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Yang WQ, Niu W, Ma YH, Zhang WZ. Quantum nonlinear effect in a dissipatively coupled optomechanical system. OPTICS EXPRESS 2024; 32:11801-11817. [PMID: 38571019 DOI: 10.1364/oe.518042] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/08/2024] [Accepted: 03/01/2024] [Indexed: 04/05/2024]
Abstract
A full-quantum approach is used to study the quantum nonlinear properties of a compound Michelson-Sagnac interferometer optomechanical system. By deriving the effective Hamiltonian, we find that the reduced system exhibits a Kerr nonlinear term with a complex coefficient, entirely induced by the dissipative and dispersive couplings. Unexpectedly, the nonlinearities resulting from the dissipative coupling possess non-Hermitian Hamiltonian-like properties preserving the quantum nature of the dispersive coupling beyond the traditional system dissipation. This protective mechanism allows the system to exhibit strong quantum nonlinear effects when the detuning (the compound cavity detuning Δc and the auxiliary cavity detuning Δe) and the tunneling coupling strength (J) of two cavities satisfy the relation J2 = ΔcΔe. Moreover, the additive effects of dispersive and dissipative couplings can produce strong anti-bunching effects, which exist in both strong and weak coupling conditions. Our work may provide a new way to study and produce strong quantum nonlinear effects in dissipatively coupled optomechanical systems.
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2
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Pokharel A, Xu H, Venkatachalam S, Collin E, Zhou X. Coupling Capacitively Distinct Mechanical Resonators for Room-Temperature Phonon-Cavity Electromechanics. NANO LETTERS 2022; 22:7351-7357. [PMID: 36083792 DOI: 10.1021/acs.nanolett.2c01848] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Coupled electromechanical resonators that can be independently driven/detected and easily integrated with external circuits are essential for exploring mechanical modes based signal processing and multifunctional integration. One of the main challenges lies in controlling energy transfers between distinct resonators experiencing nanoscale displacements. Here, we present a room temperature electromechanical system that mimics a "phonon-cavity", in analogy with optomechanics. It consists in a silicon nitride membrane capacitively coupled to an aluminum drum-head resonator. We demonstrate electromechanically induced transparency and amplification through manipulating the mechanical displacements of this coupled system, creating interferences in the measured signal. The anti-damping effects, generated by phonon-cavity force, have been observed in both movable objects. We develop an analytical model that captures the analoguous optomechanical features in the classical limit and enables to fit quantitatively the measurements. Our results open up new possibilities for building compact and multifunctional mechanical systems, and exploring phonon-phonon coupling based optomechanics.
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Affiliation(s)
- Alok Pokharel
- Université Lille, CNRS, Centrale Lille, Université Polytechnique Hauts-de-France, UMR 8520, IEMN, F-59000 Lille, France
| | - Hao Xu
- Université Lille, CNRS, Centrale Lille, Université Polytechnique Hauts-de-France, UMR 8520, IEMN, F-59000 Lille, France
| | - Srisaran Venkatachalam
- Université Lille, CNRS, Centrale Lille, Université Polytechnique Hauts-de-France, UMR 8520, IEMN, F-59000 Lille, France
| | - Eddy Collin
- Université Grenoble Alpes, Institut NEEL, CNRS UPR2940, 25 rue des Martyrs, BP 166, 38042 Grenoble, Cedex 9, France
| | - Xin Zhou
- Université Lille, CNRS, Centrale Lille, Université Polytechnique Hauts-de-France, UMR 8520, IEMN, F-59000 Lille, France
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3
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Shin D, Cupertino A, de Jong MHJ, Steeneken PG, Bessa MA, Norte RA. Spiderweb Nanomechanical Resonators via Bayesian Optimization: Inspired by Nature and Guided by Machine Learning. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2022; 34:e2106248. [PMID: 34695265 DOI: 10.1002/adma.202106248] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/10/2021] [Revised: 10/20/2021] [Indexed: 06/13/2023]
Abstract
From ultrasensitive detectors of fundamental forces to quantum networks and sensors, mechanical resonators are enabling next-generation technologies to operate in room-temperature environments. Currently, silicon nitride nanoresonators stand as a leading microchip platform in these advances by allowing for mechanical resonators whose motion is remarkably isolated from ambient thermal noise. However, to date, human intuition has remained the driving force behind design processes. Here, inspired by nature and guided by machine learning, a spiderweb nanomechanical resonator is developed that exhibits vibration modes, which are isolated from ambient thermal environments via a novel "torsional soft-clamping" mechanism discovered by the data-driven optimization algorithm. This bioinspired resonator is then fabricated, experimentally confirming a new paradigm in mechanics with quality factors above 1 billion in room-temperature environments. In contrast to other state-of-the-art resonators, this milestone is achieved with a compact design that does not require sub-micrometer lithographic features or complex phononic bandgaps, making it significantly easier and cheaper to manufacture at large scales. These results demonstrate the ability of machine learning to work in tandem with human intuition to augment creative possibilities and uncover new strategies in computing and nanotechnology.
