1
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Onah FE, Jaramillo-Ávila BR, Maldonado-Villamizar FH, Rodríguez-Lara BM. Optical coupling control of isolated mechanical resonators. Sci Rep 2024; 14:941. [PMID: 38200050 PMCID: PMC10781770 DOI: 10.1038/s41598-023-50775-0] [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: 06/02/2023] [Accepted: 12/25/2023] [Indexed: 01/12/2024] Open
Abstract
We present a Hamiltonian model describing two pairs of mechanical and optical modes under standard optomechanical interaction. The vibrational modes are mechanically isolated from each other and the optical modes couple evanescently. We recover the ranges for variables of interest, such as mechanical and optical resonant frequencies and naked coupling strengths, using a finite element model for a standard experimental realization. We show that the quantum model, under this parameter range and external optical driving, may be approximated into parametric interaction models for all involved modes. As an example, we study the effect of detuning in the optical resonant frequencies modes and optical driving resolved to mechanical sidebands and show an optical beam splitter with interaction strength dressed by the mechanical excitation number, a mechanical bidirectional coupler, and a two-mode mechanical squeezer where the optical state mediates the interaction strength between the mechanical modes.
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Affiliation(s)
- F E Onah
- Tecnológico de Monterrey, Escuela de Ingeniería y Ciencias, Ave. Eugenio Garza Sada 2501, Monterrey, N.L., 64849, Mexico
- The Division of Theoretical Physics, Physics and Astronomy, University of Nigeria Nsukka, Nsukka Campus, Nsukka, Enugu State, Nigeria
| | - B R Jaramillo-Ávila
- CONAHCYT-CICESE, Unidad Monterrey, Alianza Centro 504, PIIT, Apodaca, Nuevo Leon, 66629, Mexico.
| | - F H Maldonado-Villamizar
- CONAHCYT-Instituto Nacional de Astrofísica, Óptica y Electrónica, Calle Luis Enrique Erro No. 1, Sta. Ma. Tonantzintla, Pue., C.P. 72840, Mexico
| | - B M Rodríguez-Lara
- Universidad Politécnica de Pachuca, Carr. Pachuca-Cd. Sahagún Km.20, Ex-Hda. Santa Bárbara, Zempoala, 43830, Hidalgo, Mexico
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2
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Ignat I, Schuster B, Hafner J, Kwon M, Platz D, Schmid U. Intermodal coupling spectroscopy of mechanical modes in microcantilevers. BEILSTEIN JOURNAL OF NANOTECHNOLOGY 2023; 14:123-132. [PMID: 36743298 PMCID: PMC9874237 DOI: 10.3762/bjnano.14.13] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/23/2022] [Accepted: 01/03/2023] [Indexed: 06/18/2023]
Abstract
Atomic force microscopy (AFM) is highly regarded as a lens peering into the next discoveries of nanotechnology. Fundamental research in atomic interactions, molecular reactions, and biological cell behaviour are key focal points, demanding a continuous increase in resolution and sensitivity. While renowned fields such as optomechanics have marched towards outstanding signal-to-noise ratios, these improvements have yet to find a practical way to AFM. As a solution, we investigate here a mechanism in which individual mechanical eigenmodes of a microcantilever couple to one another, mimicking optomechanical techniques to reduce thermal noise. We have a look at the most commonly used modes in AFM, starting with the first two flexural modes of cantilevers and asses the impact of an amplified coupling between them. In the following, we expand our investigation to the sea of eigenmodes available in the same structure and find a maximum coupling of 9.38 × 103 Hz/nm between two torsional modes. Through such findings we aim to expand the field of multifrequency AFM with innumerable possibilities leading to improved signal-to-noise ratios, all accessible with no additional hardware.
