1
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Budakian R, Finkler A, Eichler A, Poggio M, Degen CL, Tabatabaei S, Lee I, Hammel PC, Eugene SP, Taminiau TH, Walsworth RL, London P, Bleszynski Jayich A, Ajoy A, Pillai A, Wrachtrup J, Jelezko F, Bae Y, Heinrich AJ, Ast CR, Bertet P, Cappellaro P, Bonato C, Altmann Y, Gauger E. Roadmap on nanoscale magnetic resonance imaging. NANOTECHNOLOGY 2024; 35:412001. [PMID: 38744268 DOI: 10.1088/1361-6528/ad4b23] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2023] [Accepted: 05/14/2024] [Indexed: 05/16/2024]
Abstract
The field of nanoscale magnetic resonance imaging (NanoMRI) was started 30 years ago. It was motivated by the desire to image single molecules and molecular assemblies, such as proteins and virus particles, with near-atomic spatial resolution and on a length scale of 100 nm. Over the years, the NanoMRI field has also expanded to include the goal of useful high-resolution nuclear magnetic resonance (NMR) spectroscopy of molecules under ambient conditions, including samples up to the micron-scale. The realization of these goals requires the development of spin detection techniques that are many orders of magnitude more sensitive than conventional NMR and MRI, capable of detecting and controlling nanoscale ensembles of spins. Over the years, a number of different technical approaches to NanoMRI have emerged, each possessing a distinct set of capabilities for basic and applied areas of science. The goal of this roadmap article is to report the current state of the art in NanoMRI technologies, outline the areas where they are poised to have impact, identify the challenges that lie ahead, and propose methods to meet these challenges. This roadmap also shows how developments in NanoMRI techniques can lead to breakthroughs in emerging quantum science and technology applications.
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Affiliation(s)
- Raffi Budakian
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Canada
- Institute for Quantum Computing, University of Waterloo, Waterloo, Canada
| | - Amit Finkler
- Department of Chemical and Biological Physics, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Alexander Eichler
- Institute for Solid State Physics, ETH Zurich, Otto-Stern-Weg 1, 8093 Zurich, Switzerland
| | - Martino Poggio
- Department of Physics and Swiss Nanoscience Institute, University of Basel, 4056 Basel, Switzerland
| | - Christian L Degen
- Institute for Solid State Physics, ETH Zurich, Otto-Stern-Weg 1, 8093 Zurich, Switzerland
| | - Sahand Tabatabaei
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Canada
- Institute for Quantum Computing, University of Waterloo, Waterloo, Canada
| | - Inhee Lee
- Department of Physics, The Ohio State University, Columbus, OH 43210, United States of America
| | - P Chris Hammel
- Department of Physics, The Ohio State University, Columbus, OH 43210, United States of America
| | - S Polzik Eugene
- Niels Bohr Institute, University of Copenhagen, 17, Copenhagen, 2100, Denmark
| | - Tim H Taminiau
- QuTech and Kavli Institute of Nanoscience, Delft University of Technology, Netherlands
| | - Ronald L Walsworth
- University of Maryland 2218 Kim Engineering Building, College Park, MD 20742, United States of America
| | - Paz London
- Department of Physics, University of California, Santa Barbara, CA 93106, United States of America
| | - Ania Bleszynski Jayich
- Department of Physics, University of California, Santa Barbara, CA 93106, United States of America
| | - Ashok Ajoy
- Department of Chemistry, University of California, Berkeley, CA 97420, United States of America
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Rd, Berkeley, CA 94720, United States of America
- Quantum Information Science Program, CIFAR, 661 University Ave., Toronto, ON M5G 1M1, Canada
| | - Arjun Pillai
- Department of Chemistry, University of California, Berkeley, CA 97420, United States of America
| | - Jörg Wrachtrup
- 3. Physikalisches Institut, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
| | - Fedor Jelezko
- Institute of Quantum Optics, Ulm University, Ulm, 89081, Germany
| | - Yujeong Bae
- Center for Quantum Nanoscience, Institute for Basic Science, Seoul 03760, Republic of Korea
- Department of Physics, Ewha Womans University, Seoul 03760, Republic of Korea
| | - Andreas J Heinrich
- Center for Quantum Nanoscience, Institute for Basic Science, Seoul 03760, Republic of Korea
- Department of Physics, Ewha Womans University, Seoul 03760, Republic of Korea
| | - Christian R Ast
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany
| | - Patrice Bertet
- Université Paris-Saclay, CEA, CNRS, SPEC, 91191 Gif-sur-Yvette, France
| | - Paola Cappellaro
- Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, MA 02139, United States of America
| | - Cristian Bonato
- SUPA, Institute of Photonics and Quantum Sciences, School of Engineering and Physical Sciences, HeriotWatt University, Edinburgh EH14 4AS, United Kingdom
| | - Yoann Altmann
- Institute of Signals, Sensors and Systems, School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom
| | - Erik Gauger
- SUPA, Institute of Photonics and Quantum Sciences, School of Engineering and Physical Sciences, HeriotWatt University, Edinburgh EH14 4AS, United Kingdom
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2
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Xu J, Mao Y, Li Z, Zuo Y, Zhang J, Yang B, Xu W, Liu N, Deng ZJ, Chen W, Xia K, Qiu CW, Zhu Z, Jing H, Liu K. Single-cavity loss-enabled nanometrology. NATURE NANOTECHNOLOGY 2024:10.1038/s41565-024-01729-8. [PMID: 39020101 DOI: 10.1038/s41565-024-01729-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/09/2023] [Accepted: 06/23/2024] [Indexed: 07/19/2024]
Abstract
Optical monitoring of the position and alignment of objects with a precision of only a few nanometres is key in applications such as smart manufacturing and force sensing. Traditional optical nanometrology requires precise nanostructure fabrication, multibeam interference or complex postprocessing algorithms, sometimes hampering wider adoption of this technology. Here we show a simplified, yet robust, approach to achieve nanometric metrology down to 2 nm resolution that eliminates the need for any reference signal for interferometric measurements. We insert an erbium-doped quartz crystal absorber into a single Fabry-Pérot cavity with a length of 3 cm and then induce exceptional points by matching the optical loss with the intercavity coupling. We experimentally achieve a displacement response enhancement of 86 times compared with lossless methods, and theoretically argue that an enhancement of over 450 times, corresponding to subnanometre resolution, may be achievable. We also show a fivefold enhancement in the signal-to-noise ratio, thus demonstrating that non-Hermitian sensors can lead to improved performances over the Hermitian counterpart.
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Affiliation(s)
- Jipeng Xu
- College of Advanced Interdisciplinary Studies, National University of Defense Technology, Changsha, China
- Hunan Provincial Key Laboratory of Novel Nano-Optoelectronic Information Materials and Devices, National University of Defense Technology, Changsha, China
| | - Yuanhao Mao
- College of Advanced Interdisciplinary Studies, National University of Defense Technology, Changsha, China
| | - Zhipeng Li
- Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore
| | - Yunlan Zuo
- Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, Department of Physics, Hunan Normal University, Changsha, China
| | - Jianfa Zhang
- College of Advanced Interdisciplinary Studies, National University of Defense Technology, Changsha, China
- Hunan Provincial Key Laboratory of Novel Nano-Optoelectronic Information Materials and Devices, National University of Defense Technology, Changsha, China
| | - Biao Yang
- College of Advanced Interdisciplinary Studies, National University of Defense Technology, Changsha, China
- Hunan Provincial Key Laboratory of Novel Nano-Optoelectronic Information Materials and Devices, National University of Defense Technology, Changsha, China
| | - Wei Xu
- College of Advanced Interdisciplinary Studies, National University of Defense Technology, Changsha, China
- Hunan Provincial Key Laboratory of Novel Nano-Optoelectronic Information Materials and Devices, National University of Defense Technology, Changsha, China
| | - Ning Liu
- College of Advanced Interdisciplinary Studies, National University of Defense Technology, Changsha, China
- Hunan Provincial Key Laboratory of Novel Nano-Optoelectronic Information Materials and Devices, National University of Defense Technology, Changsha, China
| | - Zhi Jiao Deng
- Institute for Quantum Science and Technology, College of Science, National University of Defense Technology, Changsha, China
| | - Wei Chen
- College of Meteorology and Oceanography, National University of Defense Technology, Changsha, China
| | - Keyu Xia
- College of Engineering and Applied Sciences, National Laboratory of Solid State Microstructures, Nanjing University, Nanjing, China
| | - Cheng-Wei Qiu
- Department of Electrical and Computer Engineering, National University of Singapore, Singapore, Singapore.
| | - Zhihong Zhu
- College of Advanced Interdisciplinary Studies, National University of Defense Technology, Changsha, China.
- Hunan Provincial Key Laboratory of Novel Nano-Optoelectronic Information Materials and Devices, National University of Defense Technology, Changsha, China.
| | - Hui Jing
- Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, Department of Physics, Hunan Normal University, Changsha, China.
| | - Ken Liu
- College of Advanced Interdisciplinary Studies, National University of Defense Technology, Changsha, China.
- Hunan Provincial Key Laboratory of Novel Nano-Optoelectronic Information Materials and Devices, National University of Defense Technology, Changsha, China.