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Affiliation(s)
- Dongil Shin
- Faculty of Mechanical, Maritime and Materials Engineering, Department of Materials Science and Engineering, Delft University of Technology, Delft, 2628 CD, The Netherlands
- Faculty of Mechanical, Maritime and Materials Engineering, Department of Precision and Microsystems Engineering, Delft University of Technology, Delft, 2628 CD, The Netherlands
| | - Andrea Cupertino
- Faculty of Mechanical, Maritime and Materials Engineering, Department of Precision and Microsystems Engineering, Delft University of Technology, Delft, 2628 CD, The Netherlands
| | - Matthijs H J de Jong
- Faculty of Mechanical, Maritime and Materials Engineering, Department of Precision and Microsystems Engineering, Delft University of Technology, Delft, 2628 CD, The Netherlands
- Faculty of Applied Sciences, Department of Quantum Nanoscience, Kavli Institute of Nanoscience, Delft University of Technology, Delft, 2628 CD, The Netherlands
| | - Peter G Steeneken
- Faculty of Mechanical, Maritime and Materials Engineering, Department of Precision and Microsystems Engineering, Delft University of Technology, Delft, 2628 CD, The Netherlands
- Faculty of Applied Sciences, Department of Quantum Nanoscience, Kavli Institute of Nanoscience, Delft University of Technology, Delft, 2628 CD, The Netherlands
| | - Miguel A Bessa
- Faculty of Mechanical, Maritime and Materials Engineering, Department of Materials Science and Engineering, Delft University of Technology, Delft, 2628 CD, The Netherlands
| | - Richard A Norte
- Faculty of Mechanical, Maritime and Materials Engineering, Department of Precision and Microsystems Engineering, Delft University of Technology, Delft, 2628 CD, The Netherlands
- Faculty of Applied Sciences, Department of Quantum Nanoscience, Kavli Institute of Nanoscience, Delft University of Technology, Delft, 2628 CD, The Netherlands
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4
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Zhou X, Venkatachalam S, Zhou R, Xu H, Pokharel A, Fefferman A, Zaknoune M, Collin E. High- Q Silicon Nitride Drum Resonators Strongly Coupled to Gates. NANO LETTERS 2021; 21:5738-5744. [PMID: 34132554 DOI: 10.1021/acs.nanolett.1c01477] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Silicon nitride (SiN) mechanical resonators with high quality mechanical properties are attractive for fundamental research and applications. However, it is challenging to maintain these mechanical properties while achieving strong coupling to an electrical circuit for efficient on-chip integration. Here, we present a SiN drum resonator covered with an aluminum thin film, enabling large capacitive coupling to a suspended top-gate. Implementing the full electrical measurement scheme, we demonstrate a high quality factor ∼104 (comparable to that of bare drums at room temperature) and present our ability to detect ∼10 mechanical modes at low temperature. The drum resonator is also coupled to a microwave cavity, so that we can perform optomechanical sideband pumping with a fairly good coupling strength G and demonstrate mechanical parametric amplification. This SiN drum resonator design provides efficient electrical integration and exhibits promising features for exploring mode coupling and signal processing.
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Affiliation(s)
- Xin Zhou
- Université de Lille, CNRS, Centrale Lille, Université Polytechnique Hauts-de-France, UMR 8520-IEMN, F-59000 Lille, France
| | - Srisaran Venkatachalam
- Université de Lille, CNRS, Centrale Lille, Université Polytechnique Hauts-de-France, UMR 8520-IEMN, F-59000 Lille, France
| | - Ronghua Zhou
- Université de Lille, CNRS, Centrale Lille, Université Polytechnique Hauts-de-France, UMR 8520-IEMN, F-59000 Lille, France
| | - Hao Xu
- Université de Lille, CNRS, Centrale Lille, Université Polytechnique Hauts-de-France, UMR 8520-IEMN, F-59000 Lille, France
| | - Alok Pokharel
- Université de Lille, CNRS, Centrale Lille, Université Polytechnique Hauts-de-France, UMR 8520-IEMN, F-59000 Lille, France
| | - Andrew Fefferman
- Université Grenoble Alpes, Institut NEEL, CNRS UPR2940, 25 rue des Martyrs, BP 166, 38042 Grenoble Cedex 9, France
| | - Mohammed Zaknoune
- Université de Lille, CNRS, Centrale Lille, Université Polytechnique Hauts-de-France, UMR 8520-IEMN, F-59000 Lille, France
| | - Eddy Collin
- Université Grenoble Alpes, Institut NEEL, CNRS UPR2940, 25 rue des Martyrs, BP 166, 38042 Grenoble Cedex 9, France
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5
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Pearson AN, Khosla KE, Mergenthaler M, Briggs GAD, Laird EA, Ares N. Radio-frequency optomechanical characterization of a silicon nitride drum. Sci Rep 2020; 10:1654. [PMID: 32015416 PMCID: PMC6997228 DOI: 10.1038/s41598-020-58554-x] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/25/2019] [Accepted: 01/13/2020] [Indexed: 11/09/2022] Open
Abstract
On-chip actuation and readout of mechanical motion is key to characterize mechanical resonators and exploit them for new applications. We capacitively couple a silicon nitride membrane to an off resonant radio-frequency cavity formed by a lumped element circuit. Despite a low cavity quality factor (QE ≈ 7.4) and off resonant, room temperature operation, we are able to parametrize several mechanical modes and estimate their optomechanical coupling strengths. This enables real-time measurements of the membrane's driven motion and fast characterization without requiring a superconducting cavity, thereby eliminating the need for cryogenic cooling. Finally, we observe optomechanically induced transparency and absorption, crucial for a number of applications including sensitive metrology, ground state cooling of mechanical motion and slowing of light.