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Affiliation(s)
- Ioan Ignat
- Institute of Sensor and Actuator Systems, TU Wien, Gußhaustraße 27–29, 1040 Vienna, Austria
| | - Bernhard Schuster
- Institute of Sensor and Actuator Systems, TU Wien, Gußhaustraße 27–29, 1040 Vienna, Austria
| | - Jonas Hafner
- Institute of Sensor and Actuator Systems, TU Wien, Gußhaustraße 27–29, 1040 Vienna, Austria
| | - MinHee Kwon
- Institute of Sensor and Actuator Systems, TU Wien, Gußhaustraße 27–29, 1040 Vienna, Austria
| | - Daniel Platz
- Institute of Sensor and Actuator Systems, TU Wien, Gußhaustraße 27–29, 1040 Vienna, Austria
| | - Ulrich Schmid
- Institute of Sensor and Actuator Systems, TU Wien, Gußhaustraße 27–29, 1040 Vienna, Austria
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3
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Catalini L, Rossi M, Langman EC, Schliesser A. Modeling and Observation of Nonlinear Damping in Dissipation-Diluted Nanomechanical Resonators. PHYSICAL REVIEW LETTERS 2021; 126:174101. [PMID: 33988425 DOI: 10.1103/physrevlett.126.174101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/14/2021] [Accepted: 03/29/2021] [Indexed: 06/12/2023]
Abstract
Dissipation dilution enables extremely low linear loss in stressed, high aspect ratio nanomechanical resonators, such as strings or membranes. Here, we report on the observation and theoretical modeling of nonlinear dissipation in such structures. We introduce an analytical model based on von Kármán theory, which can be numerically evaluated using finite-element models for arbitrary geometries. We use this approach to predict nonlinear loss and (Duffing) frequency shift in ultracoherent phononic membrane resonators. A set of systematic measurements with silicon nitride membranes shows good agreement with the model for low-order soft-clamped modes. Our analysis also reveals quantitative connections between these nonlinearities and dissipation dilution. This is of interest for future device design and can provide important insight when diagnosing the performance of dissipation dilution in an experimental setting.
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Affiliation(s)
- Letizia Catalini
- Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100 Copenhagen, Denmark and Center for Hybrid Quantum Networks (Hy-Q), Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Massimiliano Rossi
- Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100 Copenhagen, Denmark and Center for Hybrid Quantum Networks (Hy-Q), Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Eric C Langman
- Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100 Copenhagen, Denmark and Center for Hybrid Quantum Networks (Hy-Q), Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Albert Schliesser
- Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100 Copenhagen, Denmark and Center for Hybrid Quantum Networks (Hy-Q), Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
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4
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Singh R, Sarkar A, Guria C, Nicholl RJT, Chakraborty S, Bolotin KI, Ghosh S. Giant Tunable Mechanical Nonlinearity in Graphene-Silicon Nitride Hybrid Resonator. NANO LETTERS 2020; 20:4659-4666. [PMID: 32437616 DOI: 10.1021/acs.nanolett.0c01586] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/20/2023]
Abstract
High quality factor mechanical resonators have shown great promise in the development of classical and quantum technologies. Simultaneously, progress has been made in developing controlled mechanical nonlinearity. Here, we combine these two directions of progress in a single platform consisting of coupled silicon nitride (SiNx) and graphene mechanical resonators. We show that nonlinear response can be induced on a large area SiNx resonator mode and can be efficiently controlled by coupling it to a gate-tunable, freely suspended graphene mode. The induced nonlinear response of the hybrid modes, as measured on the SiNx resonator surface is giant, with one of the highest measured Duffing constants. We observe a novel phononic frequency comb which we use as an alternate validation of the measured values, along with numerical simulations which are in overall agreement with the measurements.
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Affiliation(s)
- Rajan Singh
- Department of Physics, Indian Institute of Technology, Kanpur UP-208016, India
| | - Arnab Sarkar
- Department of Physics, Indian Institute of Technology, Kanpur UP-208016, India
| | - Chitres Guria
- Department of Physics, Indian Institute of Technology, Kanpur UP-208016, India
| | - Ryan J T Nicholl
- Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235, United States
| | - Sagar Chakraborty
- Department of Physics, Indian Institute of Technology, Kanpur UP-208016, India
| | - Kirill I Bolotin
- Department of Physics, Freie Universitat Berlin, Arnimallee 14, Berlin 14195, Germany
| | - Saikat Ghosh
- Department of Physics, Indian Institute of Technology, Kanpur UP-208016, India
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5
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Zhang JS, Chen AX. Large mechanical squeezing beyond 3dB of hybrid atom-optomechanical systems in a highly unresolved sideband regime. OPTICS EXPRESS 2020; 28:12827-12836. [PMID: 32403771 DOI: 10.1364/oe.389588] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/31/2020] [Accepted: 04/09/2020] [Indexed: 06/11/2023]
Abstract
We propose a scheme for the generation of strong mechanical squeezing beyond 3dB in hybrid atom-optomechanical systems in the highly unresolved sideband (HURSB) regime where the decay rate of cavity is much larger than the frequency of the mechanical oscillator. The system is formed by two two-level atomic ensembles and an optomechanical system with cavity driven by two lasers with different amplitudes. In the HURSB regime, the squeezing of the movable mirror can not be larger than 3dB if no atomic ensemble or only one atomic ensemble is put into the optomechanical system. However, if two atomic ensembles are put into the optomechanical system, the strong mechanical squeezing beyond 3dB is achieved even in the HURSB regime. Our scheme paves the way toward the implementation of strong mechanical squeezing beyond 3dB in hybrid atom-optomechanical systems in experiments.
