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Loughlin H, Sudhir V. Exceptional-Point Sensors Offer No Fundamental Signal-to-Noise Ratio Enhancement. PHYSICAL REVIEW LETTERS 2024; 132:243601. [PMID: 38949374 DOI: 10.1103/physrevlett.132.243601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2024] [Accepted: 05/08/2024] [Indexed: 07/02/2024]
Abstract
Exceptional-point (EP) sensors exhibit a square-root resonant frequency bifurcation in response to external perturbations, making them appear attractive for sensing applications. However, there is an open debate as to whether or not this sensitivity advantage is negated by additional noise in the system. We settle this debate by showing that increased fundamental noises of quantum and thermal origin in EP sensors, and in particular self-excited (or PT-symmetric) EP sensors, negate the sensitivity benefit. Accordingly, EP sensing schemes are only beneficial either with further quantum enhancement or if compared to sensors limited by technical noise. As many modern sensors are limited by technical noise, EP sensors may still find practical uses despite their lack of a fundamental advantage. Alternatively, we propose a quantum-enhanced EP sensor that achieves a sensing advantage even when limited by quantum or thermal fluctuations.
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2
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Gardner JW, Gefen T, Haine SA, Hope JJ, Chen Y. Achieving the Fundamental Quantum Limit of Linear Waveform Estimation. PHYSICAL REVIEW LETTERS 2024; 132:130801. [PMID: 38613279 DOI: 10.1103/physrevlett.132.130801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/11/2023] [Revised: 10/23/2023] [Accepted: 02/20/2024] [Indexed: 04/14/2024]
Abstract
Sensing a classical signal using a linear quantum device is a pervasive application of quantum-enhanced measurement. The fundamental precision limits of linear waveform estimation, however, are not fully understood. In certain cases, there is an unexplained gap between the known waveform-estimation quantum Cramér-Rao bound and the optimal sensitivity from quadrature measurement of the outgoing mode from the device. We resolve this gap by establishing the fundamental precision limit, the waveform-estimation Holevo Cramér-Rao bound, and how to achieve it using a nonstationary measurement. We apply our results to detuned gravitational-wave interferometry to accelerate the search for postmerger remnants from binary neutron-star mergers. If we have an unequal weighting between estimating the signal's power and phase, then we propose how to further improve the signal-to-noise ratio by a factor of sqrt[2] using this nonstationary measurement.
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Affiliation(s)
- James W Gardner
- OzGrav-ANU, Centre for Gravitational Astrophysics, Research Schools of Physics, and of Astronomy and Astrophysics, The Australian National University, Canberra ACT 2601, Australia
- Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California 91125, USA
| | - Tuvia Gefen
- Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA
| | - Simon A Haine
- Department of Quantum Science and Technology and Department of Fundamental and Theoretical Physics, Research School of Physics, The Australian National University, Canberra ACT 0200, Australia
| | - Joseph J Hope
- Department of Quantum Science and Technology and Department of Fundamental and Theoretical Physics, Research School of Physics, The Australian National University, Canberra ACT 0200, Australia
| | - Yanbei Chen
- Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California 91125, USA
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3
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Gefen T, Tarafder R, Adhikari RX, Chen Y. Quantum Precision Limits of Displacement Noise-Free Interferometers. PHYSICAL REVIEW LETTERS 2024; 132:020801. [PMID: 38277601 DOI: 10.1103/physrevlett.132.020801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/07/2022] [Revised: 07/19/2023] [Accepted: 12/06/2023] [Indexed: 01/28/2024]
Abstract
Current laser-interferometric gravitational wave detectors suffer from a fundamental limit to their precision due to the displacement noise of optical elements contributed by various sources. Several schemes for displacement noise-free interferometers (DFI) have been proposed to mitigate their effects. The idea behind these schemes is similar to decoherence-free subspaces in quantum sensing; i.e., certain modes contain information about the gravitational waves but are insensitive to the mirror motion (displacement noise). We derive quantum precision limits for general DFI schemes, including optimal measurement basis and optimal squeezing schemes. We introduce a triangular cavity DFI scheme and apply our general bounds to it. Precision analysis of this scheme with different noise models shows that the DFI property leads to interesting sensitivity profiles and improved precision due to noise mitigation and larger gain from squeezing.