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Affiliation(s)
- A N Pearson
- Department of Materials, University of Oxford, Parks Road, Oxford, OX1 3PH, United Kingdom
| | - K E Khosla
- Center for Engineered Quantum Systems, The School of Mathematics and Physics, The University of Queensland, St. Lucia, Queensland, 4072, Australia.,QOLS, Blackett Laboratory, Imperial College London, London, SW7 2AZ, United Kingdom
| | - M Mergenthaler
- Department of Materials, University of Oxford, Parks Road, Oxford, OX1 3PH, United Kingdom
| | - G A D Briggs
- Department of Materials, University of Oxford, Parks Road, Oxford, OX1 3PH, United Kingdom
| | - E A Laird
- Department of Physics, Lancaster University, Lancaster, LA1 4YB, United Kingdom
| | - N Ares
- Department of Materials, University of Oxford, Parks Road, Oxford, OX1 3PH, United Kingdom.
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6
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Dong X, Dykman MI, Chan HB. Strong negative nonlinear friction from induced two-phonon processes in vibrational systems. Nat Commun 2018; 9:3241. [PMID: 30104694 PMCID: PMC6089905 DOI: 10.1038/s41467-018-05246-w] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/10/2018] [Accepted: 06/25/2018] [Indexed: 12/03/2022] Open
Abstract
Self-sustained vibrations in systems ranging from lasers to clocks to biological systems are often associated with the coefficient of linear friction, which relates the friction force to the velocity, becoming negative. The runaway of the vibration amplitude is prevented by positive nonlinear friction that increases rapidly with the amplitude. Here we use a modulated electromechanical resonator to show that nonlinear friction can be made negative and sufficiently strong to overcome positive linear friction at large vibration amplitudes. The experiment involves applying a drive that simultaneously excites two phonons of the studied mode and a phonon of a faster decaying high-frequency mode. We study generic features of the oscillator dynamics with negative nonlinear friction. Remarkably, self-sustained vibrations of the oscillator require activation in this case. When, in addition, a resonant force is applied, a branch of large-amplitude forced vibrations can emerge, isolated from the branch of the ordinary small-amplitude response. Negative linear friction is known to lead to self-sustained vibrations in many systems. Here, the authors show that when nonlinear negative friction in an electromechanical oscillator becomes larger than its positive linear counterpart such self-sustained vibrations require activation.
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Affiliation(s)
- X Dong
- Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China.,William Mong Institute of Nano Science and Technology, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China
| | - M I Dykman
- Department of Physics and Astronomy, Michigan State University, East Lansing, MI, 48824, USA
| | - H B Chan
- Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China. .,William Mong Institute of Nano Science and Technology, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China.
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7
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Mercier de Lépinay L, Pigeau B, Besga B, Arcizet O. Eigenmode orthogonality breaking and anomalous dynamics in multimode nano-optomechanical systems under non-reciprocal coupling. Nat Commun 2018; 9:1401. [PMID: 29643362 PMCID: PMC5895839 DOI: 10.1038/s41467-018-03741-8] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/11/2017] [Accepted: 03/09/2018] [Indexed: 12/02/2022] Open
Abstract
Thermal motion of nanomechanical probes directly impacts their sensitivities to external forces. Its proper understanding is therefore critical for ultimate force sensing. Here, we investigate a vectorial force field sensor: a singly-clamped nanowire oscillating along two quasi-frequency-degenerate transverse directions. Its insertion in a rotational optical force field couples its eigenmodes non-symmetrically, causing dramatic modifications of its mechanical properties. In particular, the eigenmodes lose their intrinsic orthogonality. We show that this circumstance is at the origin of an anomalous excess of noise and of a violation of the fluctuation dissipation relation. Our model, which quantitatively accounts for all observations, provides a novel modified version of the fluctuation dissipation theorem that remains valid in non-conservative rotational force fields, and that reveals the prominent role of non-axial mechanical susceptibilities. These findings help understand the intriguing properties of thermal fluctuations in non-reciprocally-coupled multimode systems. Understanding the dynamics of nanomechanical probes is important for improving high-sensitivity force field sensing. Here, the authors study the vibrations of a suspended nanowire in the presence of a rotational optical force field which breaks the orthogonality of the nanoresonator eigenmodes.