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3
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Bonvin E, Devaud L, Rossi M, Militaru A, Dania L, Bykov DS, Romero-Isart O, Northup TE, Novotny L, Frimmer M. State Expansion of a Levitated Nanoparticle in a Dark Harmonic Potential. PHYSICAL REVIEW LETTERS 2024; 132:253602. [PMID: 38996258 DOI: 10.1103/physrevlett.132.253602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/20/2023] [Revised: 03/22/2024] [Accepted: 05/03/2024] [Indexed: 07/14/2024]
Abstract
We spatially expand and subsequently contract the motional thermal state of a levitated nanoparticle using a hybrid trapping scheme. The particle's center-of-mass motion is initialized in a thermal state (temperature 155 mK) in an optical trap and then expanded by subsequent evolution in a much softer Paul trap in the absence of optical fields. We demonstrate expansion of the motional state's standard deviation in position by a factor of 24. In our system, state expansion occurs devoid of backaction from photon recoil, making this approach suitable for coherent wave function expansion.
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Affiliation(s)
| | | | | | | | | | | | - Oriol Romero-Isart
- Department of Theoretical Physics, University of Innsbruck, Technikerstraße 21a, 6020 Innsbruck, Austria
- Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Innsbruck, Austria
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4
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Engelsen NJ, Beccari A, Kippenberg TJ. Ultrahigh-quality-factor micro- and nanomechanical resonators using dissipation dilution. NATURE NANOTECHNOLOGY 2024; 19:725-737. [PMID: 38443697 DOI: 10.1038/s41565-023-01597-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/11/2023] [Accepted: 12/14/2023] [Indexed: 03/07/2024]
Abstract
Mechanical resonators are widely used in sensors, transducers and optomechanical systems, where mechanical dissipation sets the ultimate limit to performance. Over the past 15 years, the quality factors in strained mechanical resonators have increased by four orders of magnitude, surpassing the previous state of the art achieved in bulk crystalline resonators at room temperature and liquid helium temperatures. In this Review, we describe how these advances were made by leveraging 'dissipation dilution'-where dissipation is reduced through a combination of static tensile strain and geometric nonlinearity in dynamic strain. We then review the state of the art in strained nanomechanical resonators and discuss the potential for even higher quality factors in crystalline materials. Finally, we detail current and future applications of dissipation-diluted mechanical resonators.
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Affiliation(s)
- Nils Johan Engelsen
- Department of Microtechnology and Nanoscience (MC2), Chalmers University of Technology, Gothenburg, Sweden.
| | - Alberto Beccari
- Instutute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL), Lausanne, Switzerland.
- Center for Quantum Science and Engineering, Swiss Federal Institute of Technology Lausanne (EPFL), Lausanne, Switzerland.
| | - Tobias Jan Kippenberg
- Instutute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL), Lausanne, Switzerland.
- Center for Quantum Science and Engineering, Swiss Federal Institute of Technology Lausanne (EPFL), Lausanne, Switzerland.
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5
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Anai K, Enomoto Y, Omura H, Nagano K, Izumi K, Endo M, Takeda S. Quantum-enhanced optical phase-insensitive heterodyne detection beyond 3-dB noise penalty of image band. OPTICS EXPRESS 2024; 32:19372-19387. [PMID: 38859073 DOI: 10.1364/oe.498691] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/03/2023] [Accepted: 05/02/2024] [Indexed: 06/12/2024]
Abstract
Optical phase-insensitive heterodyne (beat-note) detection, which measures the relative phase of two beams at different frequencies through their interference, is a key sensing technology for various spatial/temporal measurements, such as frequency measurements in optical frequency combs. However, its sensitivity is limited not only by shot noise from the signal frequency band but also by the extra shot noise from an image band, known as the 3-dB noise penalty. Here, we propose a method to remove shot noise from all these bands using squeezed light. We also demonstrate beyond-3-dB noise reduction experimentally, confirming that our method actually reduces shot noise from both the signal and extra bands simultaneously. Our work should boost the sensitivity of various spatial/temporal measurements beyond the current limitations.
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6
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Rodrigues IC, Steele GA, Bothner D. Photon Pressure with an Effective Negative Mass Microwave Mode. PHYSICAL REVIEW LETTERS 2024; 132:203603. [PMID: 38829070 DOI: 10.1103/physrevlett.132.203603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/11/2022] [Revised: 03/11/2024] [Accepted: 03/25/2024] [Indexed: 06/05/2024]
Abstract
Harmonic oscillators belong to the most fundamental concepts in physics and are central to many current research fields such as circuit QED, cavity optomechanics, and photon pressure systems. Here, we engineer a microwave mode in a superconducting LC circuit that mimics the dynamics of a negative mass oscillator, and couple it via photon pressure to a second low-frequency circuit. We demonstrate that the effective negative mass dynamics lead to an inversion of dynamical backaction and to sideband cooling of the low-frequency circuit by a blue-detuned pump field, which can be intuitively understood by the inverted energy ladder of a negative mass oscillator.
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Affiliation(s)
- I C Rodrigues
- Kavli Institute of Nanoscience, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands
- Department of Physics, ETH Zürich, Zürich, Switzerland
| | - G A Steele
- Kavli Institute of Nanoscience, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands
| | - D Bothner
- Kavli Institute of Nanoscience, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands
- Physikalisches Institut, Center for Quantum Science (CQ) and LISA, Universität Tübingen, 72076 Tübingen, Germany
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7
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Bærentsen C, Fedorov SA, Østfeldt C, Balabas MV, Zeuthen E, Polzik ES. Squeezed light from an oscillator measured at the rate of oscillation. Nat Commun 2024; 15:4146. [PMID: 38755123 PMCID: PMC11099115 DOI: 10.1038/s41467-024-47906-0] [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: 09/06/2023] [Accepted: 04/15/2024] [Indexed: 05/18/2024] Open
Abstract
Sufficiently fast continuous measurements of the position of an oscillator approach measurements projective on position eigenstates. We evidence the transition into the projective regime for a spin oscillator within an ensemble of 2 × 1010 room-temperature atoms by observing correlations between the quadratures of the meter light field. These correlations squeeze the fluctuations of one light quadrature below the vacuum level. When the measurement is slower than the oscillation, we generate 11 . 5 - 1.5 + 2.5 dB and detect 8 . 5 - 0.1 + 0.1 dB of squeezing in a tunable band that is a fraction of the resonance frequency. When the measurement is as fast as the oscillation, we detect 4.7 dB of squeezing that spans more than one decade of frequencies below the resonance. Our results demonstrate a new regime of continuous quantum measurements on material oscillators, and set a new benchmark for the performance of a linear quantum sensor.
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Affiliation(s)
| | - Sergey A Fedorov
- Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark.
| | | | | | - Emil Zeuthen
- Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark
| | - Eugene S Polzik
- Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark.
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8
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Huang G, Beccari A, Engelsen NJ, Kippenberg TJ. Room-temperature quantum optomechanics using an ultralow noise cavity. Nature 2024; 626:512-516. [PMID: 38356070 PMCID: PMC10866701 DOI: 10.1038/s41586-023-06997-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2023] [Accepted: 12/18/2023] [Indexed: 02/16/2024]
Abstract
At room temperature, mechanical motion driven by the quantum backaction of light has been observed only in pioneering experiments in which an optical restoring force controls the oscillator stiffness1,2. For solid-state mechanical resonators in which oscillations are controlled by the material rigidity, the observation of these effects has been hindered by low mechanical quality factors, optical cavity frequency fluctuations3, thermal intermodulation noise4,5 and photothermal instabilities. Here we overcome these challenges with a phononic-engineered membrane-in-the-middle system. By using phononic-crystal-patterned cavity mirrors, we reduce the cavity frequency noise by more than 700-fold. In this ultralow noise cavity, we insert a membrane resonator with high thermal conductance and a quality factor (Q) of 180 million, engineered using recently developed soft-clamping techniques6,7. These advances enable the operation of the system within a factor of 2.5 of the Heisenberg limit for displacement sensing8, leading to the squeezing of the probe laser by 1.09(1) dB below the vacuum fluctuations. Moreover, the long thermal decoherence time of the membrane oscillator (30 vibrational periods) enables us to prepare conditional displaced thermal states of motion with an occupation of 0.97(2) phonons using a multimode Kalman filter. Our work extends the quantum control of solid-state macroscopic oscillators to room temperature.
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Affiliation(s)
- Guanhao Huang
- Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL), Lausanne, Switzerland
- Center for Quantum Science and Engineering, Swiss Federal Institute of Technology Lausanne (EPFL), Lausanne, Switzerland
| | - Alberto Beccari
- Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL), Lausanne, Switzerland
- Center for Quantum Science and Engineering, Swiss Federal Institute of Technology Lausanne (EPFL), Lausanne, Switzerland
| | - Nils J Engelsen
- Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL), Lausanne, Switzerland.
- Center for Quantum Science and Engineering, Swiss Federal Institute of Technology Lausanne (EPFL), Lausanne, Switzerland.
- Department of Microtechnology and Nanoscience (MC2), Chalmers University of Technology, Göteborg, Sweden.
| | - Tobias J Kippenberg
- Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL), Lausanne, Switzerland.
- Center for Quantum Science and Engineering, Swiss Federal Institute of Technology Lausanne (EPFL), Lausanne, Switzerland.