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Affiliation(s)
- Tuvia Gefen
- Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA
| | - Rajashik Tarafder
- Theoretical Astrophysics, Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California 91125, USA
- LIGO Laboratory, California Institute of Technology, Pasadena, California 91125, USA
| | - Rana X Adhikari
- LIGO Laboratory, California Institute of Technology, Pasadena, California 91125, USA
| | - Yanbei Chen
- Theoretical Astrophysics, Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California 91125, USA
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4
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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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5
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Korobko M, Südbeck J, Steinlechner S, Schnabel R. Mitigating Quantum Decoherence in Force Sensors by Internal Squeezing. PHYSICAL REVIEW LETTERS 2023; 131:143603. [PMID: 37862640 DOI: 10.1103/physrevlett.131.143603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/20/2023] [Accepted: 09/07/2023] [Indexed: 10/22/2023]
Abstract
The most efficient approach to laser interferometric force sensing to date uses monochromatic carrier light with its signal sideband spectrum in a squeezed vacuum state. Quantum decoherence, i.e., mixing with an ordinary vacuum state due to optical losses, is the main sensitivity limit. In this Letter, we present both theoretical and experimental evidence that quantum decoherence in high-precision laser interferometric force sensors enhanced with optical cavities and squeezed light injection can be mitigated by a quantum squeeze operation inside the sensor's cavity. Our experiment shows an enhanced measurement sensitivity that is independent of the optical readout loss in a wide range. Our results pave the way for quantum improvements in scenarios where high decoherence previously precluded the use of squeezed light. Our results hold significant potential for advancing the field of quantum sensors and enabling new experimental approaches in high-precision measurement technology.
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Affiliation(s)
- M Korobko
- Institut für Quantenphysik und Zentrum für Optische Quantentechnologien der Universität Hamburg, 5 Luruper Chaussee 149, 22761 Hamburg, Germany
| | - J Südbeck
- Institut für Quantenphysik und Zentrum für Optische Quantentechnologien der Universität Hamburg, 5 Luruper Chaussee 149, 22761 Hamburg, Germany
| | - S Steinlechner
- Faculty of Science and Engineering, Maastricht University, Duboisdomein 30, 6229 GT Maastricht, Netherlands
- Nikhef, Science Park 105, 1098 XG Amsterdam, Netherlands
| | - R Schnabel
- Institut für Quantenphysik und Zentrum für Optische Quantentechnologien der Universität Hamburg, 5 Luruper Chaussee 149, 22761 Hamburg, Germany
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6
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Yu H, Martynov D, Adhikari RX, Chen Y. Exposing gravitational waves below the quantum sensing limit. Int J Clin Exp Med 2022. [DOI: 10.1103/physrevd.106.063017] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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7
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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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8
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Zhang T, Jones P, Smetana J, Miao H, Martynov D, Freise A, Ballmer SW. Two-Carrier Scheme: Evading the 3 dB Quantum Penalty of Heterodyne Readout in Gravitational-Wave Detectors. PHYSICAL REVIEW LETTERS 2021; 126:221301. [PMID: 34152184 DOI: 10.1103/physrevlett.126.221301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/10/2020] [Revised: 10/06/2020] [Accepted: 05/05/2021] [Indexed: 06/13/2023]
Abstract
Precision measurements using a traditional heterodyne readout suffer a 3 dB quantum noise penalty compared with a homodyne readout. The extra noise is caused by the quantum fluctuations in the image vacuum. We propose a two-carrier gravitational-wave detector design that evades the 3 dB quantum penalty of the heterodyne readout. We further propose a new way of realizing frequency-dependent squeezing utilizing two-mode squeezing in our scheme. It naturally achieves more precise audio frequency signal measurements with radio frequency squeezing. In addition, the detector is compatible with other quantum nondemolition techniques.