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Affiliation(s)
| | - Benjamin Pigeau
- Institut Néel, Université Grenoble Alpes - CNRS:UPR2940, 38042, Grenoble, France
| | - Benjamin Besga
- Institut Néel, Université Grenoble Alpes - CNRS:UPR2940, 38042, Grenoble, France
| | - Olivier Arcizet
- Institut Néel, Université Grenoble Alpes - CNRS:UPR2940, 38042, Grenoble, France.
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8
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Hebestreit E, Frimmer M, Reimann R, Dellago C, Ricci F, Novotny L. Calibration and energy measurement of optically levitated nanoparticle sensors. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2018; 89:033111. [PMID: 29604723 DOI: 10.1063/1.5017119] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Optically levitated nanoparticles offer enormous potential for precision sensing. However, as for any other metrology device, the absolute measurement performance of a levitated-particle sensor is limited by the accuracy of the calibration relating the measured signal to an absolute displacement of the particle. Here, we suggest and demonstrate calibration protocols for levitated-nanoparticle sensors. Our calibration procedures include the treatment of anharmonicities in the trapping potential, as well as a protocol using a harmonic driving force, which is applicable if the sensor is coupled to a heat bath of unknown temperature. Finally, using the calibration, we determine the center-of-mass temperature of an optically levitated particle in thermal equilibrium from its motion and discuss the optimal measurement time required to determine the said temperature.
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Affiliation(s)
| | - Martin Frimmer
- Photonics Laboratory, ETH Zürich, 8093 Zürich, Switzerland
| | - René Reimann
- Photonics Laboratory, ETH Zürich, 8093 Zürich, Switzerland
| | - Christoph Dellago
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Wien, Austria
| | - Francesco Ricci
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels, Barcelona 08860, Spain
| | - Lukas Novotny
- Photonics Laboratory, ETH Zürich, 8093 Zürich, Switzerland
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9
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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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10
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Kouh T, Hanay MS, Ekinci KL. Nanomechanical Motion Transducers for Miniaturized Mechanical Systems. MICROMACHINES 2017. [PMCID: PMC6189927 DOI: 10.3390/mi8040108] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Affiliation(s)
- Taejoon Kouh
- Department of Physics, Kookmin University, Seoul 136-702, Korea
- Correspondence: ; Tel.: +82-2-910-4873
| | - M. Selim Hanay
- Department of Mechanical Engineering, and the National Nanotechnology Research Center (UNAM), Bilkent University, Ankara 06800, Turkey;
| | - Kamil L. Ekinci
- Department of Mechanical Engineering, Division of Materials Science and Engineering, and the Photonics Center, Boston University, Boston, MA 02215, USA;
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11
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Sun F, Dong X, Zou J, Dykman MI, Chan HB. Correlated anomalous phase diffusion of coupled phononic modes in a sideband-driven resonator. Nat Commun 2016; 7:12694. [PMID: 27576597 PMCID: PMC5013651 DOI: 10.1038/ncomms12694] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/27/2016] [Accepted: 07/25/2016] [Indexed: 01/01/2023] Open
Abstract
The dynamical backaction from a periodically driven optical cavity can reduce the damping of a mechanical resonator, leading to parametric instability accompanied by self-sustained oscillations. Here we study experimentally and theoretically new aspects of the backaction and the discrete time-translation symmetry of a driven system using a micromechanical resonator with two nonlinearly coupled vibrational modes with strongly differing frequencies and decay rates. We find self-sustained oscillations in both the low- and high-frequency modes. Their frequencies and amplitudes are determined by the nonlinearity, which also leads to bistability and hysteresis. The phase fluctuations of the two modes show near-perfect anti-correlation, a consequence of the discrete time-translation symmetry. Concurrently, the phase of each mode undergoes anomalous diffusion. The phase variance follows a power law time dependence, with an exponent determined by the 1/f-type resonator frequency noise. Our findings enable compensating for the fluctuations using a feedback scheme to achieve stable frequency downconversion. Dynamical backaction from a periodically driven cavity can reduce the damping of a mechanical resonator causing parametric instability. Here, the authors observe simultaneous self-sustained oscillations in both the mechanical and cavity modes and their correlated phase diffusion.
