Mechanical sources of nonlinear damping play a central role in modern physics, from solid-state physics to thermodynamics. The microscopic theory of mechanical dissipation suggests that nonlinear damping of a resonant mode can be strongly enhanced when it is coupled to a vibration mode that is close to twice its resonance frequency. To date, no experimental evidence of this enhancement has been realized. In this letter, we experimentally show that nanoresonators driven into parametric-direct internal resonance provide supporting evidence for the microscopic theory of nonlinear dissipation. By regulating the drive level, we tune the parametric resonance of a graphene nanodrum over a range of 40–70 MHz to reach successive two-to-one internal resonances, leading to a nearly two-fold increase of the nonlinear damping. Our study opens up a route towards utilizing modal interactions and parametric resonance to realize resonators with engineered nonlinear dissipation over wide frequency range. Nonlinear dissipation is frequently observed in nanomechanical resonators, but its microscopic origin remains unclear. Here, nonlinear damping is found to be enhanced in graphene nanodrums close to internal resonance conditions, providing insights on the mechanisms at the basis of this phenomenon.
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Affiliation(s)
- Ata Keşkekler
- Department of Precision and Microsystems Engineering, Delft University of Technology, Mekelweg 2, Delft, 2628 CD, The Netherlands.
| | - Oriel Shoshani
- Department of Mechanical Engineering, Ben-Gurion University of Negev, Beersheba, Israel
| | - Martin Lee
- Kavli Institute of Nanoscience, Delft University of Technology, Lorentzweg 1, Delft, 2628 CJ, The Netherlands
| | - Herre S J van der Zant
- Kavli Institute of Nanoscience, Delft University of Technology, Lorentzweg 1, Delft, 2628 CJ, The Netherlands
| | - Peter G Steeneken
- Department of Precision and Microsystems Engineering, Delft University of Technology, Mekelweg 2, Delft, 2628 CD, The Netherlands.,Kavli Institute of Nanoscience, Delft University of Technology, Lorentzweg 1, Delft, 2628 CJ, The Netherlands
| | - Farbod Alijani
- Department of Precision and Microsystems Engineering, Delft University of Technology, Mekelweg 2, Delft, 2628 CD, The Netherlands.
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Frequency stabilization and noise-induced spectral narrowing in resonators with zero dispersion. Nat Commun 2019; 10:3930. [PMID: 31477718 PMCID: PMC6718662 DOI: 10.1038/s41467-019-11946-8] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2019] [Accepted: 08/02/2019] [Indexed: 11/17/2022] Open
Abstract
Mechanical resonators are widely used as precision clocks and sensitive detectors that rely on the stability of their eigenfrequencies. The phase noise is determined by different factors including thermal noise, frequency noise of the resonator and noise in the feedback circuitry. Increasing the vibration amplitude can mitigate some of these effects but the improvements are limited by nonlinearities that are particularly strong for miniaturized micro- and nano-mechanical systems. Here we design a micromechanical resonator with non-monotonic dependence of the eigenfrequency on energy. Near the extremum, where the dispersion of the eigenfrequency is zero, the system regains certain characteristics of a linear resonator, albeit at large amplitudes. The spectral peak undergoes narrowing when the noise intensity is increased. With the resonator serving as the frequency-selecting element in a feedback loop, the phase noise at the extremum amplitude is ~3 times smaller than the minimal noise in the conventional nonlinear regime. Designing miniaturized oscillators with stable frequencies is challenging due to nonlinearities. Here, the authors demonstrate reduced phase noise using zero dispersion phenomena in a micromechanical resonator designed with non-monotonic dependence of the frequency of eigenoscillations on energy.
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Dykman MI, Rastelli G, Roukes ML, Weig EM. Resonantly Induced Friction and Frequency Combs in Driven Nanomechanical Systems. PHYSICAL REVIEW LETTERS 2019; 122:254301. [PMID: 31347858 DOI: 10.1103/physrevlett.122.254301] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/20/2019] [Revised: 05/10/2019] [Indexed: 05/20/2023]
Abstract
We propose a new mechanism of friction in resonantly driven vibrational systems. The form of the friction force follows from the time- and spatial-symmetry arguments. We consider a microscopic mechanism of this resonant force in nanomechanical systems. The friction can be negative, leading to the onset of self-sustained oscillations of the amplitude and phase of forced vibrations, which result in a frequency comb in the power spectrum.
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Affiliation(s)
- M I Dykman
- Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
| | | | - M L Roukes
- Department of Physics, California Institute of Technology, Pasadena, California 91125, USA
| | - Eva M Weig
- Fachbereich Physik, Universität Konstanz, D-78457 Konstanz, Germany
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