1
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Nguyen PT, Le TK, Nguyen HQ, Ho LB. Harnessing graph state resources for robust quantum magnetometry under noise. Sci Rep 2024; 14:20528. [PMID: 39227686 PMCID: PMC11371932 DOI: 10.1038/s41598-024-71365-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/08/2023] [Accepted: 08/26/2024] [Indexed: 09/05/2024] Open
Abstract
Precise measurement of magnetic fields is essential for various applications, such as fundamental physics, space exploration, and biophysics. Although recent progress in quantum engineering has assisted in creating advanced quantum magnetometers, there are still ongoing challenges in improving their efficiency and noise resistance. This study focuses on using symmetric graph state resources for quantum magnetometry to enhance measurement precision by analyzing the estimation theory under time-homogeneous and time-inhomogeneous noise models. The results show a significant improvement in estimating both single and multiple Larmor frequencies. In single Larmor frequency estimation, the quantum Fisher information spans a spectrum from the standard quantum limit to the Heisenberg limit within a periodic range of the Larmor frequency, and in the case of multiple Larmor frequencies, it can exceed the standard quantum limit for both noisy cases. This study highlights the potential of graph state-based methods for improving magnetic field measurements under noisy environments.
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Affiliation(s)
- Phu Trong Nguyen
- Department of Advanced Material Science and Nanotechnology, University of Science and Technology of Hanoi, Vietnam Academy of Science and Technology, Hanoi, 11307, Vietnam
| | - Trung Kien Le
- Department of Physics, University of California, Santa Barbara, Santa Barbara, USA
- Department of Applied Physics, Stanford University, Stanford, USA
| | - Hung Q Nguyen
- Nano and Energy Center, University of Science, Vietnam National University, Hanoi, 120401, Vietnam
| | - Le Bin Ho
- Frontier Research Institute for Interdisciplinary Sciences, Tohoku University, Sendai, 980-8578, Japan.
- Department of Applied Physics, Graduate School of Engineering, Tohoku University, Sendai, 980-8579, Japan.
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2
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Ye J, Zoller P. Essay: Quantum Sensing with Atomic, Molecular, and Optical Platforms for Fundamental Physics. PHYSICAL REVIEW LETTERS 2024; 132:190001. [PMID: 38804927 DOI: 10.1103/physrevlett.132.190001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/28/2024] [Indexed: 05/29/2024]
Abstract
Atomic, molecular, and optical (AMO) physics has been at the forefront of the development of quantum science while laying the foundation for modern technology. With the growing capabilities of quantum control of many atoms for engineered many-body states and quantum entanglement, a key question emerges: what critical impact will the second quantum revolution with ubiquitous applications of entanglement bring to bear on fundamental physics? In this Essay, we argue that a compelling long-term vision for fundamental physics and novel applications is to harness the rapid development of quantum information science to define and advance the frontiers of measurement physics, with strong potential for fundamental discoveries. As quantum technologies, such as fault-tolerant quantum computing and entangled quantum sensor networks, become much more advanced than today's realization, we wonder what doors of basic science can these tools unlock. We anticipate that some of the most intriguing and challenging problems, such as quantum aspects of gravity, fundamental symmetries, or new physics beyond the minimal standard model, will be tackled at the emerging quantum measurement frontier. Part of a series of Essays which concisely present author visions for the future of their field.
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Affiliation(s)
- Jun Ye
- JILA, National Institute of Standards and Technology, and Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - Peter Zoller
- Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck, Austria and Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, 6020 Innsbruck, Austria
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3
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Lewis-Swan RJ, Castro JCZ, Barberena D, Rey AM. Exploiting Nonclassical Motion of a Trapped Ion Crystal for Quantum-Enhanced Metrology of Global and Differential Spin Rotations. PHYSICAL REVIEW LETTERS 2024; 132:163601. [PMID: 38701452 DOI: 10.1103/physrevlett.132.163601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/04/2023] [Revised: 02/23/2024] [Accepted: 03/18/2024] [Indexed: 05/05/2024]
Abstract
We theoretically investigate prospects for the creation of nonclassical spin states in trapped ion arrays by coupling to a squeezed state of the collective motion of the ions. The correlations of the generated spin states can be tailored for quantum-enhanced sensing of global or differential rotations of subensembles of the spins by working with specific vibrational modes of the ion array. We propose a pair of protocols to utilize the generated states and demonstrate their viability even for small systems, while assessing limitations imposed by spin-motion entanglement and technical noise. Our work suggests new opportunities for the preparation of many-body states with tailored correlations for quantum-enhanced metrology in spin-boson systems.