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Affiliation(s)
- Teng Zhang
- School of Physics and Astronomy, and Institute of Gravitational Wave Astronomy, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom
| | - Philip Jones
- School of Physics and Astronomy, and Institute of Gravitational Wave Astronomy, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom
| | - Jiří Smetana
- School of Physics and Astronomy, and Institute of Gravitational Wave Astronomy, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom
| | - Haixing Miao
- School of Physics and Astronomy, and Institute of Gravitational Wave Astronomy, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom
| | - Denis Martynov
- School of Physics and Astronomy, and Institute of Gravitational Wave Astronomy, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom
| | - Andreas Freise
- School of Physics and Astronomy, and Institute of Gravitational Wave Astronomy, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom
- Department of Physics and Astronomy, VU Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, Netherlands
- Nikhef, Science Park 105, 1098 XG Amsterdam, Netherlands
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9
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Trad Nery M, Danilishin SL, Venneberg JR, Willke B. Fundamental limits of laser power stabilization via a radiation pressure transfer scheme. OPTICS LETTERS 2020; 45:3969-3972. [PMID: 32667330 DOI: 10.1364/ol.394547] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/08/2020] [Accepted: 06/13/2020] [Indexed: 06/11/2023]
Abstract
Traditional active laser power stabilization schemes are fundamentally limited by quantum shot noise on the in-loop photodetector. One way to overcome this limitation is to implement a nondemolition sensing scheme where laser power fluctuations are transferred to motion of a micro-oscillator, which can be sensed with a high signal-to-noise ratio. In this Letter, we analyze the power stability achievable in a nondemolition scheme limited by quantum and thermal noise. Under the assumption of realistic experimental parameters, we show that generation of a strong bright squeezed quantum state of light should be possible.
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10
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11
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Südbeck J, Steinlechner S, Korobko M, Schnabel R. Demonstration of interferometer enhancement through EPR entanglement. NATURE PHOTONICS 2020; 14:240-244. [PMID: 32231708 PMCID: PMC7104361 DOI: 10.1038/s41566-019-0583-3] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/22/2019] [Accepted: 12/22/2019] [Indexed: 06/10/2023]
Abstract
The recent series of gravitational-wave (GW) detections by the Advanced LIGO and Advanced Virgo observatories launched the new field of GW astronomy. As the sensitivity of GW detectors is limited by quantum noise of light, concepts from quantum metrology have been adapted to increase the observational range. Since 2010, squeezed light with reduced quantum noise has been used for improved sensitivity at signal frequencies above 100 Hz. However, 100 m long optical filter resonators would be required to also improve the sensitivity at lower frequencies, adding significant cost and complexity. Here we report on a proof-of-principle setup of an alternative concept that achieves the broadband noise reduction by using Einstein-Podolsky-Rosen (EPR) entangled states instead. We show that the desired sensitivity improvement can then be obtained with the signal-recycling resonator that is already part of current observatories, providing the viable alternative to high-cost filter cavities.
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Affiliation(s)
- Jan Südbeck
- Institut für Laserphysik und Zentrum für Optische Quantentechnologien der Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Sebastian Steinlechner
- Institut für Laserphysik und Zentrum für Optische Quantentechnologien der Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Mikhail Korobko
- Institut für Laserphysik und Zentrum für Optische Quantentechnologien der Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Roman Schnabel
- Institut für Laserphysik und Zentrum für Optische Quantentechnologien der Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
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12
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Korobko M, Ma Y, Chen Y, Schnabel R. Quantum expander for gravitational-wave observatories. LIGHT, SCIENCE & APPLICATIONS 2019; 8:118. [PMID: 31839938 PMCID: PMC6904558 DOI: 10.1038/s41377-019-0230-2] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/15/2019] [Revised: 11/13/2019] [Accepted: 11/28/2019] [Indexed: 05/14/2023]
Abstract
The quantum uncertainty of laser light limits the sensitivity of gravitational-wave observatories. Over the past 30 years, techniques for squeezing the quantum uncertainty, as well as for enhancing gravitational-wave signals with optical resonators have been invented. Resonators, however, have finite linewidths, and the high signal frequencies that are produced during the highly scientifically interesting ring-down of astrophysical compact-binary mergers still cannot be resolved. Here, we propose a purely optical approach for expanding the detection bandwidth. It uses quantum uncertainty squeezing inside one of the optical resonators, compensating for the finite resonators' linewidths while keeping the low-frequency sensitivity unchanged. This quantum expander is intended to enhance the sensitivity of future gravitational-wave detectors, and we suggest the use of this new tool in other cavity-enhanced metrological experiments.