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9
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Kaczmarek P, Lubiatowski P, Cisowski P, Bręborowicz E, Ogrodowicz P, Grygorowicz M, Laver L, Dudziński W, Romanowski L. Handball players have superior shoulder proprioception: a prospective controlled study. J Shoulder Elbow Surg 2024; 33:e1-e12. [PMID: 37625691 DOI: 10.1016/j.jse.2023.07.028] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 02/21/2023] [Revised: 07/11/2023] [Accepted: 07/21/2023] [Indexed: 08/27/2023]
Abstract
BACKGROUND Proper proprioceptive and neuromuscular control is crucial for the overhead athlete's performance. The aim of the present study was to evaluate the shoulder joint position sense (JPS) levels in overhead throwing athletes. The secondary aim was to confront the proprioceptive abilities with glenohumeral adaptive changes and pathologies among athletes. METHODS Ninety professional handball players and 32 healthy volunteers were recruited. JPS levels were measured by an electronic goniometer and expressed as values of an active reproduction of the joint position (ARJP) and as error of ARJP (EARJP) in 3 different reference positions for each movement (abduction and flexion at 60°, 90°, and 120°; internal [IR] and external rotation [ER] at 30°, 45°, and 60°). RESULTS Side-to-side differences revealed significantly better values of EARJP for the throwing shoulders in abduction at 90° and 120°, flexion at 90° and 120°, IR at 60°, and ER at 30° and 60° compared with the nonthrowing shoulders. Handball players showed significantly better proprioceptive levels in their throwing shoulder compared to the dominant shoulder of the control group in abduction at 90° (P = .037) and 120° (P = .001), flexion at 120° (P = .035), IR at 60° (P = .045), and in ER at 60° (P = .012). DISCUSSION Handball players present superior shoulder JPS in their dominant throwing shoulder at high range of motion angles when compared to a nonathlete population and to their own nondominant shoulder.
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Affiliation(s)
| | - Przemysław Lubiatowski
- Rehasport Clinic, Poznań, Poland; Department of Traumatology, Orthopaedics and Hand Surgery, Poznań University of Medical Sciences, Poznań, Poland.
| | - Paweł Cisowski
- Rehasport Clinic, Poznań, Poland; Department of Spine Disorders and Pediatric Orthopedics, Poznań University of Medical Sciences, Poznań, Poland
| | - Ewa Bręborowicz
- Department of Traumatology, Orthopaedics and Hand Surgery, Poznań University of Medical Sciences, Poznań, Poland
| | - Piotr Ogrodowicz
- Rehasport Clinic, Poznań, Poland; Department of Traumatology, Orthopaedics and Hand Surgery, Poznań University of Medical Sciences, Poznań, Poland
| | | | - Lior Laver
- Hillel Yaffe Medical Center, Hadera, Israel; ArthroSport Clinic, Tel-Aviv, Israel
| | | | - Leszek Romanowski
- Department of Traumatology, Orthopaedics and Hand Surgery, Poznań University of Medical Sciences, Poznań, Poland
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10
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Gietka K, Hotter C, Ritsch H. Unique Steady-State Squeezing in a Driven Quantum Rabi Model. PHYSICAL REVIEW LETTERS 2023; 131:223604. [PMID: 38101370 DOI: 10.1103/physrevlett.131.223604] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/22/2023] [Accepted: 11/06/2023] [Indexed: 12/17/2023]
Abstract
Squeezing is essential to many quantum technologies and our understanding of quantum physics. Here, we show a novel type of steady-state squeezing that can be generated in the closed and open quantum Rabi as well as Dicke model. To this end, we eliminate the spin dynamics which effectively leads to an abstract harmonic oscillator whose eigenstates are squeezed with respect to the noninteracting harmonic oscillator. By driving the system, we generate squeezing which has the unique property of time-independent uncertainties and squeezed dynamics. Such squeezing might find applications in continuous backaction evading measurements and should already be observable in optomechanical systems and Coulomb crystals.
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Affiliation(s)
- Karol Gietka
- Institut für Theoretische Physik, Universität Innsbruck, A-6020 Innsbruck, Austria
| | - Christoph Hotter
- Institut für Theoretische Physik, Universität Innsbruck, A-6020 Innsbruck, Austria
| | - Helmut Ritsch
- Institut für Theoretische Physik, Universität Innsbruck, A-6020 Innsbruck, Austria
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11
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Motazedifard A, Dalafi A, Naderi MH. Negative cavity photon spectral function in an optomechanical system with two parametrically-driven mechanical modes. OPTICS EXPRESS 2023; 31:36615-36637. [PMID: 38017809 DOI: 10.1364/oe.499409] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2023] [Accepted: 10/05/2023] [Indexed: 11/30/2023]
Abstract
We propose an experimentally feasible optomechanical scheme to realize a negative cavity photon spectral function (CPSF) which is equivalent to a negative absorption. The system under consideration is an optomechanical system consisting of two mechanical (phononic) modes which are linearly coupled to a common cavity mode via the radiation pressure while parametrically driven through the coherent time-modulation of their spring coefficients. Using the equations of motion for the cavity retarded Green's function obtained in the framework of the generalized linear response theory, we show that in the red-detuned and weak-coupling regimes a frequency-dependent effective cavity damping rate (ECDR) corresponding to a negative CPSF can be realized by controlling the cooperativities and modulation parameters while the system still remains in the stable regime. Nevertheless, such a negativity which acts as an optomechanical gain never occurs in a standard (an unmodulated bare) cavity optomechanical system. Besides, we find that the presence of two modulated mechanical degrees of freedom provides more controllability over the magnitude and bandwidth of the negativity of CPSF, in comparison to the setup with a single modulated mechanical oscillator. Interestingly, the introduced negativity may open a new platform to realize an extraordinary (modified) optomechanically induced transparency (in which the input signal is amplified in the output) leading to a perfect tunable optomechanical filter with switchable bandwidth which can be used as an optical transistor.
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12
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Jia J, Novikov V, Brasil TB, Zeuthen E, Müller JH, Polzik ES. Acoustic frequency atomic spin oscillator in the quantum regime. Nat Commun 2023; 14:6396. [PMID: 37828042 PMCID: PMC10570288 DOI: 10.1038/s41467-023-42059-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/16/2023] [Accepted: 09/28/2023] [Indexed: 10/14/2023] Open
Abstract
Quantum noise reduction and entanglement-enhanced sensing in the acoustic frequency range is an outstanding challenge relevant for a number of applications including magnetometry and broadband noise reduction in gravitational wave detectors. Here we experimentally demonstrate quantum behavior of a macroscopic atomic spin oscillator in the acoustic frequency range. Quantum back-action of the spin measurement, ponderomotive squeezing of light, and virtual spring softening are observed at oscillation frequencies down to the sub-kHz range. Quantum noise sources characteristic of spin oscillators operating in the near-DC frequency range are identified and means for their mitigation are presented.
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Affiliation(s)
- Jun Jia
- Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark
| | - Valeriy Novikov
- Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark
- Russian Quantum Center, Skolkovo, Moscow, Russia
| | | | - Emil Zeuthen
- Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark
| | | | - Eugene S Polzik
- Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark.
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13
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Ho LB. Quantum backaction effects in sequential measurements. ANNALS OF PHYSICS 2023; 453:169310. [DOI: 10.1016/j.aop.2023.169310] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/01/2023]
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14
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Subhash S, Das S, Dey TN, Li Y, Davuluri S. Enhancing the force sensitivity of a squeezed light optomechanical interferometer. OPTICS EXPRESS 2023; 31:177-191. [PMID: 36606959 DOI: 10.1364/oe.476672] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/29/2022] [Accepted: 12/01/2022] [Indexed: 06/17/2023]
Abstract
Application of frequency-dependent squeezed vacuum improves the force sensitivity of an optomechanical interferometer beyond the standard quantum limit by a factor of e-r, where r is the squeezing parameter. In this work, we show that the application of squeezed light along with quantum back-action nullifying meter in an optomechanical cavity with mechanical mirror in middle configuration can enhance the sensitivity beyond the standard quantum limit by a factor of e-reff, where reff = r + ln(4Δ/ζ)/2, for 0 < ζ/Δ < 1, with ζ as the optomechanical cavity decay rate and Δ as the detuning between cavity eigenfrequency and driving field. The technique described in this work is restricted to frequencies much smaller than the resonance frequency of the mechanical mirror. We further studied the sensitivity as a function of temperature, mechanical mirror reflectivity, and input laser power.
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15
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Xiong B, Chao S, Shan C, Liu J. Optomechanical squeezing with pulse modulation. OPTICS LETTERS 2022; 47:5545-5548. [PMID: 37219265 DOI: 10.1364/ol.471230] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/22/2022] [Accepted: 09/28/2022] [Indexed: 05/24/2023]
Abstract
Quantum control technology provides an increasingly useful toolbox for quantum information tasks. In this Letter, by introducing a pulsed coupling to a standard optomechanical system, we show that stronger squeezing can be obtained with pulse modulation due to the reduction of the heating coefficient. Also, the general squeezed states, such as the squeezed vacuum, squeezed coherent, and squeezed cat states, can be obtained with their squeezing level exceeding 3 dB. Moreover, our scheme is robust to cavity decay, thermal temperature, and classical noise, which is friendly to experiments. The present work can extend the application of quantum engineering technology in optomechanical systems.