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Affiliation(s)
- R J Lewis-Swan
- Homer L. Dodge Department of Physics and Astronomy, The University of Oklahoma, Norman, Oklahoma 73019, USA
- Center for Quantum Research and Technology, The University of Oklahoma, Norman, Oklahoma 73019, USA
| | - J C Zuñiga Castro
- Homer L. Dodge Department of Physics and Astronomy, The University of Oklahoma, Norman, Oklahoma 73019, USA
- Center for Quantum Research and Technology, The University of Oklahoma, Norman, Oklahoma 73019, USA
| | - D Barberena
- JILA, NIST, and Department of Physics, University of Colorado, Boulder, Colorado, USA
- Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado, USA
| | - A M Rey
- JILA, NIST, and Department of Physics, University of Colorado, Boulder, Colorado, USA
- Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado, USA
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4
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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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5
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Kim DH, Hong S, Kim YS, Kim Y, Lee SW, Pooser RC, Oh K, Lee SY, Lee C, Lim HT. Distributed quantum sensing of multiple phases with fewer photons. Nat Commun 2024; 15:266. [PMID: 38212341 PMCID: PMC10784500 DOI: 10.1038/s41467-023-44204-z] [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: 09/19/2023] [Accepted: 12/04/2023] [Indexed: 01/13/2024] Open
Abstract
Distributed quantum metrology has drawn intense interest as it outperforms the optimal classical counterparts in estimating multiple distributed parameters. However, most schemes so far have required entangled resources consisting of photon numbers equal to or more than the parameter numbers, which is a fairly demanding requirement as the number of nodes increases. Here, we present a distributed quantum sensing scenario in which quantum-enhanced sensitivity can be achieved with fewer photons than the number of parameters. As an experimental demonstration, using a two-photon entangled state, we estimate four phases distributed 3 km away from the central node, resulting in a 2.2 dB sensitivity enhancement from the standard quantum limit. Our results show that the Heisenberg scaling can be achieved even when using fewer photons than the number of parameters. We believe our scheme will open a pathway to perform large-scale distributed quantum sensing with currently available entangled sources.
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Affiliation(s)
- Dong-Hyun Kim
- Center for Quantum Information, Korea Institute of Science and Technology (KIST), Seoul, 02792, Korea
- Department of Physics, Yonsei University, Seoul, 03722, Korea
| | - Seongjin Hong
- Department of Physics, Chung-Ang University, Seoul, 06974, Korea
| | - Yong-Su Kim
- Center for Quantum Information, Korea Institute of Science and Technology (KIST), Seoul, 02792, Korea
- Division of Nanoscience and Technology, KIST School, Korea University of Science and Technology, Seoul, 02792, Korea
| | - Yosep Kim
- Center for Quantum Information, Korea Institute of Science and Technology (KIST), Seoul, 02792, Korea
- Department of Physics, Korea University, Seoul, 02841, Korea
| | - Seung-Woo Lee
- Center for Quantum Information, Korea Institute of Science and Technology (KIST), Seoul, 02792, Korea
| | | | - Kyunghwan Oh
- Department of Physics, Yonsei University, Seoul, 03722, Korea
| | - Su-Yong Lee
- Emerging Science and Technology Directorate, Agency for Defense Development, Daejeon, 34186, Korea
- Weapon Systems Engineering, ADD School, University of Science and Technology, Daejeon, 34060, Korea
| | - Changhyoup Lee
- Korea Research Institute of Standards and Science, Daejeon, 34113, Korea
| | - Hyang-Tag Lim
- Center for Quantum Information, Korea Institute of Science and Technology (KIST), Seoul, 02792, Korea.
- Division of Nanoscience and Technology, KIST School, Korea University of Science and Technology, Seoul, 02792, Korea.
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6
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Le TK, Nguyen HQ, Ho LB. Variational quantum metrology for multiparameter estimation under dephasing noise. Sci Rep 2023; 13:17775. [PMID: 37853037 PMCID: PMC10584960 DOI: 10.1038/s41598-023-44786-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2023] [Accepted: 10/12/2023] [Indexed: 10/20/2023] Open
Abstract
We present a hybrid quantum-classical variational scheme to enhance precision in quantum metrology. In the scheme, both the initial state and the measurement basis in the quantum part are parameterized and optimized via the classical part. It enables the maximization of information gained about the measured quantity. We discuss specific applications to 3D magnetic field sensing under several dephasing noise models. Indeed, we demonstrate its ability to simultaneously estimate all parameters and surpass the standard quantum limit, making it a powerful tool for metrological applications.