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Affiliation(s)
- Mikhail Korobko
- Institut für Laserphysik und Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Yiqiu Ma
- Theoretical Astrophysics 350-17, California Institute of Technology, Pasadena, CA 91125 USA
| | - Yanbei Chen
- Theoretical Astrophysics 350-17, California Institute of Technology, Pasadena, CA 91125 USA
| | - Roman Schnabel
- Institut für Laserphysik und Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
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13
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Barsotti L, Harms J, Schnabel R. Squeezed vacuum states of light for gravitational wave detectors. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2019; 82:016905. [PMID: 29569572 DOI: 10.1088/1361-6633/aab906] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
A century after Einstein's formulation of general relativity, the detectors of the Laser Interferometer Gravitational-wave Observatory (LIGO) made the first direct detection of gravitational waves. This historic achievement was the culmination of a world-wide effort and decades of instrument research. While sufficient for this monumental discovery, the current generation of gravitational-wave detectors represent the least sensitive devices necessary for the task; improved detectors will be required to fully exploit this new window on the Universe. In this paper, we review the application of squeezed vacuum states of light to gravitational-wave detectors as a way to reduce quantum noise, which currently limits their performance in much of the detection band.
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Affiliation(s)
- Lisa Barsotti
- LIGO, Massachusetts Institute of Technology, Cambridge, MA 02139, United States of America
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14
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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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15
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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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16
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Page M, Qin J, La Fontaine J, Zhao C, Ju L, Blair D. Enhanced detection of high frequency gravitational waves using optically diluted optomechanical filters. Int J Clin Exp Med 2018. [DOI: 10.1103/physrevd.97.124060] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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17
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Danilishin SL, Knyazev E, Voronchev NV, Khalili FY, Gräf C, Steinlechner S, Hennig JS, Hild S. A new quantum speed-meter interferometer: measuring speed to search for intermediate mass black holes. LIGHT, SCIENCE & APPLICATIONS 2018; 7:11. [PMID: 30839613 PMCID: PMC6107026 DOI: 10.1038/s41377-018-0004-2] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/27/2017] [Revised: 02/12/2018] [Accepted: 02/13/2018] [Indexed: 06/09/2023]
Abstract
The recent discovery of gravitational waves (GW) by Advanced LIGO (Laser Interferometric Gravitational-wave Observatory) has impressively launched the novel field of gravitational astronomy and allowed us to glimpse exciting objects about which we could previously only speculate. Further sensitivity improvements at the low-frequency end of the detection band of future GW observatories must rely on quantum non-demolition (QND) methods to suppress fundamental quantum fluctuations of the light fields used to readout the GW signal. Here we present a novel concept of how to turn a conventional Michelson interferometer into a QND speed-meter interferometer with coherently suppressed quantum back-action noise. We use two orthogonal polarizations of light and an optical circulator to couple them. We carry out a detailed analysis of how imperfections and optical loss influence the achievable sensitivity. We find that the proposed configuration significantly enhances the low-frequency sensitivity and increases the observable event rate of binary black-hole coalescences in the range of 1 0 2 - 1 0 3 M ⊙ by a factor of up to ~300.