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Affiliation(s)
- F Sun
- Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China
| | - X Dong
- Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China
| | - J Zou
- Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China
| | - M I Dykman
- Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
| | - H B Chan
- Department of Physics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China
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12
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Tunable micro- and nanomechanical resonators. SENSORS 2015; 15:26478-566. [PMID: 26501294 PMCID: PMC4634492 DOI: 10.3390/s151026478] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/28/2015] [Accepted: 10/09/2015] [Indexed: 01/02/2023]
Abstract
Advances in micro- and nanofabrication technologies have enabled the development of novel micro- and nanomechanical resonators which have attracted significant attention due to their fascinating physical properties and growing potential applications. In this review, we have presented a brief overview of the resonance behavior and frequency tuning principles by varying either the mass or the stiffness of resonators. The progress in micro- and nanomechanical resonators using the tuning electrode, tuning fork, and suspended channel structures and made of graphene have been reviewed. We have also highlighted some major influencing factors such as large-amplitude effect, surface effect and fluid effect on the performances of resonators. More specifically, we have addressed the effects of axial stress/strain, residual surface stress and adsorption-induced surface stress on the sensing and detection applications and discussed the current challenges. We have significantly focused on the active and passive frequency tuning methods and techniques for micro- and nanomechanical resonator applications. On one hand, we have comprehensively evaluated the advantages and disadvantages of each strategy, including active methods such as electrothermal, electrostatic, piezoelectrical, dielectric, magnetomotive, photothermal, mode-coupling as well as tension-based tuning mechanisms, and passive techniques such as post-fabrication and post-packaging tuning processes. On the other hand, the tuning capability and challenges to integrate reliable and customizable frequency tuning methods have been addressed. We have additionally concluded with a discussion of important future directions for further tunable micro- and nanomechanical resonators.
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13
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Olcum S, Cermak N, Wasserman SC, Manalis SR. High-speed multiple-mode mass-sensing resolves dynamic nanoscale mass distributions. Nat Commun 2015; 6:7070. [PMID: 25963304 PMCID: PMC4432639 DOI: 10.1038/ncomms8070] [Citation(s) in RCA: 91] [Impact Index Per Article: 10.1] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2014] [Accepted: 03/28/2015] [Indexed: 11/09/2022] Open
Abstract
Simultaneously measuring multiple eigenmode frequencies of nanomechanical resonators can determine the position and mass of surface-adsorbed proteins, and could ultimately reveal the mass tomography of nanoscale analytes. However, existing measurement techniques are slow (<1 Hz bandwidth), limiting throughput and preventing use with resonators generating fast transient signals. Here we develop a general platform for independently and simultaneously oscillating multiple modes of mechanical resonators, enabling frequency measurements that can precisely track fast transient signals within a user-defined bandwidth that exceeds 500 Hz. We use this enhanced bandwidth to resolve signals from multiple nanoparticles flowing simultaneously through a suspended nanochannel resonator and show that four resonant modes are sufficient for determining their individual position and mass with an accuracy near 150 nm and 40 attograms throughout their 150-ms transit. We envision that our method can be readily extended to other systems to increase bandwidth, number of modes, or number of resonators.
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Affiliation(s)
- Selim Olcum
- Koch Institute for Integrative Cancer Research, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Nathan Cermak
- Program in Computational and Systems Biology, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Steven C. Wasserman
- Department of Biological Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Scott R. Manalis
- Koch Institute for Integrative Cancer Research, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Program in Computational and Systems Biology, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Department of Biological Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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14
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Villanueva LG, Schmid S. Evidence of Surface Loss as Ubiquitous Limiting Damping Mechanism in SiN Micro- and Nanomechanical Resonators. PHYSICAL REVIEW LETTERS 2014; 113:227201. [PMID: 25494083 DOI: 10.1103/physrevlett.113.227201] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/26/2014] [Indexed: 06/04/2023]
Abstract
Silicon nitride (SiN) micro- and nanomechanical resonators have attracted a lot of attention in various research fields due to their exceptionally high quality factors (Qs). Despite their popularity, the origin of the limiting loss mechanisms in these structures has remained controversial. In this Letter we propose an analytical model combining acoustic radiation loss with intrinsic loss. The model accurately predicts the resulting mode-dependent Qs of low-stress silicon-rich and high-stress stoichiometric SiN membranes. The large acoustic mismatch of the low-stress membrane to the substrate seems to minimize radiation loss and Qs of higher modes (n∧m≥3) are limited by intrinsic losses. The study of these intrinsic losses in low-stress membranes reveals a linear dependence with the membrane thickness. This finding was confirmed by comparing the intrinsic dissipation of arbitrary (membranes, strings, and cantilevers) SiN resonators extracted from literature, suggesting surface loss as ubiquitous damping mechanism in thin SiN resonators with Q_{surf}=βh and β=6×10^{10}±4×10^{10} m^{-1}. Based on the intrinsic loss the maximal achievable Qs and Qf products for SiN membranes and strings are outlined.