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Affiliation(s)
- Trung Kien Le
- Department of Physics, University of California, Santa Barbara, Santa Barbara, USA
- Department of Applied Physics, Stanford University, Stanford, California, 94305, USA
| | - Hung Q Nguyen
- Nano and Energy Center, University of Science, Vietnam National University, Hanoi, 120401, Vietnam
| | - Le Bin Ho
- Frontier Research Institute for Interdisciplinary Sciences, Tohoku University, Sendai, 980-8578, Japan.
- Department of Applied Physics, Graduate School of Engineering, Tohoku University, Sendai, 980-8579, Japan.
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7
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Conlon LO, Lam PK, Assad SM. Multiparameter Estimation with Two-Qubit Probes in Noisy Channels. ENTROPY (BASEL, SWITZERLAND) 2023; 25:1122. [PMID: 37628152 PMCID: PMC10453296 DOI: 10.3390/e25081122] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/31/2023] [Revised: 07/21/2023] [Accepted: 07/24/2023] [Indexed: 08/27/2023]
Abstract
This work compares the performance of single- and two-qubit probes for estimating several phase rotations simultaneously under the action of different noisy channels. We compute the quantum limits for this simultaneous estimation using collective and individual measurements by evaluating the Holevo and Nagaoka-Hayashi Cramér-Rao bounds, respectively. Several quantum noise channels are considered, namely the decohering channel, the amplitude damping channel, and the phase damping channel. For each channel, we find the optimal single- and two-qubit probes. Where possible we demonstrate an explicit measurement strategy that saturates the appropriate bound and we investigate how closely the Holevo bound can be approached through collective measurements on multiple copies of the same probe. We find that under the action of the considered channels, two-qubit probes show enhanced parameter estimation capabilities over single-qubit probes for almost all non-identity channels, i.e., the achievable precision with a single-qubit probe degrades faster with increasing exposure to the noisy environment than that of the two-qubit probe. However, in sufficiently noisy channels, we show that it is possible for single-qubit probes to outperform maximally entangled two-qubit probes. This work shows that, in order to reach the ultimate precision limits allowed by quantum mechanics, entanglement is required in both the state preparation and state measurement stages. It is hoped the tutorial-esque nature of this paper will make it easily accessible.
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Affiliation(s)
- Lorcán O. Conlon
- Centre for Quantum Computation and Communication Technology, Department of Quantum Science, Australian National University, Canberra, ACT 2601, Australia
- Institute of Materials Research and Engineering, Agency for Science Technology and Research (A*STAR), 2 Fusionopolis Way, 08-03 Innovis, Singapore 138634, Singapore
| | - Ping Koy Lam
- Centre for Quantum Computation and Communication Technology, Department of Quantum Science, Australian National University, Canberra, ACT 2601, Australia
- Institute of Materials Research and Engineering, Agency for Science Technology and Research (A*STAR), 2 Fusionopolis Way, 08-03 Innovis, Singapore 138634, Singapore
| | - Syed M. Assad
- Centre for Quantum Computation and Communication Technology, Department of Quantum Science, Australian National University, Canberra, ACT 2601, Australia
- Institute of Materials Research and Engineering, Agency for Science Technology and Research (A*STAR), 2 Fusionopolis Way, 08-03 Innovis, Singapore 138634, Singapore
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8
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Distributed quantum sensing with mode-entangled spin-squeezed atomic states. Nature 2022; 612:661-665. [PMID: 36418400 DOI: 10.1038/s41586-022-05363-z] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/12/2022] [Accepted: 08/16/2022] [Indexed: 11/25/2022]
Abstract
Quantum sensors are used for precision timekeeping, field sensing and quantum communication1-3. Comparisons among a distributed network of these sensors are capable of, for example, synchronizing clocks at different locations4-8. The performance of a sensor network is limited by technical challenges as well as the inherent noise associated with the quantum states used to realize the network9. For networks with only spatially localized entanglement at each node, the noise performance of the network improves at best with the square root of the number of nodes10. Here we demonstrate that spatially distributed entanglement between network nodes offers better scaling with network size. A shared quantum nondemolition measurement entangles a clock network with up to four nodes. This network provides up to 4.5 decibels better precision than one without spatially distributed entanglement, and 11.6 decibels improvement as compared to a network of sensors operating at the quantum projection noise limit. We demonstrate the generality of the approach with atomic clock and atomic interferometer protocols, in scientific and technologically relevant configurations optimized for intrinsically differential comparisons of sensor outputs.