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Affiliation(s)
- Stefan L. Danilishin
- Institut für Theoretische Physik, Leibniz Universität Hannover and Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut), Callinstraße 38, D-30167 Hannover, Germany
- SUPA, School of Physics and Astronomy, University of Glasgow, Glasgow, G12 8QQ United Kingdom
| | - Eugene Knyazev
- M.V. Lomonosov Moscow State University, Faculty of Physics, Moscow, 119991 Russia
| | - Nikita V. Voronchev
- M.V. Lomonosov Moscow State University, Faculty of Physics, Moscow, 119991 Russia
| | - Farid Ya. Khalili
- M.V. Lomonosov Moscow State University, Faculty of Physics, Moscow, 119991 Russia
| | - Christian Gräf
- SUPA, School of Physics and Astronomy, University of Glasgow, Glasgow, G12 8QQ United Kingdom
| | - Sebastian Steinlechner
- Institut für Laserphysik und Zentrum für Optische Quantentechnologien der Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Jan-Simon Hennig
- SUPA, School of Physics and Astronomy, University of Glasgow, Glasgow, G12 8QQ United Kingdom
| | - Stefan Hild
- SUPA, School of Physics and Astronomy, University of Glasgow, Glasgow, G12 8QQ United Kingdom
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18
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Heurs M. Gravitational wave detection using laser interferometry beyond the standard quantum limit. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2018; 376:rsta.2017.0289. [PMID: 29661977 DOI: 10.1098/rsta.2017.0289] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 12/12/2017] [Indexed: 05/14/2023]
Abstract
Interferometric gravitational wave detectors (such as advanced LIGO) employ high-power solid-state lasers to maximize their detection sensitivity and hence their reach into the universe. These sophisticated light sources are ultra-stabilized with regard to output power, emission frequency and beam geometry; this is crucial to obtain low detector noise. However, even when all laser noise is reduced as far as technically possible, unavoidable quantum noise of the laser still remains. This is a consequence of the Heisenberg Uncertainty Principle, the basis of quantum mechanics: in this case, it is fundamentally impossible to simultaneously reduce both the phase noise and the amplitude noise of a laser to arbitrarily low levels. This fact manifests in the detector noise budget as two distinct noise sources-photon shot noise and quantum radiation pressure noise-which together form a lower boundary for current-day gravitational wave detector sensitivities, the standard quantum limit of interferometry. To overcome this limit, various techniques are being proposed, among them different uses of non-classical light and alternative interferometer topologies. This article explains how quantum noise enters and manifests in an interferometric gravitational wave detector, and gives an overview of some of the schemes proposed to overcome this seemingly fundamental limitation, all aimed at the goal of higher gravitational wave event detection rates.This article is part of a discussion meeting issue 'The promises of gravitational-wave astronomy'.
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Affiliation(s)
- M Heurs
- Institute for Gravitational Physics, Leibniz Universität Hannover, Callinstrasse 38, 30167 Hannover, Germany
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19
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Cripe J, Danz B, Lane B, Lorio MC, Falcone J, Cole GD, Corbitt T. Observation of an optical spring with a beam splitter. OPTICS LETTERS 2018; 43:2193-2196. [PMID: 29714787 DOI: 10.1364/ol.43.002193] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/09/2018] [Accepted: 04/03/2018] [Indexed: 06/08/2023]
Abstract
We present the experimental observation of an optical spring without the use of an optical cavity. The optical spring is produced by interference at a beam splitter and, in principle, does not have the damping force associated with optical springs created in detuned cavities. The experiment consists of a Michelson-Sagnac interferometer (with no recycling cavities) with a partially reflective GaAs microresonator as the beam splitter that produces the optical spring. Our experimental measurements at input powers of up to 360 mW show the shift of the optical spring frequency as a function of power and are in excellent agreement with theoretical predictions. In addition, we show that the optical spring is able to keep the interferometer stable and locked without the use of external feedback.