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Affiliation(s)
- L G Villanueva
- Advanced NEMS Group, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - S Schmid
- Department of Micro-and Nanotechnology, Technical University of Denmark, DTU Nanotech, DK-2800 Kongens Lyngby, Denmark
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15
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Biswas TS, Miriyala N, Doolin C, Liu X, Thundat T, Davis JP. Femtogram-scale photothermal spectroscopy of explosive molecules on nanostrings. Anal Chem 2014; 86:11368-72. [PMID: 25329453 DOI: 10.1021/ac503318e] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We demonstrate detection of femtogram-scale quantities of the explosive molecule 1,3,5-trinitroperhydro-1,3,5-triazine (RDX) via combined nanomechanical photothermal spectroscopy and mass desorption. Photothermal spectroscopy provides a spectroscopic fingerprint of the molecule, which is unavailable using mass adsorption/desorption alone. Our measurement, based on thermomechanical measurement of silicon nitride nanostrings, represents the highest mass resolution ever demonstrated via nanomechanical photothermal spectroscopy. This detection scheme is quick, label-free, and is compatible with parallelized molecular analysis of multicomponent targets.
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Affiliation(s)
- T S Biswas
- Department of Physics, University of Alberta , Edmonton, Alberta T6G 2E9, Canada
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16
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Stabilization of a linear nanomechanical oscillator to its thermodynamic limit. Nat Commun 2014; 4:2860. [PMID: 24326974 DOI: 10.1038/ncomms3860] [Citation(s) in RCA: 43] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/18/2013] [Accepted: 11/04/2013] [Indexed: 12/11/2022] Open
Abstract
The rapid development of micro- and nanomechanical oscillators in the past decade has led to the emergence of novel devices and sensors that are opening new frontiers in both applied and fundamental science. The potential of these devices is however affected by their increased sensitivity to external perturbations. Here we report a non-perturbative optomechanical stabilization technique and apply the method to stabilize a linear nanomechanical beam at its thermodynamic limit at room temperature. The reported ability to stabilize a nanomechanical oscillator to the thermodynamic limit can be extended to a variety of systems and increases the sensitivity range of nanomechanical sensors in both fundamental and applied studies.
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17
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Carvalho NC, Fan Y, Le Floch JM, Tobar ME. Piezoelectric voltage coupled reentrant cavity resonator. THE REVIEW OF SCIENTIFIC INSTRUMENTS 2014; 85:104705. [PMID: 25362432 DOI: 10.1063/1.4897482] [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
A piezoelectric voltage coupled microwave reentrant cavity has been developed. The central cavity post is bonded to a piezoelectric actuator allowing the voltage control of small post displacements over a high dynamic range. We show that such a cavity can be implemented as a voltage tunable resonator, a transducer for exciting and measuring mechanical modes of the structure, and a transducer for measuring comparative sensitivity of the piezoelectric material. Experiments were conducted at room and cryogenic temperatures with results verified using Finite Element software.
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Affiliation(s)
- N C Carvalho
- School of Physics, The University of Western Australia, 35 Stirling Hwy, 6009 Crawley, Western Australia, Australia
| | - Y Fan
- School of Physics, The University of Western Australia, 35 Stirling Hwy, 6009 Crawley, Western Australia, Australia
| | - J-M Le Floch
- School of Physics, The University of Western Australia, 35 Stirling Hwy, 6009 Crawley, Western Australia, Australia
| | - M E Tobar
- School of Physics, The University of Western Australia, 35 Stirling Hwy, 6009 Crawley, Western Australia, Australia
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18
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Bagci T, Simonsen A, Schmid S, Villanueva LG, Zeuthen E, Appel J, Taylor JM, Sørensen A, Usami K, Schliesser A, Polzik ES. Optical detection of radio waves through a nanomechanical transducer. Nature 2014; 507:81-5. [DOI: 10.1038/nature13029] [Citation(s) in RCA: 323] [Impact Index Per Article: 32.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/12/2013] [Accepted: 01/13/2014] [Indexed: 11/09/2022]
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19
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Rieger J, Isacsson A, Seitner MJ, Kotthaus JP, Weig EM. Energy losses of nanomechanical resonators induced by atomic force microscopy-controlled mechanical impedance mismatching. Nat Commun 2014; 5:3345. [PMID: 24594876 PMCID: PMC3959189 DOI: 10.1038/ncomms4345] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2013] [Accepted: 01/29/2014] [Indexed: 11/25/2022] Open
Abstract
Clamping losses are a widely discussed damping mechanism in nanoelectromechanical systems, limiting the performance of these devices. Here we present a method to investigate this dissipation channel. Using an atomic force microscope tip as a local perturbation in the clamping region of a nanoelectromechanical resonator, we increase the energy loss of its flexural modes by at least one order of magnitude. We explain this by a transfer of vibrational energy into the cantilever, which is theoretically described by a reduced mechanical impedance mismatch between the resonator and its environment. A theoretical model for this mismatch, in conjunction with finite element simulations of the evanescent strain field of the mechanical modes in the clamping region, allows us to quantitatively analyse data on position and force dependence of the tip-induced damping. Our experiments yield insights into the damping of nanoelectromechanical systems with the prospect of engineering the energy exchange in resonator networks. Minimizing vibrational energy loss between mechanical resonators and their supports in nanomechanical systems is highly desirable. Here, the authors use the tip of an atomic force microscope to press down on the clamping region of the resonator, so as to study and control energy loss of different vibrational modes.