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6
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Stress-Controlled Frequency Tuning and Parametric Amplification of the Vibrations of Coupled Nanomembranes. APPLIED SCIENCES-BASEL 2019. [DOI: 10.3390/app9224845] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
Noninvasive tuning of the mechanical resonance frequencies of suspended parallel nanomembranes in various monolithic arrays is achieved by piezoelectric control of their tensile stress. Parametric amplification of their thermal fluctuations is shown to be enhanced by the piezoelectric actuation and amplification factors of up to 20 dB in the sub-parametric oscillation threshold regime are observed.
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7
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Zhou X, Zhao C, Xiao D, Sun J, Sobreviela G, Gerrard DD, Chen Y, Flader I, Kenny TW, Wu X, Seshia AA. Dynamic modulation of modal coupling in microelectromechanical gyroscopic ring resonators. Nat Commun 2019; 10:4980. [PMID: 31672971 PMCID: PMC6823415 DOI: 10.1038/s41467-019-12796-0] [Citation(s) in RCA: 36] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2019] [Accepted: 09/18/2019] [Indexed: 11/09/2022] Open
Abstract
Understanding and controlling modal coupling in micro/nanomechanical devices is integral to the design of high-accuracy timing references and inertial sensors. However, insight into specific physical mechanisms underlying modal coupling, and the ability to tune such interactions is limited. Here, we demonstrate that tuneable mode coupling can be achieved in capacitive microelectromechanical devices with dynamic electrostatic fields enabling strong coupling between otherwise uncoupled modes. A vacuum-sealed microelectromechanical silicon ring resonator is employed in this work, with relevance to the gyroscopic lateral modes of vibration. It is shown that a parametric pumping scheme can be implemented through capacitive electrodes surrounding the device that allows for the mode coupling strength to be dynamically tuned, as well as allowing greater flexibility in the control of the coupling stiffness. Electrostatic pump based sideband coupling is demonstrated, and compared to conventional strain-mediated sideband operations. Electrostatic coupling is shown to be very efficient, enabling strong, tunable dynamical coupling.
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Affiliation(s)
- Xin Zhou
- Nanoscience Centre, University of Cambridge, Cambridge, CB3 0FF, UK.,Department of Intelligent Machinery and Instruments, College of Intelligence Science, National University of Defense Technology, Changsha, 410073, China
| | - Chun Zhao
- Nanoscience Centre, University of Cambridge, Cambridge, CB3 0FF, UK
| | - Dingbang Xiao
- Department of Intelligent Machinery and Instruments, College of Intelligence Science, National University of Defense Technology, Changsha, 410073, China.
| | - Jiangkun Sun
- Nanoscience Centre, University of Cambridge, Cambridge, CB3 0FF, UK.,Department of Intelligent Machinery and Instruments, College of Intelligence Science, National University of Defense Technology, Changsha, 410073, China
| | | | - Dustin D Gerrard
- Department of Mechanical Engineering, Stanford University, Stanford, CA, 94305, USA
| | - Yunhan Chen
- Department of Mechanical Engineering, Stanford University, Stanford, CA, 94305, USA
| | - Ian Flader
- Department of Mechanical Engineering, Stanford University, Stanford, CA, 94305, USA
| | - Thomas W Kenny
- Department of Mechanical Engineering, Stanford University, Stanford, CA, 94305, USA
| | - Xuezhong Wu
- Department of Intelligent Machinery and Instruments, College of Intelligence Science, National University of Defense Technology, Changsha, 410073, China
| | - Ashwin A Seshia
- Nanoscience Centre, University of Cambridge, Cambridge, CB3 0FF, UK.