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16
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Junker J, Wilken D, Johny N, Steinmeyer D, Heurs M. Frequency-Dependent Squeezing from a Detuned Squeezer. PHYSICAL REVIEW LETTERS 2022; 129:033602. [PMID: 35905360 DOI: 10.1103/physrevlett.129.033602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/03/2022] [Accepted: 05/31/2022] [Indexed: 06/15/2023]
Abstract
Frequency-dependent squeezing is a promising technique to overcome the standard quantum limit in optomechanical force measurements, e.g., gravitational wave detectors. For the first time, we show that frequency-dependent squeezing can be produced by detuning an optical parametric oscillator from resonance. Its frequency-dependent Wigner function is reconstructed quantum tomographically and exhibits a rotation by 39°, along which the noise is reduced by up to 5.5 dB. Our setup is suitable for realizing effective negative-mass oscillators required for coherent quantum noise cancellation.
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Affiliation(s)
- Jonas Junker
- Max Planck Institute for Gravitational Physics (Albert Einstein Institute), and Institute for Gravitational Physics, Leibniz Universität Hannover, Callinstraße 38, 30167 Hannover, Germany
| | - Dennis Wilken
- Max Planck Institute for Gravitational Physics (Albert Einstein Institute), and Institute for Gravitational Physics, Leibniz Universität Hannover, Callinstraße 38, 30167 Hannover, Germany
| | - Nived Johny
- Max Planck Institute for Gravitational Physics (Albert Einstein Institute), and Institute for Gravitational Physics, Leibniz Universität Hannover, Callinstraße 38, 30167 Hannover, Germany
| | - Daniel Steinmeyer
- Max Planck Institute for Gravitational Physics (Albert Einstein Institute), and Institute for Gravitational Physics, Leibniz Universität Hannover, Callinstraße 38, 30167 Hannover, Germany
| | - Michèle Heurs
- Max Planck Institute for Gravitational Physics (Albert Einstein Institute), and Institute for Gravitational Physics, Leibniz Universität Hannover, Callinstraße 38, 30167 Hannover, Germany
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17
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Pereira L, García-Ripoll JJ, Ramos T. Complete Physical Characterization of Quantum Nondemolition Measurements via Tomography. PHYSICAL REVIEW LETTERS 2022; 129:010402. [PMID: 35841584 DOI: 10.1103/physrevlett.129.010402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/29/2021] [Accepted: 06/03/2022] [Indexed: 06/15/2023]
Abstract
We introduce a self-consistent tomography for arbitrary quantum nondemolition (QND) detectors. Based on this, we build a complete physical characterization of the detector, including the measurement processes and a quantification of the fidelity, ideality, and backaction of the measurement. This framework is a diagnostic tool for the dynamics of QND detectors, allowing us to identify errors, and to improve their calibration and design. We illustrate this on a realistic Jaynes-Cummings simulation of a superconducting qubit readout. We characterize nondispersive errors, quantify the backaction introduced by the readout cavity, and calibrate the optimal measurement point.
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Affiliation(s)
- L Pereira
- Instituto de Física Fundamental IFF-CSIC, Calle Serrano 113b, Madrid 28006, Spain
| | - J J García-Ripoll
- Instituto de Física Fundamental IFF-CSIC, Calle Serrano 113b, Madrid 28006, Spain
| | - T Ramos
- Instituto de Física Fundamental IFF-CSIC, Calle Serrano 113b, Madrid 28006, Spain
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18
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Tsinovoy A, Katz O, Landau A, Moiseyev N. Enhanced Coupling of Electron and Nuclear Spins by Quantum Tunneling Resonances. PHYSICAL REVIEW LETTERS 2022; 128:013401. [PMID: 35061487 DOI: 10.1103/physrevlett.128.013401] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/20/2020] [Revised: 09/10/2021] [Accepted: 11/29/2021] [Indexed: 06/14/2023]
Abstract
Noble-gas spins feature hours-long coherence times, owing to their great isolation from the environment, and find practical usage in various applications. However, this isolation leads to extremely slow preparation times, relying on weak spin transfer from an electron-spin ensemble. Here we propose a controllable mechanism to enhance this transfer rate. We analyze the spin dynamics of helium-3 atoms with hot, optically excited potassium atoms and reveal the formation of quasibound states in resonant binary collisions. We find a resonant enhancement of the spin-exchange cross section by up to 6 orders of magnitude and 2 orders of magnitude enhancement for the thermally averaged, polarization rate coefficient. We further examine the effect for various other noble gases and find that the enhancement is universal. We outline feasible conditions under which the enhancement may be experimentally observed and practically utilized.
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Affiliation(s)
- Anatoli Tsinovoy
- Faculty of Physics, Solid State Institute, Technion-Israel Institute of Technology, Haifa 3200003, Israel
- Rafael, Ltd., Haifa 3102102, Israel
| | - Or Katz
- Rafael, Ltd., Haifa 3102102, Israel
| | - Arie Landau
- Institute of Advanced Studies in Theoretical Chemistry, Technion-Israel Institute of Technology, Haifa 3200003, Israel
- Schulich Faculty of Chemistry, Technion-Israel Institute of Technology, Haifa 3200003, Israel
| | - Nimrod Moiseyev
- Faculty of Physics, Solid State Institute, Technion-Israel Institute of Technology, Haifa 3200003, Israel
- Schulich Faculty of Chemistry, Technion-Israel Institute of Technology, Haifa 3200003, Israel
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19
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Thomas RA, Østfeldt C, Bærentsen C, Parniak M, Polzik ES. Calibration of spin-light coupling by coherently induced Faraday rotation. OPTICS EXPRESS 2021; 29:23637-23653. [PMID: 34614626 DOI: 10.1364/oe.425613] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/25/2021] [Accepted: 06/08/2021] [Indexed: 06/13/2023]
Abstract
Calibrating the strength of the light-matter interaction is an important experimental task in quantum information and quantum state engineering protocols. The strength of the off-resonant light-matter interaction in multi-atom spin oscillators can be characterized by the readout rate ΓS. Here we introduce the method named Coherently Induced FAraday Rotation (CIFAR) for determining the readout rate. The method is suited for both continuous and pulsed readout of the spin oscillator, relying only on applying a known polarization modulation to the probe laser beam and detecting a known optical polarization component. Importantly, the method does not require changes to the optical and magnetic fields performing the state preparation and probing. The CIFAR signal is also independent of the probe beam photo-detection quantum efficiency, and allows direct extraction of other parameters of the interaction, such as the tensor coupling ζS, and the damping rate γS. We verify this method in the continuous wave regime, probing a strongly coupled spin oscillator prepared in a warm cesium atomic vapour.
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20
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Boulebnane S, Woods MP, Renes JM. Waveform Estimation from Approximate Quantum Nondemolition Measurements. PHYSICAL REVIEW LETTERS 2021; 127:010502. [PMID: 34270289 DOI: 10.1103/physrevlett.127.010502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/07/2020] [Revised: 03/22/2021] [Accepted: 05/07/2021] [Indexed: 06/13/2023]
Abstract
With the advent of gravitational wave detectors employing squeezed light, quantum waveform estimation-estimating a time-dependent signal by means of a quantum-mechanical probe-is of increasing importance. As is well known, backaction of quantum measurement limits the precision with which the waveform can be estimated, though these limits can, in principle, be overcome by "quantum nondemolition" (QND) measurement setups found in the literature. Strictly speaking, however, their implementation would require infinite energy, as their mathematical description involves Hamiltonians unbounded from below. This raises the question of how well one may approximate nondemolition setups with finite energy or finite-dimensional realizations. Here we consider a finite-dimensional waveform estimation setup based on the "quasi-ideal clock" and show that the estimation errors due to approximating the QND condition decrease slowly, as a power law, with increasing dimension. As a result, we find that approximating QND with this system requires large energy or dimensionality. We argue that this result can be expected to also hold for setups based on truncated oscillators or spin systems.
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Affiliation(s)
- Sami Boulebnane
- Department of Computer Science, University College London, London WC1E 6EA, United Kingdom
- Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland
| | - Mischa P Woods
- Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland
| | - Joseph M Renes
- Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland
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21
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Chao SL, Yang Z, Zhao CS, Peng R, Zhou L. Force sensing in a dual-mode optomechanical system with linear-quadratic coupling and modulated photon hopping. OPTICS LETTERS 2021; 46:3075-3078. [PMID: 34197384 DOI: 10.1364/ol.425484] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/19/2021] [Accepted: 06/01/2021] [Indexed: 06/13/2023]
Abstract
A weak force sensor scheme is presented in an optomechanical system, in which the two cavity modes couple to a mechanical mode with linear and quadratic coupling. Due to introducing time-dependent hopping, the linear and quadratic coupling terms coexist under the rotating-wave approximation in the interaction picture. Compared with the quantum non-demolition measurement (ignoring the quadratic optomechanical coupling), the current scheme can decrease the additional noise to a lower level. Our proposal provides a promising platform for improving the detection of a weak force.
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22
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Mercier de Lépinay L, Ockeloen-Korppi CF, Woolley MJ, Sillanpää MA. Quantum mechanics-free subsystem with mechanical oscillators. Science 2021; 372:625-629. [PMID: 33958476 DOI: 10.1126/science.abf5389] [Citation(s) in RCA: 27] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/04/2020] [Accepted: 03/01/2021] [Indexed: 11/02/2022]
Abstract
Quantum mechanics sets a limit for the precision of continuous measurement of the position of an oscillator. We show how it is possible to measure an oscillator without quantum back-action of the measurement by constructing one effective oscillator from two physical oscillators. We realize such a quantum mechanics-free subsystem using two micromechanical oscillators, and show the measurements of two collective quadratures while evading the quantum back-action by 8 decibels on both of them, obtaining a total noise within a factor of 2 of the full quantum limit. This facilitates the detection of weak forces and the generation and measurement of nonclassical motional states of the oscillators. Moreover, we directly verify the quantum entanglement of the two oscillators by measuring the Duan quantity 1.4 decibels below the separability bound.