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Affiliation(s)
- Johannes Rieger
- Center for NanoScience (CeNS) and Fakultät für Physik, Ludwig-Maximilians-Universität, Geschwister-Scholl-Platz 1, 80539 München, Germany
| | - Andreas Isacsson
- Department of Applied Physics, Chalmers University of Technology, S-412 96 Göteborg, Sweden
| | - Maximilian J Seitner
- 1] Center for NanoScience (CeNS) and Fakultät für Physik, Ludwig-Maximilians-Universität, Geschwister-Scholl-Platz 1, 80539 München, Germany [2]
| | - Jörg P Kotthaus
- Center for NanoScience (CeNS) and Fakultät für Physik, Ludwig-Maximilians-Universität, Geschwister-Scholl-Platz 1, 80539 München, Germany
| | - Eva M Weig
- 1] Center for NanoScience (CeNS) and Fakultät für Physik, Ludwig-Maximilians-Universität, Geschwister-Scholl-Platz 1, 80539 München, Germany [2]
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20
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Casimir forces on a silicon micromechanical chip. Nat Commun 2013; 4:1845. [PMID: 23673630 DOI: 10.1038/ncomms2842] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/19/2012] [Accepted: 04/08/2013] [Indexed: 11/08/2022] Open
Abstract
Quantum fluctuations give rise to van der Waals and Casimir forces that dominate the interaction between electrically neutral objects at sub-micron separations. Under the trend of miniaturization, such quantum electrodynamical effects are expected to play an important role in micro- and nano-mechanical devices. Nevertheless, utilization of Casimir forces on the chip level remains a major challenge because all experiments so far require an external object to be manually positioned close to the mechanical element. Here by integrating a force-sensing micromechanical beam and an electrostatic actuator on a single chip, we demonstrate the Casimir effect between two micromachined silicon components on the same substrate. A high degree of parallelism between the two near-planar interacting surfaces can be achieved because they are defined in a single lithographic step. Apart from providing a compact platform for Casimir force measurements, this scheme also opens the possibility of tailoring the Casimir force using lithographically defined components of non-conventional shapes.
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21
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Tallur S, Bhave SA. Rayleigh scattering boosted multi-GHz displacement sensitivity in whispering gallery opto-mechanical resonators. OPTICS EXPRESS 2013; 21:27780-27788. [PMID: 24514293 DOI: 10.1364/oe.21.027780] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Finite photon lifetimes for light fields in an opto-mechanical cavity impose a bandwidth limit on displacement sensing at mechanical resonance frequencies beyond the loaded cavity photon decay rate. Opto-mechanical modulation efficiency can be enhanced via multi-GHz transduction techniques such as piezo-opto-mechanics at the cost of on-chip integration. In this paper, we present a novel high bandwidth displacement sense scheme employing Rayleigh scattering in photonic resonators. Using this technique in conjunction with on-chip electrostatic drive in silicon enables efficient modulation at frequencies up to 9.1GHz. Being independent of the drive mechanism, this scheme could readily be extended to piezo-opto-mechanical and all optical transduced systems.
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22
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Lee S, Adiga VP, Barton RA, van der Zande AM, Lee GH, Ilic BR, Gondarenko A, Parpia JM, Craighead HG, Hone J. Graphene metallization of high-stress silicon nitride resonators for electrical integration. NANO LETTERS 2013; 13:4275-4279. [PMID: 23905749 DOI: 10.1021/nl4020414] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
High stress stoichiometric silicon nitride resonators, whose quality factors exceed one million, have shown promise for applications in sensing, signal processing, and optomechanics. Yet, electrical integration of the insulating silicon nitride resonators has been challenging, as depositing even a thin layer of metal degrades the quality factor significantly. In this work, we show that graphene used as a conductive coating for Si3N4 membranes reduces the quality factor by less than 30% on average, which is minimal when compared to the effect of conventional metallization layers such as chromium or aluminum. The electrical integration of Si3N4-Graphene (SiNG) heterostructure resonators is demonstrated with electrical readout and electrostatic tuning of the frequency by up to 0.3% per volt. These studies demonstrate the feasibility of hybrid graphene/nitride mechanical resonators in which the electrical properties of graphene are combined with the superior mechanical performance of silicon nitride.
