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Yu M, Li X, Chu Y, Mera B, Ünal FN, Yang P, Liu Y, Goldman N, Cai J. Experimental demonstration of topological bounds in quantum metrology. Natl Sci Rev 2024; 11:nwae065. [PMID: 39301073 PMCID: PMC11409888 DOI: 10.1093/nsr/nwae065] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2023] [Revised: 12/22/2023] [Accepted: 02/25/2024] [Indexed: 09/22/2024] Open
Abstract
Quantum metrology is deeply connected to quantum geometry, through the fundamental notion of quantum Fisher information. Inspired by advances in topological matter, it was recently suggested that the Berry curvature and Chern numbers of band structures can dictate strict lower bounds on metrological properties, hence establishing a strong connection between topology and quantum metrology. In this work, we provide a first experimental verification of such topological bounds, by performing optimal quantum multi-parameter estimation and achieving the best possible measurement precision. By emulating the band structure of a Chern insulator, we experimentally determine the metrological potential across a topological phase transition, and demonstrate strong enhancement in the topologically non-trivial regime. Our work opens the door to metrological applications empowered by topology, with potential implications for quantum many-body systems.
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Affiliation(s)
- Min Yu
- School of Physics, Hubei Key Laboratory of Gravitation and Quantum Physics, Institute for Quantum Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
- International Joint Laboratory on Quantum Sensing and Quantum Metrology, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Xiangbei Li
- School of Physics, Hubei Key Laboratory of Gravitation and Quantum Physics, Institute for Quantum Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
- International Joint Laboratory on Quantum Sensing and Quantum Metrology, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Yaoming Chu
- School of Physics, Hubei Key Laboratory of Gravitation and Quantum Physics, Institute for Quantum Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
- International Joint Laboratory on Quantum Sensing and Quantum Metrology, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Bruno Mera
- Advanced Institute for Materials Research (WPI-AIMR), Tohoku University, Sendai 980-8577, Japan
| | - F Nur Ünal
- TCM Group, Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, UK
| | - Pengcheng Yang
- School of Physics, Hubei Key Laboratory of Gravitation and Quantum Physics, Institute for Quantum Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
- International Joint Laboratory on Quantum Sensing and Quantum Metrology, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Yu Liu
- International Joint Laboratory on Quantum Sensing and Quantum Metrology, Huazhong University of Science and Technology, Wuhan 430074, China
- Institut für Theoretische Physik and IQST, Universität Ulm, Ulm D-89081 Germany
| | - Nathan Goldman
- Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, Brussels B-1050, Belgium
- Laboratoire Kastler Brossel, Collège de France, Paris 75005, France
| | - Jianming Cai
- School of Physics, Hubei Key Laboratory of Gravitation and Quantum Physics, Institute for Quantum Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
- International Joint Laboratory on Quantum Sensing and Quantum Metrology, Huazhong University of Science and Technology, Wuhan 430074, China
- Shanghai Key Laboratory of Magnetic Resonance, East China Normal University, Shanghai 200062, China
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Alushi U, Górecki W, Felicetti S, Di Candia R. Optimality and Noise Resilience of Critical Quantum Sensing. PHYSICAL REVIEW LETTERS 2024; 133:040801. [PMID: 39121399 DOI: 10.1103/physrevlett.133.040801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/29/2024] [Accepted: 06/10/2024] [Indexed: 08/11/2024]
Abstract
We compare critical quantum sensing to passive quantum strategies to perform frequency estimation, in the case of single-mode quadratic Hamiltonians. We show that, while in the unitary case both strategies achieve precision scaling quadratic with the number of photons, in the presence of dissipation this is true only for critical strategies. We also establish that working at the exceptional point or beyond threshold provides suboptimal performance. This critical enhancement is due to the emergence of a transient regime in the open critical dynamics, and is invariant to temperature changes. When considering both time and system size as resources, for both strategies the precision scales linearly with the product of the total time and the number of photons, in accordance with fundamental bounds. However, we show that critical protocols outperform optimal passive strategies if preparation and measurement times are not negligible. Our results are applicable to a broad variety of critical sensors whose phenomenology can be reduced to that of a single-mode quadratic Hamiltonian, including systems described by finite-component and fully connected models.
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Mukherjee V, Divakaran U. The promises and challenges of many-body quantum technologies: A focus on quantum engines. Nat Commun 2024; 15:3170. [PMID: 38609387 PMCID: PMC11014963 DOI: 10.1038/s41467-024-47638-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/30/2022] [Accepted: 04/08/2024] [Indexed: 04/14/2024] Open
Affiliation(s)
- Victor Mukherjee
- Department of Physical Sciences, Indian Institute of Science Education and Research Berhampur, Berhampur, 760010, India.