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Affiliation(s)
- Laure Mercier de Lépinay
- QTF Centre of Excellence, Department of Applied Physics, Aalto University, FI-00076 Aalto, Finland
| | - Caspar F Ockeloen-Korppi
- QTF Centre of Excellence, Department of Applied Physics, Aalto University, FI-00076 Aalto, Finland
| | - Matthew J Woolley
- School of Engineering and Information Technology, UNSW Canberra, Canberra, ACT 2600, Australia
| | - Mika A Sillanpää
- QTF Centre of Excellence, Department of Applied Physics, Aalto University, FI-00076 Aalto, Finland.
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23
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Affiliation(s)
- Hoi-Kwan Lau
- Department of Physics, Simon Fraser University, Burnaby, BC, Canada
| | - Aashish A Clerk
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, IL, USA.
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24
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Katz O, Shaham R, Firstenberg O. Coupling light to a nuclear spin gas with a two-photon linewidth of five millihertz. SCIENCE ADVANCES 2021; 7:eabe9164. [PMID: 33811073 PMCID: PMC11057697 DOI: 10.1126/sciadv.abe9164] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/22/2020] [Accepted: 02/12/2021] [Indexed: 06/12/2023]
Abstract
Nuclear spins of noble gases feature extremely long coherence times but are inaccessible to optical photons. Here, we realize a coherent interface between light and noble-gas spins that is mediated by alkali atoms. We demonstrate the optical excitation of the noble-gas spins and observe the coherent back action on the light in the form of high-contrast two-photon spectra. We report on a record two-photon linewidth of 5 ± 0.7 mHz above room temperature, corresponding to a 1-min coherence time. This experiment provides a demonstration of coherent bidirectional coupling between light and noble-gas spins, rendering their long-lived spin coherence accessible for manipulations in the optical domain.
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Affiliation(s)
- Or Katz
- Department of Physics of Complex Systems, Weizmann Institute of Science, 7610001 Rehovot, Israel
- Rafael Ltd, IL-31021 Haifa, Israel
| | - Roy Shaham
- Department of Physics of Complex Systems, Weizmann Institute of Science, 7610001 Rehovot, Israel
- Rafael Ltd, IL-31021 Haifa, Israel
| | - Ofer Firstenberg
- Department of Physics of Complex Systems, Weizmann Institute of Science, 7610001 Rehovot, Israel.
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25
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Davuluri S. Quantum optomechanics without the radiation pressure force noise. OPTICS LETTERS 2021; 46:904-907. [PMID: 33577544 DOI: 10.1364/ol.412822] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/16/2020] [Accepted: 01/13/2021] [Indexed: 06/12/2023]
Abstract
This Letter proposes a new method to eliminate the quantum radiation pressure force noise in optomechanics at frequencies much smaller than the resonance frequency of the optomechanical mirror. With no radiation pressure force noise, the shot noise and thermal noise together determine the total noise in the system. The force sensitivity of the optomechanical cavity is improved beyond standard quantum limit at frequencies much smaller than the resonance frequency of the mechanical oscillator. Finally, optimum optomechanical cavity design parameters for attaining the best sensitivity are discussed.
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26
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Thomas RA, Parniak M, Østfeldt C, Møller CB, Bærentsen C, Tsaturyan Y, Schliesser A, Appel J, Zeuthen E, Polzik ES. Entanglement between distant macroscopic mechanical and spin systems. NATURE PHYSICS 2021; 17:228-233. [PMID: 0 DOI: 10.1038/s41567-020-1031-5] [Citation(s) in RCA: 22] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/01/2020] [Accepted: 08/06/2020] [Indexed: 05/24/2023]
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27
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Wu KD, Bäumer E, Tang JF, Hovhannisyan KV, Perarnau-Llobet M, Xiang GY, Li CF, Guo GC. Minimizing Backaction through Entangled Measurements. PHYSICAL REVIEW LETTERS 2020; 125:210401. [PMID: 33275014 DOI: 10.1103/physrevlett.125.210401] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/14/2020] [Accepted: 10/05/2020] [Indexed: 06/12/2023]
Abstract
When an observable is measured on an evolving coherent quantum system twice, the first measurement generally alters the statistics of the second one, which is known as measurement backaction. We introduce, and push to its theoretical and experimental limits, a novel method of backaction evasion, whereby entangled collective measurements are performed on several copies of the system. This method is inspired by a similar idea designed for the problem of measuring quantum work [Perarnau-Llobet et al., Phys. Rev. Lett. 118, 070601 (2017)PRLTAO0031-900710.1103/PhysRevLett.118.070601]. By using entanglement as a resource, we show that the backaction can be extremely suppressed compared to all previous schemes. Importantly, the backaction can be eliminated in highly coherent processes.
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Affiliation(s)
- Kang-Da Wu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Elisa Bäumer
- Institute for Theoretical Physics, ETH Zurich, 8093 Zürich, Switzerland
| | - Jun-Feng Tang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Karen V Hovhannisyan
- The Abdus Salam International Centre for Theoretical Physics (ICTP), Strada Costiera 11, 34151 Trieste, Italy
| | | | - Guo-Yong Xiang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Chuan-Feng Li
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Guang-Can Guo
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
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28
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Retrodiction beyond the Heisenberg uncertainty relation. Nat Commun 2020; 11:5658. [PMID: 33168831 PMCID: PMC7652952 DOI: 10.1038/s41467-020-19495-1] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/28/2020] [Accepted: 10/14/2020] [Indexed: 11/23/2022] Open
Abstract
In quantum mechanics, the Heisenberg uncertainty relation presents an ultimate limit to the precision by which one can predict the outcome of position and momentum measurements on a particle. Heisenberg explicitly stated this relation for the prediction of “hypothetical future measurements”, and it does not describe the situation where knowledge is available about the system both earlier and later than the time of the measurement. Here, we study what happens under such circumstances with an atomic ensemble containing 1011 rubidium atoms, initiated nearly in the ground state in the presence of a magnetic field. The collective spin observables of the atoms are then well described by canonical position and momentum observables, \documentclass[12pt]{minimal}
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\begin{document}$$[{\hat{x}}_{\text{A}},{\hat{p}}_{\text{A}}]=i\hslash$$\end{document}[x^A,p^A]=iℏ. Quantum non-demolition measurements of \documentclass[12pt]{minimal}
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\begin{document}$${\hat{p}}_{\text{A}}$$\end{document}p^A before and of \documentclass[12pt]{minimal}
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\begin{document}$${\hat{x}}_{\text{A}}$$\end{document}x^A after time t allow precise estimates of both observables at time t. By means of the past quantum state formalism, we demonstrate that outcomes of measurements of both the \documentclass[12pt]{minimal}
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\begin{document}$${\hat{p}}_{A}$$\end{document}p^A observables can be inferred with errors below the standard quantum limit. The capability of assigning precise values to multiple observables and to observe their variation during physical processes may have implications in quantum state estimation and sensing. If we have access to information about a quantum system both before and after a measurement, we are not in the usual remit of the Heisenberg uncertainty principle anymore. Here, the authors demonstrate that, in such a scenario, one can retrodict position and momentum measurements without being limited by HUR.
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29
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Squeezed-light-driven force detection with an optomechanical cavity in a Mach-Zehnder interferometer. Sci Rep 2020; 10:17496. [PMID: 33060770 PMCID: PMC7567122 DOI: 10.1038/s41598-020-74629-1] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2020] [Accepted: 09/30/2020] [Indexed: 12/03/2022] Open
Abstract
We analyze the performance of a force detector based on balanced measurements with a Mach–Zehnder interferometer incorporating a standard optomechanical cavity. The system is driven by a coherent superposition of coherent light and squeezed vacuum field, providing quantum correlation along with optical coherence in order to enhance the measurement sensitivity beyond the standard quantum limit. We analytically find the optimal measurement strength, squeezing direction, and squeezing strength at which the symmetrized power spectral density for the measurement noise is minimized below the standard quantum limit. This force detection scheme based on a balanced Mach–Zehnder interferometer provides better sensitivity compared to that based on balanced homodyne detection with a local oscillator in the low frequency regime.
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30
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Sequino V, Bawaj M. Quantum fluctuations have been shown to affect macroscopic objects. Nature 2020; 583:31-32. [DOI: 10.1038/d41586-020-01914-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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31
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Quantum correlations between light and the kilogram-mass mirrors of LIGO. Nature 2020; 583:43-47. [DOI: 10.1038/s41586-020-2420-8] [Citation(s) in RCA: 68] [Impact Index Per Article: 17.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/03/2020] [Accepted: 05/04/2020] [Indexed: 11/09/2022]
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32
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Karg TM, Gouraud B, Ngai CT, Schmid GL, Hammerer K, Treutlein P. Light-mediated strong coupling between a mechanical oscillator and atomic spins 1 meter apart. Science 2020; 369:174-179. [DOI: 10.1126/science.abb0328] [Citation(s) in RCA: 28] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/27/2020] [Accepted: 04/28/2020] [Indexed: 11/02/2022]
Abstract
Engineering strong interactions between quantum systems is essential for many phenomena of quantum physics and technology. Typically, strong coupling relies on short-range forces or on placing the systems in high-quality electromagnetic resonators, which restricts the range of the coupling to small distances. We used a free-space laser beam to strongly couple a collective atomic spin and a micromechanical membrane over a distance of 1 meter in a room-temperature environment. The coupling is highly tunable and allows the observation of normal-mode splitting, coherent energy exchange oscillations, two-mode thermal noise squeezing, and dissipative coupling. Our approach to engineering coherent long-distance interactions with light makes it possible to couple very different systems in a modular way, opening up a range of opportunities for quantum control and coherent feedback networks.