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Affiliation(s)
- Sunwoo Lee
- Department of Electrical Engineering , Columbia University , New York, New York 10027, United States
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23
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Vanner MR, Hofer J, Cole GD, Aspelmeyer M. Cooling-by-measurement and mechanical state tomography via pulsed optomechanics. Nat Commun 2013; 4:2295. [DOI: 10.1038/ncomms3295] [Citation(s) in RCA: 118] [Impact Index Per Article: 10.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2013] [Accepted: 07/11/2013] [Indexed: 11/10/2022] Open
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24
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Thijssen R, Verhagen E, Kippenberg TJ, Polman A. Plasmon nanomechanical coupling for nanoscale transduction. NANO LETTERS 2013; 13:3293-3297. [PMID: 23746212 DOI: 10.1021/nl4015028] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
We demonstrate plasmon-mechanical coupling in a metalized nanomechanical oscillator. A coupled surface plasmon is excited in the 25 nm wide gap between two metalized silicon nitride beams. The strong plasmonic dispersion allows the nanomechanical beams' thermal motion at a frequency of 4.4 MHz to be efficiently transduced to the optical transmission, with a measured displacement spectral density of 1.11 × 10(-13) m/Hz(1/2). When exciting the second-order plasmonic mode at λ = 780 nm we observe optical-power-induced frequency shifts of the mechanical oscillator. Our results show that novel functionality of plasmonic nanostructures can be achieved through coupling to engineered nanoscale mechanical oscillators.
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Affiliation(s)
- Rutger Thijssen
- Center for Nanophotonics, FOM Institute AMOLF , Science Park 104, 1098XG Amsterdam, The Netherlands
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25
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Kiselev MN, Kikoin KA, Gorelik LY, Shekhter RI. Kondo force in shuttling devices: dynamical probe for a Kondo cloud. PHYSICAL REVIEW LETTERS 2013; 110:066804. [PMID: 23432289 DOI: 10.1103/physrevlett.110.066804] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/20/2012] [Indexed: 06/01/2023]
Abstract
We consider the electromechanical properties of a single-electronic device consisting of a movable quantum dot attached to a vibrating cantilever, forming a tunnel contact with a nonmovable source electrode. We show that the resonance Kondo tunneling of electrons amplifies exponentially the strength of nanoelectromechanical (NEM) coupling in such a device and make the latter insensitive to mesoscopic fluctuations of electronic levels in a nanodot. It is also shown that the study of a Kondo-NEM phenomenon provides additional (as compared with standard conductance measurements in a nonmechanical device) information on retardation effects in the formation of a many-particle cloud accompanying the Kondo tunneling. A possibility for superhigh tunability of mechanical dissipation as well as supersensitive detection of mechanical displacement is demonstrated.
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Affiliation(s)
- M N Kiselev
- The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, I-34151 Trieste, Italy
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26
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Massel F, Cho SU, Pirkkalainen JM, Hakonen PJ, Heikkilä TT, Sillanpää MA. Multimode circuit optomechanics near the quantum limit. Nat Commun 2012; 3:987. [PMID: 22871806 PMCID: PMC3432470 DOI: 10.1038/ncomms1993] [Citation(s) in RCA: 50] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/04/2012] [Accepted: 07/06/2012] [Indexed: 11/27/2022] Open
Abstract
The coupling of distinct systems underlies nearly all physical phenomena. A basic instance is that of interacting harmonic oscillators, giving rise to, for example, the phonon eigenmodes in a lattice. Of particular importance are the interactions in hybrid quantum systems, which can combine the benefits of each part in quantum technologies. Here we investigate a hybrid optomechanical system having three degrees of freedom, consisting of a microwave cavity and two micromechanical beams with closely spaced frequencies around 32 MHz and no direct interaction. We record the first evidence of tripartite optomechanical mixing, implying that the eigenmodes are combinations of one photonic and two phononic modes. We identify an asymmetric dark mode having a long lifetime. Simultaneously, we operate the nearly macroscopic mechanical modes close to the motional quantum ground state, down to 1.8 thermal quanta, achieved by back-action cooling. These results constitute an important advance towards engineering of entangled motional states. Optomechanical systems allow for the exploration of macroscopic behaviour at or near the quantum limit. Massel et al. use micromechanical resonators to study the hybridisation of one photonic and two phononic modes with phonon numbers down to 1.8, showing a coupling between all three degrees of freedom.
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Affiliation(s)
- Francesco Massel
- Low Temperature Laboratory, Aalto University School of Science, P.O. Box 15100, FI-00076 Espoo, Finland
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27
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Faust T, Rieger J, Seitner MJ, Krenn P, Kotthaus JP, Weig EM. Nonadiabatic dynamics of two strongly coupled nanomechanical resonator modes. PHYSICAL REVIEW LETTERS 2012; 109:037205. [PMID: 22861892 DOI: 10.1103/physrevlett.109.037205] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/19/2012] [Indexed: 06/01/2023]
Abstract
The Landau-Zener transition is a fundamental concept for dynamical quantum systems and has been studied in numerous fields of physics. Here, we present a classical mechanical model system exhibiting analogous behavior using two inversely tunable, strongly coupled modes of the same nanomechanical beam resonator. In the adiabatic limit, the anticrossing between the two modes is observed and the coupling strength extracted. Sweeping an initialized mode across the coupling region allows mapping of the progression from diabatic to adiabatic transitions as a function of the sweep rate.
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Affiliation(s)
- Thomas Faust
- Center for NanoScience (CeNS) and Fakultät für Physik, Ludwig-Maximilians-Universität, Geschwister-Scholl-Platz 1, München 80539, Germany
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