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20
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Møller CB, Thomas RA, Vasilakis G, Zeuthen E, Tsaturyan Y, Balabas M, Jensen K, Schliesser A, Hammerer K, Polzik ES. Quantum back-action-evading measurement of motion in a negative mass reference frame. Nature 2017; 547:191-195. [DOI: 10.1038/nature22980] [Citation(s) in RCA: 115] [Impact Index Per Article: 16.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2016] [Accepted: 05/19/2017] [Indexed: 11/09/2022]
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Korobko M, Kleybolte L, Ast S, Miao H, Chen Y, Schnabel R. Beating the Standard Sensitivity-Bandwidth Limit of Cavity-Enhanced Interferometers with Internal Squeezed-Light Generation. PHYSICAL REVIEW LETTERS 2017; 118:143601. [PMID: 28430507 DOI: 10.1103/physrevlett.118.143601] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/12/2017] [Indexed: 05/27/2023]
Abstract
The shot-noise limited peak sensitivity of cavity-enhanced interferometric measurement devices, such as gravitational-wave detectors, can be improved by increasing the cavity finesse, even when comparing fixed intracavity light powers. For a fixed light power inside the detector, this comes at the price of a proportional reduction in the detection bandwidth. High sensitivity over a large span of signal frequencies, however, is essential for astronomical observations. It is possible to overcome this standard sensitivity-bandwidth limit using nonclassical correlations in the light field. Here, we investigate the internal squeezing approach, where the parametric amplification process creates a nonclassical correlation directly inside the interferometer cavity. We theoretically analyze the limits of the approach and measure 36% increase in the sensitivity-bandwidth product compared to the classical case. To our knowledge, this is the first experimental demonstration of an improvement in the sensitivity-bandwidth product using internal squeezing, opening the way for a new class of optomechanical force sensing devices.
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Affiliation(s)
- M Korobko
- Institut für Laserphysik und Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - L Kleybolte
- Institut für Laserphysik und Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - S Ast
- Institut für Gravitationsphysik, Leibniz Universität Hannover and Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut), Callinstraße 38, 30167 Hannover, Germany
| | - H Miao
- Institute of Gravitational Wave Astronomy, University of Birmingham, Birmingham B15 2TT, United Kingdom
| | - Y Chen
- Theoretical Astrophysics 350-17, California Institute of Technology, Pasadena, California 91125, USA
| | - R Schnabel
- Institut für Laserphysik und Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
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22
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Pang S, Jordan AN. Optimal adaptive control for quantum metrology with time-dependent Hamiltonians. Nat Commun 2017; 8:14695. [PMID: 28276428 PMCID: PMC5512879 DOI: 10.1038/ncomms14695] [Citation(s) in RCA: 80] [Impact Index Per Article: 11.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2016] [Accepted: 01/24/2017] [Indexed: 12/02/2022] Open
Abstract
Quantum metrology has been studied for a wide range of systems with time-independent Hamiltonians. For systems with time-dependent Hamiltonians, however, due to the complexity of dynamics, little has been known about quantum metrology. Here we investigate quantum metrology with time-dependent Hamiltonians to bridge this gap. We obtain the optimal quantum Fisher information for parameters in time-dependent Hamiltonians, and show proper Hamiltonian control is generally necessary to optimize the Fisher information. We derive the optimal Hamiltonian control, which is generally adaptive, and the measurement scheme to attain the optimal Fisher information. In a minimal example of a qubit in a rotating magnetic field, we find a surprising result that the fundamental limit of T2 time scaling of quantum Fisher information can be broken with time-dependent Hamiltonians, which reaches T4 in estimating the rotation frequency of the field. We conclude by considering level crossings in the derivatives of the Hamiltonians, and point out additional control is necessary for that case. Quantum metrology investigates the improvement given to precision measurements by exploiting quantum mechanics, but it has been mostly limited to systems with static Hamiltonians. Here the authors study it in the general case of time-varying Hamiltonians, showing that optimizing the quantum Fisher information via quantum control provides an advantage.