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8
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Wallin CB, De Alba R, Westly D, Holland G, Grutzik S, Rand RH, Zehnder AT, Aksyuk VA, Krylov S, Ilic BR. Nondegenerate Parametric Resonance in Large Ensembles of Coupled Micromechanical Cantilevers with Varying Natural Frequencies. PHYSICAL REVIEW LETTERS 2018; 121:264301. [PMID: 30636140 PMCID: PMC6507417 DOI: 10.1103/physrevlett.121.264301] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/10/2018] [Indexed: 06/09/2023]
Abstract
We investigate the collective dynamics and nondegenerate parametric resonance (NPR) of coplanar, interdigitated arrays of microcantilevers distinguished by their cantilevers having linearly expanding lengths and thus varying natural frequencies. Within a certain excitation frequency range, the resonators begin oscillating via NPR across the entire array consisting of 200 single-crystal silicon cantilevers. Tunable coupling generated from fringing electrostatic fields provides a mechanism to vary the scope of the NPR. Our experimental results are supported by a reduced-order model that reproduces the leading features of our data including the NPR band. The potential for tailoring the coupled response of suspended mechanical structures using NPR presents new possibilities in mass, force, and energy sensing applications, energy harvesting devices, and optomechanical systems.
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Affiliation(s)
- Christopher B. Wallin
- Physical Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
- Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, MD 20742, USA
| | - Roberto De Alba
- Physical Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
- Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, MD 20742, USA
| | - Daron Westly
- Physical Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
| | - Glenn Holland
- Physical Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
| | - Scott Grutzik
- Component Science and Mechanics, Sandia National Laboratories, Albuquerque, NM 87185, USA
| | - Richard H. Rand
- Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA
- Department of Mathematics, Cornell University, Ithaca, NY 14853, USA
| | - Alan T. Zehnder
- Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA
| | - Vladimir A. Aksyuk
- Physical Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
| | - Slava Krylov
- School of Mechanical Engineering, Faculty of Engineering, Tel Aviv University, Ramat Aviv 69978 Tel Aviv Israel
| | - B. Robert Ilic
- Physical Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
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9
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Gu WJ, Yi Z, Sun LH, Yan Y. Generation of mechanical squeezing and entanglement via mechanical modulations. OPTICS EXPRESS 2018; 26:30773-30785. [PMID: 30469969 DOI: 10.1364/oe.26.030773] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/01/2018] [Accepted: 10/29/2018] [Indexed: 06/09/2023]
Abstract
We discuss the generation of strong stationary mechanical squeezing and entanglement in the modulated two-and three-mode optomechanics. Following the reservoir engineering scheme, the beam-splitter and parametric optomechanical interactions can be simultaneously achieved through appropriately choosing the modulation frequency on mechanical motion, which is essential to strong squeezing and entanglement. In the two-mode modulated optomechanics, squeezing is tunable by the relative ratio of parametric and beam-splitter couplings, and also robust to thermal noise due to the simultaneously optically induced cooling process. In the three-mode modulated optomechanics, strong EPR-type entanglement is also attainable, which can surpass the 3dB limit of nondegenerate parametric interaction. However, the ideal entanglement is impossible since only one of mechanical Bogoliubov modes is cooled by the cavity mode, which also makes the entanglement fragile to the mechanical noise.
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10
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Ding S, Maslennikov G, Hablützel R, Matsukevich D. Quantum Simulation with a Trilinear Hamiltonian. PHYSICAL REVIEW LETTERS 2018; 121:130502. [PMID: 30312083 DOI: 10.1103/physrevlett.121.130502] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/28/2018] [Revised: 08/12/2018] [Indexed: 06/08/2023]
Abstract
Interaction among harmonic oscillators described by a trilinear Hamiltonian ℏξ(a^{†}bc+ab^{†}c^{†}) is one of the most fundamental models in quantum optics. By employing the anharmonicity of the Coulomb potential in a linear trapped three-ion crystal, we experimentally implement it among three normal modes of motion in the strong-coupling regime, where the coupling strength is much larger than the decoherence rate of the ion motion. We use it to simulate the interaction of an atom and light as described by the Tavis-Cummings model and the process of nondegenerate parametric down-conversion in the regime of a depleted pump.