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Affiliation(s)
- Thomas M. Karg
- Department of Physics and Swiss Nanoscience Institute, University of Basel, 4056 Basel, Switzerland
| | - Baptiste Gouraud
- Department of Physics and Swiss Nanoscience Institute, University of Basel, 4056 Basel, Switzerland
| | - Chun Tat Ngai
- Department of Physics and Swiss Nanoscience Institute, University of Basel, 4056 Basel, Switzerland
| | - Gian-Luca Schmid
- Department of Physics and Swiss Nanoscience Institute, University of Basel, 4056 Basel, Switzerland
| | - Klemens Hammerer
- Institute for Theoretical Physics and Institute for Gravitational Physics (Albert Einstein Institute), Leibniz Universität Hannover, 30167 Hannover, Germany
| | - Philipp Treutlein
- Department of Physics and Swiss Nanoscience Institute, University of Basel, 4056 Basel, Switzerland
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33
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Gu WJ, Wang YY, Yi Z, Yang WX, Sun LH. Force measurement in squeezed dissipative optomechanics in the presence of laser phase noise. OPTICS EXPRESS 2020; 28:12460-12474. [PMID: 32403743 DOI: 10.1364/oe.389854] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/04/2020] [Accepted: 04/06/2020] [Indexed: 06/11/2023]
Abstract
We investigate the force measurement sensitivity in a squeezed dissipative optomechanics within the free-mass regime under the influence of shot noise (SN) from the photon number fluctuations, laser phase noise from the pump laser, thermal noise from the environment, and optical losses from outcoupling and detection inefficiencies. Generally, squeezed light could generate a reduced SN on the squeezed quadrature and an enlarged quantum backaction noise (QBA) due to the antisqueezed conjugate quadrature. With an appropriate choice of phase angle in homodyne detection, QBA is cancellable, leading to an exponentially improved measurement sensitivity for the SN-dominated regime. By now, the effects of laser phase noise that is proportional to laser power emerge. The balance between squeezed SN and phase noise can lead to an sub-SQL sensitivity at an exponentially lower input power. However, the improvement by squeezing is limited by optical losses because high sensitivity is delicate and easily destroyed by optical losses.
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34
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Katz O, Shaham R, Polzik ES, Firstenberg O. Long-Lived Entanglement Generation of Nuclear Spins Using Coherent Light. PHYSICAL REVIEW LETTERS 2020; 124:043602. [PMID: 32058754 DOI: 10.1103/physrevlett.124.043602] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/24/2019] [Indexed: 06/10/2023]
Abstract
Nuclear spins of noble-gas atoms are exceptionally isolated from the environment and can maintain their quantum properties for hours at room temperature. Here we develop a mechanism for entangling two such distant macroscopic ensembles by using coherent light input. The interaction between the light and the noble-gas spins in each ensemble is mediated by spin-exchange collisions with alkali-metal spins, which are only virtually excited. The relevant conditions for experimental realizations with ^{3}He or ^{129}Xe are outlined.
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Affiliation(s)
- Or Katz
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel
- Rafael Ltd, IL-31021 Haifa, Israel
| | - Roy Shaham
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel
- Rafael Ltd, IL-31021 Haifa, Israel
| | - Eugene S Polzik
- Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, DK-2100 Copenhagen, Denmark
| | - Ofer Firstenberg
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel
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35
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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: 15] [Impact Index Per Article: 3.0] [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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36
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Muhonen JT, La Gala GR, Leijssen R, Verhagen E. State Preparation and Tomography of a Nanomechanical Resonator with Fast Light Pulses. PHYSICAL REVIEW LETTERS 2019; 123:113601. [PMID: 31573245 DOI: 10.1103/physrevlett.123.113601] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2018] [Indexed: 06/10/2023]
Abstract
Pulsed optomechanical measurements enable squeezing, nonclassical state creation, and backaction-free sensing. We demonstrate pulsed measurement of a cryogenic nanomechanical resonator with record precision close to the quantum regime. We use these to prepare thermally squeezed and purified conditional mechanical states, and to perform full state tomography. These demonstrations exploit large vacuum optomechanical coupling in a nanophotonic cavity to reach a single-pulse imprecision of 9 times the mechanical zero-point amplitude x_{zpf}. We study the effect of other mechanical modes that limit the conditional state width to 58x_{zpf}, and show how decoherence causes the state to grow in time.
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Affiliation(s)
- Juha T Muhonen
- Center for Nanophotonics, AMOLF, Science Park 104, 1098 XG Amsterdam, Netherlands
- Department of Physics and Nanoscience Center, University of Jyväskylä, P.O. Box 35, FI-40014 University of Jyväskylä, Finland
| | - Giada R La Gala
- Center for Nanophotonics, AMOLF, Science Park 104, 1098 XG Amsterdam, Netherlands
| | - Rick Leijssen
- Center for Nanophotonics, AMOLF, Science Park 104, 1098 XG Amsterdam, Netherlands
| | - Ewold Verhagen
- Center for Nanophotonics, AMOLF, Science Park 104, 1098 XG Amsterdam, Netherlands
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37
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Brunelli M, Malz D, Nunnenkamp A. Conditional Dynamics of Optomechanical Two-Tone Backaction-Evading Measurements. PHYSICAL REVIEW LETTERS 2019; 123:093602. [PMID: 31524454 DOI: 10.1103/physrevlett.123.093602] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/15/2019] [Indexed: 06/10/2023]
Abstract
Backaction-evading measurements of mechanical motion can achieve precision below the zero-point uncertainty and quantum squeezing, which makes them a resource for quantum metrology and quantum information processing. We provide an exact expression for the conditional state of an optomechanical system in a two-tone backaction-evading measurement beyond the standard adiabatic approximation and perform extensive numerical simulations to go beyond the usual rotating-wave approximation. We predict the simultaneous presence of conditional mechanical squeezing, intracavity squeezing, and optomechanical entanglement. We further apply an analogous analysis to the multimode optomechanical system of two mechanical and one cavity mode and find conditional mechanical Einstein-Podolski-Rosen entanglement and genuinely tripartite optomechanical entanglement. Our analysis is of direct relevance for ultrasensitive measurements and measurement-based control in high-cooperativity optomechanical sensors operating beyond the adiabatic limit.
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Affiliation(s)
- Matteo Brunelli
- Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, United Kingdom
| | - Daniel Malz
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, D-85748 Garching, Germany
| | - Andreas Nunnenkamp
- Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, United Kingdom
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38
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Cherroret N, Hemmerling M, Nador V, Walraven JTM, Kaiser R. Robust Coherent Transport of Light in Multilevel Hot Atomic Vapors. PHYSICAL REVIEW LETTERS 2019; 122:183203. [PMID: 31144888 DOI: 10.1103/physrevlett.122.183203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2018] [Indexed: 06/09/2023]
Abstract
Using a model system, we demonstrate both experimentally and theoretically that coherent scattering of light can be robust in hot atomic vapors despite a significant Doppler effect. By operating in a linear regime of far-detuned light scattering, we also unveil the emergence of interference triggered by inelastic Stokes and anti-Stokes transitions involving the atomic hyperfine structure.
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Affiliation(s)
- N Cherroret
- Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-PSL University, Collège de France, 4 Place Jussieu, 75005 Paris, France
| | - M Hemmerling
- Instituto de Física de São Carlos, Universidade de São Paulo, 13560-970 São Carlos, São Paulo, Brazil
- Université Côte d'Azur, CNRS, Institut de Physique de Nice, Valbonne F-06560, France
| | - V Nador
- Université Côte d'Azur, CNRS, Institut de Physique de Nice, Valbonne F-06560, France
| | - J T M Walraven
- Van der Waals-Zeeman Institute, Institute of Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
| | - R Kaiser
- Université Côte d'Azur, CNRS, Institut de Physique de Nice, Valbonne F-06560, France
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39
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Optical backaction-evading measurement of a mechanical oscillator. Nat Commun 2019; 10:2086. [PMID: 31064984 PMCID: PMC6504947 DOI: 10.1038/s41467-019-10024-3] [Citation(s) in RCA: 35] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/28/2018] [Accepted: 03/19/2019] [Indexed: 11/11/2022] Open
Abstract
Quantum mechanics imposes a limit on the precision of a continuous position measurement of a harmonic oscillator, due to backaction arising from quantum fluctuations in the measurement field. This standard quantum limit can be surpassed by monitoring only one of the two non-commuting quadratures of the motion, known as backaction-evading measurement. This technique has not been implemented using optical interferometers to date. Here we demonstrate, in a cavity optomechanical system operating in the optical domain, a continuous two-tone backaction-evading measurement of a localized gigahertz-frequency mechanical mode of a photonic-crystal nanobeam cryogenically and optomechanically cooled close to the ground state. Employing quantum-limited optical heterodyne detection, we explicitly show the transition from conventional to backaction-evading measurement. We observe up to 0.67 dB (14%) reduction of total measurement noise, thereby demonstrating the viability of backaction-evading measurements in nanomechanical resonators for optical ultrasensitive measurements of motion and force. Measurements of motion that avoid quantum backaction, with the potential to surpass the standard quantum limit, have so far been demonstrated using microwave radiation. Here, Shomroni, Qiu et al. demonstrate a backaction-evading measurement of the motion of a nanomechanical beam using laser light.