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Affiliation(s)
- Shengshi Pang
- Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA.,Center for Coherence and Quantum Optics, University of Rochester, Rochester, New York 14627, USA
| | - Andrew N Jordan
- Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA.,Center for Coherence and Quantum Optics, University of Rochester, Rochester, New York 14627, USA.,Institute for Quantum Studies, Chapman University, 1 University Drive, Orange, California 92866, USA
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23
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Bond C, Brown D, Freise A, Strain KA. Interferometer techniques for gravitational-wave detection. LIVING REVIEWS IN RELATIVITY 2017; 19:3. [PMID: 28260967 PMCID: PMC5315762 DOI: 10.1007/s41114-016-0002-8] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/04/2015] [Accepted: 07/21/2016] [Indexed: 05/25/2023]
Abstract
Several km-scale gravitational-wave detectors have been constructed worldwide. These instruments combine a number of advanced technologies to push the limits of precision length measurement. The core devices are laser interferometers of a new kind; developed from the classical Michelson topology these interferometers integrate additional optical elements, which significantly change the properties of the optical system. Much of the design and analysis of these laser interferometers can be performed using well-known classical optical techniques; however, the complex optical layouts provide a new challenge. In this review, we give a textbook-style introduction to the optical science required for the understanding of modern gravitational wave detectors, as well as other high-precision laser interferometers. In addition, we provide a number of examples for a freely available interferometer simulation software and encourage the reader to use these examples to gain hands-on experience with the discussed optical methods.
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Affiliation(s)
- Charlotte Bond
- School of Physics and Astronomy, University of Birmingham, Birmingham, B15 2TT UK
| | - Daniel Brown
- School of Physics and Astronomy, University of Birmingham, Birmingham, B15 2TT UK
| | - Andreas Freise
- School of Physics and Astronomy, University of Birmingham, Birmingham, B15 2TT UK
| | - Kenneth A. Strain
- School of Physics and Astronomy, University of Glasgow, Glasgow, G12 8QQ UK
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24
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Reinhardt C, Müller T, Sankey JC. Simple delay-limited sideband locking with heterodyne readout. OPTICS EXPRESS 2017; 25:1582-1597. [PMID: 28158040 DOI: 10.1364/oe.25.001582] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We present a robust sideband laser locking technique ideally suited for applications requiring low probe power and heterodyne readout. By feeding back to a high-bandwidth voltage-controlled oscillator, we lock a first-order phase-modulation sideband to a high-finesse Fabry-Perot cavity in ambient conditions, achieving a closed-loop bandwidth of 3.5 MHz (with a single integrator) limited fundamentally by the signal delay. The measured transfer function of the closed loop agrees with a simple model based on ideal system components, and from this we suggest a modified design that should achieve a bandwidth exceeding 6 MHz with a near-causally limited feedback gain as high as 4 × 107 at 1 kHz. The off-resonance optical carrier enables alignment-free heterodyne readout, alleviating the need for additional lasers or optical modulators.
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25
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Teufel JD, Lecocq F, Simmonds RW. Overwhelming Thermomechanical Motion with Microwave Radiation Pressure Shot Noise. PHYSICAL REVIEW LETTERS 2016; 116:013602. [PMID: 26799018 DOI: 10.1103/physrevlett.116.013602] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/20/2015] [Indexed: 06/05/2023]
Abstract
We measure the fundamental noise processes associated with a continuous linear position measurement of a micromechanical membrane incorporated in a microwave cavity optomechanical circuit. We observe the trade-off between the two fundamental sources of noise that enforce the standard quantum limit: the measurement imprecision and radiation pressure backaction from photon shot noise. We demonstrate that the quantum backaction of the measurement can overwhelm the intrinsic thermal motion by 24 dB, entering a new regime for cavity optomechanical systems.