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Affiliation(s)
- Shiqian Ding
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543, Singapore
| | - Gleb Maslennikov
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543, Singapore
| | - Roland Hablützel
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543, Singapore
| | - Dzmitry Matsukevich
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543, Singapore
- Department of Physics, National University of Singapore, 2 Science Drive 3, 117551, Singapore
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11
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Anomalous Decay of Nanomechanical Modes Going Through Nonlinear Resonance. Sci Rep 2017; 7:18091. [PMID: 29273755 PMCID: PMC5741793 DOI: 10.1038/s41598-017-17184-6] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/26/2017] [Accepted: 11/20/2017] [Indexed: 11/08/2022] Open
Abstract
Because of the small size of nanomechanical systems, their vibrations become nonlinear already for small amplitudes. Many nontrivial aspects of the vibration dynamics arise from the coexistence of several nonlinearly coupled modes. We show that such coupling can lead to anomalous decay of the modes where they go through nonlinear resonance, so that their amplitude-dependent frequencies become commensurate. We demonstrate the possibility of a strongly nonmonotonic dependence of the decay rate on the amplitude if one of the modes serves as a thermal reservoir for another mode. Where the decay of both modes is slow compared to the rate of resonant energy exchange, the decay is accompanied by amplitude oscillations. Depending on the initial conditions, with increasing time it can display an extremely sharp or a comparatively smooth crossover between different regimes. The results provide insight into recent experimental results by several groups and suggest new ways of characterizing and controlling nanomechanical systems.
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12
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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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13
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Ockeloen-Korppi CF, Damskägg E, Pirkkalainen JM, Clerk AA, Woolley MJ, Sillanpää MA. Quantum Backaction Evading Measurement of Collective Mechanical Modes. PHYSICAL REVIEW LETTERS 2016; 117:140401. [PMID: 27740800 DOI: 10.1103/physrevlett.117.140401] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/08/2016] [Indexed: 06/06/2023]
Abstract
The standard quantum limit constrains the precision of an oscillator position measurement. It arises from a balance between the imprecision and the quantum backaction of the measurement. However, a measurement of only a single quadrature of the oscillator can evade the backaction and be made with arbitrary precision. Here we demonstrate quantum backaction evading measurements of a collective quadrature of two mechanical oscillators, both coupled to a common microwave cavity. The work allows for quantum state tomography of two mechanical oscillators, and provides a foundation for macroscopic mechanical entanglement and force sensing beyond conventional quantum limits.
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Affiliation(s)
- C F Ockeloen-Korppi
- Department of Applied Physics, Aalto University, P.O. Box 15100, FI-00076 AALTO, Finland
| | - E Damskägg
- Department of Applied Physics, Aalto University, P.O. Box 15100, FI-00076 AALTO, Finland
| | - J-M Pirkkalainen
- Department of Applied Physics, Aalto University, P.O. Box 15100, FI-00076 AALTO, Finland
| | - A A Clerk
- Department of Physics, McGill University, 3600 rue University, Montréal, Quebec H3A 2T8, Canada
| | - M J Woolley
- School of Engineering and Information Technology, UNSW Canberra, Australian Capital Territory 2600, Australia
| | - M A Sillanpää
- Department of Applied Physics, Aalto University, P.O. Box 15100, FI-00076 AALTO, Finland
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14
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De Alba R, Massel F, Storch IR, Abhilash TS, Hui A, McEuen PL, Craighead HG, Parpia JM. Tunable phonon-cavity coupling in graphene membranes. NATURE NANOTECHNOLOGY 2016; 11:741-6. [PMID: 27294504 DOI: 10.1038/nnano.2016.86] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/18/2015] [Accepted: 04/26/2016] [Indexed: 05/05/2023]
Abstract
A major achievement of the past decade has been the realization of macroscopic quantum systems by exploiting the interactions between optical cavities and mechanical resonators. In these systems, phonons are coherently annihilated or created in exchange for photons. Similar phenomena have recently been observed through phonon-cavity coupling-energy exchange between the modes of a single system mediated by intrinsic material nonlinearity. This has so far been demonstrated primarily for bulk crystalline, high-quality-factor (Q > 10(5)) mechanical systems operated at cryogenic temperatures. Here, we propose graphene as an ideal candidate for the study of such nonlinear mechanics. The large elastic modulus of this material and capability for spatial symmetry breaking via electrostatic forces is expected to generate a wealth of nonlinear phenomena, including tunable intermodal coupling. We have fabricated circular graphene membranes and report strong phonon-cavity effects at room temperature, despite the modest Q factor (∼100) of this system. We observe both amplification into parametric instability (mechanical lasing) and the cooling of Brownian motion in the fundamental mode through excitation of cavity sidebands. Furthermore, we characterize the quenching of these parametric effects at large vibrational amplitudes, offering a window on the all-mechanical analogue of cavity optomechanics, where the observation of such effects has proven elusive.