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40
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Shkarin AB, Kashkanova AD, Brown CD, Garcia S, Ott K, Reichel J, Harris JGE. Quantum Optomechanics in a Liquid. PHYSICAL REVIEW LETTERS 2019; 122:153601. [PMID: 31050504 DOI: 10.1103/physrevlett.122.153601] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/26/2018] [Indexed: 06/09/2023]
Abstract
We measure the quantum fluctuations of a single acoustic mode in a volume of superfluid He that is coupled to an optical cavity. Specifically, we monitor the Stokes and anti-Stokes light scattered by a standing acoustic wave that is confined by the cavity mirrors. The intensity of these signals (and their cross-correlation) exhibits the characteristic features of the acoustic wave's zero-point motion and the quantum backaction of the intracavity light. While these features are also observed in the vibrations of solid objects and ultracold atomic gases, their observation in superfluid He opens the possibility of exploiting the remarkable properties of this material to access new regimes of quantum optomechanics.
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Affiliation(s)
- A B Shkarin
- Department of Physics, Yale University, New Haven, Connecticut 06520, USA
| | - A D Kashkanova
- Department of Physics, Yale University, New Haven, Connecticut 06520, USA
| | - C D Brown
- Department of Physics, Yale University, New Haven, Connecticut 06520, USA
| | - S Garcia
- Laboratoire Kastler Brossel, ENS-Université PSL, CNRS, Sorbonne Université, Collège de France 24 rue Lhomond, 75005 Paris, France
| | - K Ott
- Laboratoire Kastler Brossel, ENS-Université PSL, CNRS, Sorbonne Université, Collège de France 24 rue Lhomond, 75005 Paris, France
| | - J Reichel
- Laboratoire Kastler Brossel, ENS-Université PSL, CNRS, Sorbonne Université, Collège de France 24 rue Lhomond, 75005 Paris, France
| | - J G E Harris
- Department of Physics, Yale University, New Haven, Connecticut 06520, USA
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA
- Yale Quantum Institute, Yale University, New Haven, Connecticut 06520, USA
- Wright Laboratory, Department of Physics, Yale University, New Haven, Connecticut 06520, USA
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41
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Quantum mechanics and the covariance of physical laws in quantum reference frames. Nat Commun 2019; 10:494. [PMID: 30700718 PMCID: PMC6353997 DOI: 10.1038/s41467-018-08155-0] [Citation(s) in RCA: 79] [Impact Index Per Article: 15.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2018] [Accepted: 12/17/2018] [Indexed: 12/02/2022] Open
Abstract
In physics, every observation is made with respect to a frame of reference. Although reference frames are usually not considered as degrees of freedom, in all practical situations it is a physical system which constitutes a reference frame. Can a quantum system be considered as a reference frame and, if so, which description would it give of the world? Here, we introduce a general method to quantise reference frame transformations, which generalises the usual reference frame transformation to a “superposition of coordinate transformations”. We describe states, measurement, and dynamical evolution in different quantum reference frames, without appealing to an external, absolute reference frame, and find that entanglement and superposition are frame-dependent features. The transformation also leads to a generalisation of the notion of covariance of dynamical physical laws, to an extension of the weak equivalence principle, and to the possibility of defining the rest frame of a quantum system. Reference frames are ultimately physical systems, and thus it should be possible to quantise them in a consistent way. Here, the authors use a relational formalism to quantise a reference frame and show the covariance of physical laws under transformations between such quantum reference frames.
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42
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Lu YK, Peng P, Cao QT, Xu D, Wiersig J, Gong Q, Xiao YF. Spontaneous T-symmetry breaking and exceptional points in cavity quantum electrodynamics systems. Sci Bull (Beijing) 2018; 63:1096-1100. [PMID: 36658988 DOI: 10.1016/j.scib.2018.07.020] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/03/2018] [Revised: 07/22/2018] [Accepted: 07/24/2018] [Indexed: 01/21/2023]
Abstract
Spontaneous symmetry breaking has revolutionized the understanding in numerous fields of modern physics. Here, we theoretically demonstrate the spontaneous time-reversal symmetry breaking in a cavity quantum electrodynamics system in which an atomic ensemble interacts coherently with a single resonant cavity mode. The interacting system can be effectively described by two coupled oscillators with positive and negative mass, when the two-level atoms are prepared in their excited states. The occurrence of symmetry breaking is controlled by the atomic detuning and the coupling to the cavity mode, which naturally divides the parameter space into the symmetry broken and symmetry unbroken phases. The two phases are separated by a spectral singularity, a so-called exceptional point, where the eigenstates of the Hamiltonian coalesce. When encircling the singularity in the parameter space, the quasi-adiabatic dynamics shows chiral mode switching which enables topological manipulation of quantum states.
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Affiliation(s)
- Yu-Kun Lu
- State Key Laboratory for Mesoscopic Physics and Collaborative Innovation Center of Quantum Matter, School of Physics, Peking University, Beijing 100871, China; Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
| | - Pai Peng
- State Key Laboratory for Mesoscopic Physics and Collaborative Innovation Center of Quantum Matter, School of Physics, Peking University, Beijing 100871, China; Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Qi-Tao Cao
- State Key Laboratory for Mesoscopic Physics and Collaborative Innovation Center of Quantum Matter, School of Physics, Peking University, Beijing 100871, China; Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
| | - Da Xu
- State Key Laboratory for Mesoscopic Physics and Collaborative Innovation Center of Quantum Matter, School of Physics, Peking University, Beijing 100871, China; Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
| | - Jan Wiersig
- Institut für Physik, Otto-von-Guericke-Universität Magdeburg, Postfach 4120, D-39016 Magdeburg, Germany
| | - Qihuang Gong
- State Key Laboratory for Mesoscopic Physics and Collaborative Innovation Center of Quantum Matter, School of Physics, Peking University, Beijing 100871, China; Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
| | - Yun-Feng Xiao
- State Key Laboratory for Mesoscopic Physics and Collaborative Innovation Center of Quantum Matter, School of Physics, Peking University, Beijing 100871, China; Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China.
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43
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Branford D, Miao H, Datta A. Fundamental Quantum Limits of Multicarrier Optomechanical Sensors. PHYSICAL REVIEW LETTERS 2018; 121:110505. [PMID: 30265105 DOI: 10.1103/physrevlett.121.110505] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/13/2018] [Revised: 07/27/2018] [Indexed: 06/08/2023]
Abstract
Optomechanical sensors involving multiple optical carriers can experience mechanically mediated interactions causing multimode correlations across the optical fields. One instance is laser-interferometric gravitational wave detectors which introduce multiple carrier frequencies for classical sensing and control purposes. An outstanding question is whether such multicarrier optomechanical sensors outperform their single-carrier counterpart in terms of quantum-limited sensitivity. We show that the best precision is achieved by a single-carrier instance of the sensor. For the current LIGO detection system this precision is already reachable.
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Affiliation(s)
- Dominic Branford
- Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - Haixing Miao
- School of Physics and Astronomy, Institute of Gravitational Wave Astronomy, University of Birmingham, Birmingham B15 2TT, United Kingdom
| | - Animesh Datta
- Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom
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44
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Zhang K, Zhou L, Meystre P, Zhang W. Relativistic Measurement Backaction in the Quantum Dirac Oscillator. PHYSICAL REVIEW LETTERS 2018; 121:110401. [PMID: 30265115 DOI: 10.1103/physrevlett.121.110401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2018] [Revised: 08/15/2018] [Indexed: 06/08/2023]
Abstract
An elegant method to circumvent quantum measurement backaction is the use of quantum mechanics free subsystems (QMFS), with one approach involving the use of two oscillators with effective masses of opposite signs. Since negative energies, and hence masses, are a characteristic of relativistic systems a natural question is to what extent QMFS can be realized in this context. Using the example of a one-dimensional Dirac oscillator we investigate conditions under which this can be achieved, and identify Zitterbewegung or virtual pair creation as the physical mechanism that fundamentally limits the feasibility of the scheme. We propose a tabletop implementation of a Dirac oscillator system based on a spin-orbit coupled ultracold atomic sample that allows for a direct observation of the corresponding analog of virtual pair creation on quantum measurement backaction.