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Affiliation(s)
- J D Teufel
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
| | - F Lecocq
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
| | - R W Simmonds
- National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
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26
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Diósi L. Testing spontaneous wave-function collapse models on classical mechanical oscillators. PHYSICAL REVIEW LETTERS 2015; 114:050403. [PMID: 25699424 DOI: 10.1103/physrevlett.114.050403] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/24/2014] [Indexed: 06/04/2023]
Abstract
We show that the heating effect of spontaneous wave-function collapse models implies an experimentally significant increment ΔT(sp) of equilibrium temperature in a mechanical oscillator. The obtained new form ΔT(sp) is linear in the oscillator's relaxation time τ and independent of the mass. The oscillator can be in a classical thermal state, also the effect ΔT(sp) is classical for a wide range of frequencies and quality factors. We note that the test of ΔT(sp) does not necessitate quantum state monitoring just tomography. In both the gravity-related and the continuous spontaneous localization models the strong-effect edge of their parameter range can be challenged in existing experiments on classical oscillators. For the continuous spontaneous localization theory, the conjectured highest collapse rate parameter values become immediately constrained by evidences from current experiments on extreme slow-ring-down oscillators.
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Affiliation(s)
- Lajos Diósi
- Wigner Research Center for Physics, H-1525 Budapest 114. P.O. Box 49, Hungary
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27
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Nimmrichter S, Hornberger K, Hammerer K. Optomechanical sensing of spontaneous wave-function collapse. PHYSICAL REVIEW LETTERS 2014; 113:020405. [PMID: 25062146 DOI: 10.1103/physrevlett.113.020405] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/29/2014] [Indexed: 06/03/2023]
Abstract
Quantum experiments with nanomechanical oscillators are regarded as a test bed for hypothetical modifications of the Schrödinger equation, which predict a breakdown of the superposition principle and induce classical behavior at the macroscale. It is generally believed that the sensitivity to these unconventional effects grows with the mass of the mechanical quantum system. Here we show that the opposite is the case for optomechanical systems in the presence of generic noise sources, such as thermal and measurement noise. We determine conditions for distinguishing these decoherence processes from possible collapse-induced decoherence in continuous optomechanical force measurements.
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Affiliation(s)
- Stefan Nimmrichter
- Faculty of Physics, University of Duisburg-Essen, Lotharstraße 1, 47048 Duisburg, Germany
| | - Klaus Hornberger
- Faculty of Physics, University of Duisburg-Essen, Lotharstraße 1, 47048 Duisburg, Germany
| | - Klemens Hammerer
- Institute for Theoretical Physics and Institute for Gravitational Physics (Albert Einstein Institute), Leibniz University Hannover, Callinstraße 38, 30167 Hannover, Germany
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28
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Perreca A, Lough J, Kelley D, Ballmer SW. Multidimensional optical trapping of a mirror. Int J Clin Exp Med 2014. [DOI: 10.1103/physrevd.89.122002] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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29
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Yang H, Miao H, Lee DS, Helou B, Chen Y. Macroscopic quantum mechanics in a classical spacetime. PHYSICAL REVIEW LETTERS 2013; 110:170401. [PMID: 23679686 DOI: 10.1103/physrevlett.110.170401] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/09/2012] [Revised: 01/19/2013] [Indexed: 06/02/2023]
Abstract
We apply the many-particle Schrödinger-Newton equation, which describes the coevolution of a many-particle quantum wave function and a classical space-time geometry, to macroscopic mechanical objects. By averaging over motions of the objects' internal degrees of freedom, we obtain an effective Schrödinger-Newton equation for their centers of mass, which can be monitored and manipulated at quantum levels by state-of-the-art optomechanics experiments. For a single macroscopic object moving quantum mechanically within a harmonic potential well, its quantum uncertainty is found to evolve at a frequency different from its classical eigenfrequency-with a difference that depends on the internal structure of the object-and can be observable using current technology. For several objects, the Schrödinger-Newton equation predicts semiclassical motions just like Newtonian physics, yet quantum uncertainty cannot be transferred from one object to another.
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Affiliation(s)
- Huan Yang
- Theoretical Astrophysics 350-17, California Institute of Technology, Pasadena, California 91125, USA
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30
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Voronchev NV, Danilishin SL, Khalili FY. Trade-off between quantum and thermal fluctuations in mirror coatings yields improved sensitivity of gravitational-wave interferometers. Int J Clin Exp Med 2012. [DOI: 10.1103/physrevd.86.122003] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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