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Affiliation(s)
- R De Alba
- Department of Physics, Cornell University, Ithaca, New York 14853, USA
| | - F Massel
- Department of Physics, Nanoscience Center, University of Jyväskylä, Jyväskylä FI-40014, Finland
| | - I R Storch
- Department of Physics, Cornell University, Ithaca, New York 14853, USA
| | - T S Abhilash
- Department of Physics, Cornell University, Ithaca, New York 14853, USA
| | - A Hui
- School of Applied &Engineering Physics, Cornell University, Ithaca, New York 14853, USA
| | - P L McEuen
- Department of Physics, Cornell University, Ithaca, New York 14853, USA
- Kavli Institute at Cornell for Nanoscale Science, Ithaca, New York 14853, USA
| | - H G Craighead
- School of Applied &Engineering Physics, Cornell University, Ithaca, New York 14853, USA
| | - J M Parpia
- Department of Physics, Cornell University, Ithaca, New York 14853, USA
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15
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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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16
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Lemonde MA, Didier N, Clerk AA. Enhanced nonlinear interactions in quantum optomechanics via mechanical amplification. Nat Commun 2016; 7:11338. [PMID: 27108814 PMCID: PMC4848487 DOI: 10.1038/ncomms11338] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/18/2015] [Accepted: 03/14/2016] [Indexed: 11/09/2022] Open
Abstract
The quantum nonlinear regime of optomechanics is reached when nonlinear effects of the radiation pressure interaction are observed at the single-photon level. This requires couplings larger than the mechanical frequency and cavity-damping rate, and is difficult to achieve experimentally. Here we show how to exponentially enhance the single-photon optomechanical coupling strength using only additional linear resources. Our method is based on using a large-amplitude, strongly detuned mechanical parametric drive to amplify mechanical zero-point fluctuations and hence enhance the radiation pressure interaction. It has the further benefit of allowing time-dependent control, enabling pulsed schemes. For a two-cavity optomechanical set-up, we show that our scheme generates photon blockade for experimentally accessible parameters, and even makes the production of photonic states with negative Wigner functions possible. We discuss how our method is an example of a more general strategy for enhancing boson-mediated two-particle interactions and nonlinearities. Optomechanics harnesses the interaction between mechanical resonators and light, but weak matter–single-photon interactions limit studies to the linear regime. Here, the authors show that the interaction can be enhanced by modulating the spring constant of the resonator.
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Affiliation(s)
- Marc-Antoine Lemonde
- Department of Physics, McGill University, 3600 rue University, Montreal, Quebec, Canada H3A 2T8
| | - Nicolas Didier
- Department of Physics, McGill University, 3600 rue University, Montreal, Quebec, Canada H3A 2T8.,Départment de Physique, Université de Sherbrooke, 2500 Boulevard de l'Université, Sherbrooke, Québec, Canada J1K 2R1
| | - Aashish A Clerk
- Department of Physics, McGill University, 3600 rue University, Montreal, Quebec, Canada H3A 2T8
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17
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Pontin A, Bonaldi M, Borrielli A, Marconi L, Marino F, Pandraud G, Prodi GA, Sarro PM, Serra E, Marin F. Dynamical Two-Mode Squeezing of Thermal Fluctuations in a Cavity Optomechanical System. PHYSICAL REVIEW LETTERS 2016; 116:103601. [PMID: 27015479 DOI: 10.1103/physrevlett.116.103601] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/08/2015] [Indexed: 06/05/2023]
Abstract
We report the experimental observation of two-mode squeezing in the oscillation quadratures of a thermal micro-oscillator. This effect is obtained by parametric modulation of the optical spring in a cavity optomechanical system. In addition to stationary variance measurements, we describe the dynamic behavior in the regime of pulsed parametric excitation, showing an enhanced squeezing effect surpassing the stationary 3 dB limit. While the present experiment is in the classical regime, our technique can be exploited to produce entangled, macroscopic quantum optomechanical modes.