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9
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Hong S, Ur Rehman J, Kim YS, Cho YW, Lee SW, Jung H, Moon S, Han SW, Lim HT. Quantum enhanced multiple-phase estimation with multi-mode N00N states. Nat Commun 2021; 12:5211. [PMID: 34471118 PMCID: PMC8410777 DOI: 10.1038/s41467-021-25451-4] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/25/2021] [Accepted: 08/11/2021] [Indexed: 02/07/2023] Open
Abstract
Quantum metrology can achieve enhanced sensitivity for estimating unknown parameters beyond the standard quantum limit. Recently, multiple-phase estimation exploiting quantum resources has attracted intensive interest for its applications in quantum imaging and sensor networks. For multiple-phase estimation, the amount of enhanced sensitivity is dependent on quantum probe states, and multi-mode N00N states are known to be a key resource for this. However, its experimental demonstration has been missing so far since generating such states is highly challenging. Here, we report generation of multi-mode N00N states and experimental demonstration of quantum enhanced multiple-phase estimation using the multi-mode N00N states. In particular, we show that the quantum Cramer-Rao bound can be saturated using our two-photon four-mode N00N state and measurement scheme using a 4 × 4 multi-mode beam splitter. Our multiple-phase estimation strategy provides a faithful platform to investigate multiple parameter estimation scenarios.
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Affiliation(s)
- Seongjin Hong
- Center for Quantum Information, Korea Institute of Science and Technology (KIST), Seoul, Korea
| | - Junaid Ur Rehman
- Center for Quantum Information, Korea Institute of Science and Technology (KIST), Seoul, Korea
- Department of Electronics and Information Convergence Engineering, Kyung Hee University, Yongin, Korea
| | - Yong-Su Kim
- Center for Quantum Information, Korea Institute of Science and Technology (KIST), Seoul, Korea
- Division of Nano and Information Technology, KIST School, Korea University of Science and Technology, Seoul, Korea
| | - Young-Wook Cho
- Center for Quantum Information, Korea Institute of Science and Technology (KIST), Seoul, Korea
- Department of Physics, Yonsei University, Seoul, Korea
| | - Seung-Woo Lee
- Center for Quantum Information, Korea Institute of Science and Technology (KIST), Seoul, Korea
| | - Hojoong Jung
- Center for Quantum Information, Korea Institute of Science and Technology (KIST), Seoul, Korea
| | - Sung Moon
- Center for Quantum Information, Korea Institute of Science and Technology (KIST), Seoul, Korea
- Division of Nano and Information Technology, KIST School, Korea University of Science and Technology, Seoul, Korea
| | - Sang-Wook Han
- Center for Quantum Information, Korea Institute of Science and Technology (KIST), Seoul, Korea
- Division of Nano and Information Technology, KIST School, Korea University of Science and Technology, Seoul, Korea
| | - Hyang-Tag Lim
- Center for Quantum Information, Korea Institute of Science and Technology (KIST), Seoul, Korea.
- Division of Nano and Information Technology, KIST School, Korea University of Science and Technology, Seoul, Korea.
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10
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Yadin B, Fadel M, Gessner M. Metrological complementarity reveals the Einstein-Podolsky-Rosen paradox. Nat Commun 2021; 12:2410. [PMID: 33893281 PMCID: PMC8065158 DOI: 10.1038/s41467-021-22353-3] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2020] [Accepted: 03/11/2021] [Indexed: 02/02/2023] Open
Abstract
The Einstein-Podolsky-Rosen (EPR) paradox plays a fundamental role in our understanding of quantum mechanics, and is associated with the possibility of predicting the results of non-commuting measurements with a precision that seems to violate the uncertainty principle. This apparent contradiction to complementarity is made possible by nonclassical correlations stronger than entanglement, called steering. Quantum information recognises steering as an essential resource for a number of tasks but, contrary to entanglement, its role for metrology has so far remained unclear. Here, we formulate the EPR paradox in the framework of quantum metrology, showing that it enables the precise estimation of a local phase shift and of its generating observable. Employing a stricter formulation of quantum complementarity, we derive a criterion based on the quantum Fisher information that detects steering in a larger class of states than well-known uncertainty-based criteria. Our result identifies useful steering for quantum-enhanced precision measurements and allows one to uncover steering of non-Gaussian states in state-of-the-art experiments.