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Affiliation(s)
- Keye Zhang
- Quantum Institute for Light and Atoms, School of Physics and Material Science, East China Normal University, Shanghai 200241, People's Republic of China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, People's Republic of China
| | - Lu Zhou
- Quantum Institute for Light and Atoms, School of Physics and Material Science, East China Normal University, Shanghai 200241, People's Republic of China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, People's Republic of China
| | - Pierre Meystre
- Department of Physics and College of Optical Sciences, University of Arizona, Tucson, Arizona 85721, USA
| | - Weiping Zhang
- Department of Physics and Astronomy, Shanghai Jiao Tong University, and Tsung-Dao Lee Institute, Shanghai 200240, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, People's Republic of China
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45
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Huang X, Zeuthen E, Vasilyev DV, He Q, Hammerer K, Polzik ES. Unconditional Steady-State Entanglement in Macroscopic Hybrid Systems by Coherent Noise Cancellation. PHYSICAL REVIEW LETTERS 2018; 121:103602. [PMID: 30240274 DOI: 10.1103/physrevlett.121.103602] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/08/2018] [Indexed: 06/08/2023]
Abstract
The generation of entanglement between disparate physical objects is a key ingredient in the field of quantum technologies, since they can have different functionalities in a quantum network. Here we propose and analyze a generic approach to steady-state entanglement generation between two oscillators with different temperatures and decoherence properties coupled in cascade to a common unidirectional light field. The scheme is based on a combination of coherent noise cancellation and dynamical cooling techniques for two oscillators with effective masses of opposite signs, such as quasispin and motional degrees of freedom, respectively. The interference effect provided by the cascaded setup can be tuned to implement additional noise cancellation leading to improved entanglement even in the presence of a hot thermal environment. The unconditional entanglement generation is advantageous since it provides a ready-to-use quantum resource. Remarkably, by comparing to the conditional entanglement achievable in the dynamically stable regime, we find our unconditional scheme to deliver a virtually identical performance when operated optimally.
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Affiliation(s)
- Xinyao Huang
- State Key Laboratory of Mesoscopic Physics, School of Physics, Peking University, Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
- Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen, Denmark
| | - Emil Zeuthen
- Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen, Denmark
| | - Denis V Vasilyev
- Center for Quantum Physics, Faculty of Mathematics, Computer Science and Physics, University of Innsbruck, A-6020 Innsbruck, Austria
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck, Austria
| | - Qiongyi He
- State Key Laboratory of Mesoscopic Physics, School of Physics, Peking University, Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
| | - Klemens Hammerer
- Institute for Theoretical Physics and Institute for Gravitational Physics (Albert Einstein Institute), Leibniz Universität Hannover, Callinstraße 38, 30167 Hannover, Germany
| | - Eugene S Polzik
- Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen, Denmark
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46
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Dellantonio L, Kyriienko O, Marquardt F, Sørensen AS. Quantum nondemolition measurement of mechanical motion quanta. Nat Commun 2018; 9:3621. [PMID: 30190532 PMCID: PMC6127154 DOI: 10.1038/s41467-018-06070-y] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2018] [Accepted: 07/26/2018] [Indexed: 11/15/2022] Open
Abstract
The fields of optomechanics and electromechanics have facilitated numerous advances in the areas of precision measurement and sensing, ultimately driving the studies of mechanical systems into the quantum regime. To date, however, the quantization of the mechanical motion and the associated quantum jumps between phonon states remains elusive. For optomechanical systems, the coupling to the environment was shown to make the detection of the mechanical mode occupation difficult, typically requiring the single-photon strong-coupling regime. Here, we propose and analyse an electromechanical setup, which allows us to overcome this limitation and resolve the energy levels of a mechanical oscillator. We found that the heating of the membrane, caused by the interaction with the environment and unwanted couplings, can be suppressed for carefully designed electromechanical systems. The results suggest that phonon number measurement is within reach for modern electromechanical setups. Although electro-and optomechanics has recently moved towards the quantum regime, the quantized energy spectrum of a mechanical oscillator has not been directly observed. Here Dellantonio et al. propose an electromechanical setup with a membrane resonator that could enable phonon number measurements.
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Affiliation(s)
- Luca Dellantonio
- The Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100, Copenhagen Ø, Denmark. .,Center for Hybrid Quantum Networks (Hy-Q), The Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100, Copenhagen Ø, Denmark.
| | - Oleksandr Kyriienko
- The Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100, Copenhagen Ø, Denmark.,NORDITA, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, 106 91, Stockholm, Sweden
| | - Florian Marquardt
- Institute for Theoretical Physics, University Erlangen-Nürnberg, Staudstraße 7, 91058, Erlangen, Germany.,Max Planck Institute for the Science of Light, Günther-Scharowsky-Straße 1, 91058, Erlangen, Germany
| | - Anders S Sørensen
- The Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100, Copenhagen Ø, Denmark.,Center for Hybrid Quantum Networks (Hy-Q), The Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100, Copenhagen Ø, Denmark
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47
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Khalili FY, Polzik ES. Overcoming the Standard Quantum Limit in Gravitational Wave Detectors Using Spin Systems with a Negative Effective Mass. PHYSICAL REVIEW LETTERS 2018; 121:031101. [PMID: 30085801 DOI: 10.1103/physrevlett.121.031101] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/29/2017] [Revised: 05/11/2018] [Indexed: 06/08/2023]
Abstract
Quantum backaction (QBA) of a measurement limits the precision of observation of the motion of a free mass. This profound effect, dubbed the "Heisenberg microscope" in the early days of quantum mechanics, leads to the standard quantum limit (SQL) stemming from the balance between the measurement sensitivity and the QBA. We consider the measurement of motion of a free mass performed in a quantum reference frame with an effective negative mass which is not limited by QBA. As a result, the disturbance on the motion of a free mass can be measured beyond the SQL. QBA-limited detection of motion for a free mass is extremely challenging, but there are devices where this effect is expected to play an essential role, namely, gravitational wave detectors (GWDs) such as LIGO and Virgo. Recent reports on the observations of gravitational waves have opened new horizons in cosmology and astrophysics. We present a general idea and a detailed numerical analysis for QBA-evading measurement of the gravitational wave effect on the GWD mirrors, which can be considered free masses under relevant conditions. The measurement is performed by two entangled beams of light, probing the GWD and an auxiliary atomic spin ensemble, respectively. The latter plays the role of a free negative mass. We show that under realistic conditions the sensitivity of the GWD in m/sqrt[Hz] can be increased by 6 dB over the entire frequency band of interest.
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Affiliation(s)
- F Ya Khalili
- Faculty of Physics, M.V. Lomonosov Moscow State University, 119991 Moscow, Russia and Russian Quantum Center, Skolkovo 143025, Russia
| | - E S Polzik
- Niels Bohr Institute, University of Copenhagen, Copenhagen 2100, Denmark
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48
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Yang D, Laflamme C, Vasilyev DV, Baranov MA, Zoller P. Theory of a Quantum Scanning Microscope for Cold Atoms. PHYSICAL REVIEW LETTERS 2018; 120:133601. [PMID: 29694173 DOI: 10.1103/physrevlett.120.133601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/06/2017] [Indexed: 06/08/2023]
Abstract
We propose and analyze a scanning microscope to monitor "live" the quantum dynamics of cold atoms in a cavity QED setup. The microscope measures the atomic density with subwavelength resolution via dispersive couplings to a cavity and homodyne detection within the framework of continuous measurement theory. We analyze two modes of operation. First, for a fixed focal point the microscope records the wave packet dynamics of atoms with time resolution set by the cavity lifetime. Second, a spatial scan of the microscope acts to map out the spatial density of stationary quantum states. Remarkably, in the latter case, for a good cavity limit, the microscope becomes an effective quantum nondemolition device, such that the spatial distribution of motional eigenstates can be measured backaction free in single scans, as an emergent quantum nondemolition measurement.
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Affiliation(s)
- D Yang
- Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria and Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck, Austria
| | - C Laflamme
- Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria and Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck, Austria
| | - D V Vasilyev
- Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria and Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck, Austria
| | - M A Baranov
- Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria and Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck, Austria
| | - P Zoller
- Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria and Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck, Austria
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49
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Kohler J, Gerber JA, Dowd E, Stamper-Kurn DM. Negative-Mass Instability of the Spin and Motion of an Atomic Gas Driven by Optical Cavity Backaction. PHYSICAL REVIEW LETTERS 2018; 120:013601. [PMID: 29350956 DOI: 10.1103/physrevlett.120.013601] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/12/2017] [Indexed: 06/07/2023]
Abstract
We realize a spin-orbit interaction between the collective spin precession and center-of-mass motion of a trapped ultracold atomic gas, mediated by spin- and position-dependent dispersive coupling to a driven optical cavity. The collective spin, precessing near its highest-energy state in an applied magnetic field, can be approximated as a negative-mass harmonic oscillator. When the Larmor precession and mechanical motion are nearly resonant, cavity mediated coupling leads to a negative-mass instability, driving exponential growth of a correlated mode of the hybrid system. We observe this growth imprinted on modulations of the cavity field and estimate the full covariance of the resulting two-mode state by observing its transient decay during subsequent free evolution.
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Affiliation(s)
- Jonathan Kohler
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Justin A Gerber
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Emma Dowd
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Dan M Stamper-Kurn
- Department of Physics, University of California, Berkeley, California 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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50
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Tsang M. Quantum limits on the time-bandwidth product of an optical resonator. OPTICS LETTERS 2018; 43:150-153. [PMID: 29328219 DOI: 10.1364/ol.43.000150] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/05/2017] [Accepted: 12/03/2017] [Indexed: 06/07/2023]
Abstract
A thought-provoking proposal by Tsakmakidis et al. [Science356, 1260 (2017)SCIEAS0036-807510.1126/science.aam6662] suggests that nonreciprocal optics can break a time-bandwidth limit to passive resonators. Here I quantize their resonator model and show that quantum mechanics does impose a limit, or requires extra noise to be added in the same fashion as amplified spontaneous emission in an active resonator. I also use thermodynamics to argue that extra dissipation or noise must be present in their proposed device.
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