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Affiliation(s)
- A Pontin
- Dipartimento di Fisica e Astronomia, Università di Firenze, Via Sansone 1, I-50019 Sesto Fiorentino (FI), Italy
- INFN, Sezione di Firenze, Via Sansone 1, I-50019 Sesto Fiorentino (FI), Italy
| | - M Bonaldi
- Institute of Materials for Electronics and Magnetism, Nanoscience-Trento-FBK Division, 38123 Povo, Trento, Italy
- Istituto Nazionale di Fisica Nucleare (INFN), Trento Institute for Fundamental Physics and Application, I-38123 Povo, Trento, Italy
| | - A Borrielli
- Institute of Materials for Electronics and Magnetism, Nanoscience-Trento-FBK Division, 38123 Povo, Trento, Italy
- Istituto Nazionale di Fisica Nucleare (INFN), Trento Institute for Fundamental Physics and Application, I-38123 Povo, Trento, Italy
| | - L Marconi
- Dipartimento di Fisica e Astronomia, Università di Firenze, Via Sansone 1, I-50019 Sesto Fiorentino (FI), Italy
| | - F Marino
- INFN, Sezione di Firenze, Via Sansone 1, I-50019 Sesto Fiorentino (FI), Italy
- CNR-INO, Largo Enrico Fermi 6, I-50125 Firenze, Italy
| | - G Pandraud
- Department of Microelectronics and Computer Engineering /ECTM/DIMES, Delft University of Technology, Feldmanweg 17, 2628 CT Delft, Netherlands
| | - G A Prodi
- Istituto Nazionale di Fisica Nucleare (INFN), Trento Institute for Fundamental Physics and Application, I-38123 Povo, Trento, Italy
- Dipartimento di Fisica, Università di Trento, I-38123 Povo, Trento, Italy
| | - P M Sarro
- Department of Microelectronics and Computer Engineering /ECTM/DIMES, Delft University of Technology, Feldmanweg 17, 2628 CT Delft, Netherlands
| | - E Serra
- Istituto Nazionale di Fisica Nucleare (INFN), Trento Institute for Fundamental Physics and Application, I-38123 Povo, Trento, Italy
- Department of Microelectronics and Computer Engineering /ECTM/DIMES, Delft University of Technology, Feldmanweg 17, 2628 CT Delft, Netherlands
| | - F Marin
- Dipartimento di Fisica e Astronomia, Università di Firenze, Via Sansone 1, I-50019 Sesto Fiorentino (FI), Italy
- INFN, Sezione di Firenze, Via Sansone 1, I-50019 Sesto Fiorentino (FI), Italy
- CNR-INO, Largo Enrico Fermi 6, I-50125 Firenze, Italy
- European Laboratory for Non-Linear Spectroscopy (LENS), Via Carrara 1, I-50019 Sesto Fiorentino (FI), Italy
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18
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Dong Y, Bariani F, Meystre P. Phonon Cooling by an Optomechanical Heat Pump. PHYSICAL REVIEW LETTERS 2015; 115:223602. [PMID: 26650304 DOI: 10.1103/physrevlett.115.223602] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2015] [Indexed: 06/05/2023]
Abstract
We propose and analyze theoretically a cavity optomechanical analog of a heat pump that uses a polariton fluid to cool mechanical modes coupled to a single precooled phonon mode via external modulation of the substrate of the mechanical resonator. This approach permits us to cool phonon modes of arbitrary frequencies not limited by the cavity-optical field detuning deep into the quantum regime from room temperature.
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Affiliation(s)
- Ying Dong
- Department of Physics, Hangzhou Normal University, Hangzhou, Zhejiang 310036, China
- B2 Institute, Department of Physics and College of Optical Sciences, University of Arizona, Tucson, Arizona 85721, USA
| | - F Bariani
- B2 Institute, Department of Physics and College of Optical Sciences, University of Arizona, Tucson, Arizona 85721, USA
| | - P Meystre
- B2 Institute, Department of Physics and College of Optical Sciences, University of Arizona, Tucson, Arizona 85721, USA
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