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Affiliation(s)
- Benjamin Yadin
- grid.4563.40000 0004 1936 8868School of Mathematical Sciences and Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham, UK ,grid.4991.50000 0004 1936 8948Wolfson College, University of Oxford, Oxford, UK
| | - Matteo Fadel
- grid.6612.30000 0004 1937 0642Department of Physics, University of Basel, Basel, Switzerland
| | - Manuel Gessner
- grid.462844.80000 0001 2308 1657Laboratoire Kastler Brossel, ENS-Université PSL, CNRS, Sorbonne Université, Collège de France, Paris, France
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11
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Abstract
The extraordinary sensitivity of plasmonic sensors is well-known in the optics and photonics community. These sensors exploit simultaneously the enhancement and the localization of electromagnetic fields close to the interface between a metal and a dielectric. This enables, for example, the design of integrated biochemical sensors at scales far below the diffraction limit. Despite their practical realization and successful commercialization, the sensitivity and associated precision of plasmonic sensors are starting to reach their fundamental classical limit given by quantum fluctuations of light-known as the shot-noise limit. To improve the sensing performance of these sensors beyond the classical limit, quantum resources are increasingly being employed. This area of research has become known as "quantum plasmonic sensing", and it has experienced substantial activity in recent years for applications in chemical and biological sensing. This review aims to cover both plasmonic and quantum techniques for sensing, and it shows how they have been merged to enhance the performance of plasmonic sensors beyond traditional methods. We discuss the general framework developed for quantum plasmonic sensing in recent years, covering the basic theory behind the advancements made, and describe the important works that made these advancements. We also describe several key works in detail, highlighting their motivation, the working principles behind them, and their future impact. The intention of the review is to set a foundation for a burgeoning field of research that is currently being explored out of intellectual curiosity and for a wide range of practical applications in biochemistry, medicine, and pharmaceutical research.
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Affiliation(s)
- Changhyoup Lee
- Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany.,Quantum Universe Center, Korea Institute for Advanced Study, Seoul 02455, Republic of Korea
| | - Benjamin Lawrie
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States
| | - Raphael Pooser
- Quantum Information Science Group, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States
| | - Kwang-Geol Lee
- Department of Physics, Hanyang University, Seoul 04763, Republic of Korea
| | - Carsten Rockstuhl
- Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany.,Institute of Nanotechnology, Karlsruhe Institute of Technology, 76021Karlsruhe, Germany.,Max Planck School of Photonics, 07745 Jena, Germany
| | - Mark Tame
- Department of Physics, Stellenbosch University, Stellenbosch 7602, South Africa
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12
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Fuentes J. Quantum control operations with fuzzy evolution trajectories based on polyharmonic magnetic fields. Sci Rep 2020; 10:22256. [PMID: 33335278 PMCID: PMC7746755 DOI: 10.1038/s41598-020-79309-8] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2020] [Accepted: 12/07/2020] [Indexed: 11/09/2022] Open
Abstract
We explore a class of quantum control operations based on a wide family of harmonic magnetic fields that vary softly in time. Depending on the magnetic field amplitudes taking part, these control operations can produce either squeezing or loop (orbit) effects, and even parametric resonances, on the canonical variables. For these purposes we focus our attention on the evolution of observables whose dynamical picture is ascribed to a quadratic Hamiltonian that depends explicitly on time. In the first part of this work we survey such operations in terms of biharmonic magnetic fields. The dynamical analysis is simplified using a stability diagram in the amplitude space, where the points of each region will characterise a specific control operation. We discuss how the evolution loop effects are formed by fuzzy (non-commutative) trajectories that can be closed or open, in the latter case, even hiding some features that can be used to manipulate the operational time. In the second part, we generalise the case of biharmonic fields and translate the discussion to the case of polyharmonic fields. Using elementary properties of the Toeplitz matrices, we can derive exact solutions of the problem in a symmetric evolution interval, leading to the temporal profile of those magnetic fields suitable to achieve specific control operations. Some of the resulting fuzzy orbits can be destroyed by the influence of external forces, while others simply remain stable.
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Affiliation(s)
- Jesús Fuentes
- División de Ciencias e Ingenierías, Departamento de Física, Universidad de Guanajuato, Loma del Bosque 103, 37150, León, Guanajuato, Mexico.
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