| | - Uma Divakaran
- Department of Physics, Indian Institute of Technology Palakkad, Palakkad, Kerala, 678623, India
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Shi HL, Guan XW, Yang J. Universal Shot-Noise Limit for Quantum Metrology with Local Hamiltonians. PHYSICAL REVIEW LETTERS 2024; 132:100803. [PMID: 38518317 DOI: 10.1103/physrevlett.132.100803] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/10/2023] [Accepted: 02/05/2024] [Indexed: 03/24/2024]
Abstract
Quantum many-body interactions can induce quantum entanglement among particles, rendering them valuable resources for quantum-enhanced sensing. In this work, we establish a link between the bound on the growth of the quantum Fisher information and the Lieb-Robinson bound, which characterizes the operator growth in locally interacting quantum many-body systems. We show that for initial separable states, despite the use of local many-body interactions, the precision cannot surpass the shot noise limit at all times. This conclusion also holds for an initial state that is the nondegenerate ground state of a local and gapped Hamiltonian. These findings strongly hint that when one can only prepare separable initial states, nonlocal and long-range interactions are essential resources for surpassing the shot noise limit. This observation is confirmed through numerical analysis on the long-range Ising model. Our results bridge the field of many-body quantum sensing and operator growth in many-body quantum systems and open the possibility to investigate the interplay between quantum sensing and control, many-body physics and information scrambling.
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Affiliation(s)
- Hai-Long Shi
- Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
- QSTAR and INO-CNR, Largo Enrico Fermi 2, 50125 Firenze, Italy
- Hefei National Laboratory, Hefei 230088, China
| | - Xi-Wen Guan
- Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
- Hefei National Laboratory, Hefei 230088, China
- Department of Fundamental and Theoretical Physics, Research School of Physics, Australian National University, Canberra ACT 0200, Australia
| | - Jing Yang
- Nordita, KTH Royal Institute of Technology and Stockholm University, Hannes Alfvéns vag 12, 10691 Stockholm, Sweden
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He X, Yousefjani R, Bayat A. Stark Localization as a Resource for Weak-Field Sensing with Super-Heisenberg Precision. PHYSICAL REVIEW LETTERS 2023; 131:010801. [PMID: 37478450 DOI: 10.1103/physrevlett.131.010801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2023] [Accepted: 06/05/2023] [Indexed: 07/23/2023]
Abstract
Gradient fields can effectively suppress particle tunneling in a lattice and localize the wave function at all energy scales, a phenomenon known as Stark localization. Here, we show that Stark systems can be used as a probe for the precise measurement of gradient fields, particularly in the weak-field regime where most sensors do not operate optimally. In the extended phase, Stark probes achieve super-Heisenberg precision, which is well beyond most of the known quantum sensing schemes. In the localized phase, the precision drops in a universal way showing fast convergence to the thermodynamic limit. For single-particle probes, we show that quantum-enhanced sensitivity, with super-Heisenberg precision, can be achieved through a simple position measurement for all the eigenstates across the entire spectrum. For such probes, we have identified several critical exponents of the Stark localization transition and established their relationship. Thermal fluctuations, whose universal behavior is identified, reduce the precision from super-Heisenberg to Heisenberg, still outperforming classical sensors. Multiparticle interacting probes also achieve super-Heisenberg scaling in their extended phase, which shows even further enhancement near the transition point. Quantum-enhanced sensitivity is still achievable even when state preparation time is included in resource analysis.
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Affiliation(s)
- Xingjian He
- Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610051, China
| | - Rozhin Yousefjani
- Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610051, China
| | - Abolfazl Bayat
- Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610051, China
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Salvia R, Mehboudi M, Perarnau-Llobet M. Critical Quantum Metrology Assisted by Real-Time Feedback Control. PHYSICAL REVIEW LETTERS 2023; 130:240803. [PMID: 37390423 DOI: 10.1103/physrevlett.130.240803] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/07/2022] [Revised: 03/27/2023] [Accepted: 05/30/2023] [Indexed: 07/02/2023]
Abstract
We investigate critical quantum metrology, that is, the estimation of parameters in many-body systems close to a quantum critical point, through the lens of Bayesian inference theory. We first derive a no-go result stating that any nonadaptive strategy will fail to exploit quantum critical enhancement (i.e., precision beyond the shot-noise limit) for a sufficiently large number of particles N whenever our prior knowledge is limited. We then consider different adaptive strategies that can overcome this no-go result and illustrate their performance in the estimation of (i) a magnetic field using a probe of 1D spin Ising chain and (ii) the coupling strength in a Bose-Hubbard square lattice. Our results show that adaptive strategies with real-time feedback control can achieve sub-shot-noise scaling even with few measurements and substantial prior uncertainty.
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Affiliation(s)
- Raffaele Salvia
- Scuola Normale Superiore, I-56127 Pisa, Italy
- Département de Physique Appliquée, Université de Genève, 1211 Genève, Switzerland
| | - Mohammad Mehboudi
- Département de Physique Appliquée, Université de Genève, 1211 Genève, Switzerland
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Montenegro V, Jones GS, Bose S, Bayat A. Sequential Measurements for Quantum-Enhanced Magnetometry in Spin Chain Probes. PHYSICAL REVIEW LETTERS 2022; 129:120503. [PMID: 36179207 DOI: 10.1103/physrevlett.129.120503] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/02/2022] [Accepted: 08/23/2022] [Indexed: 06/16/2023]
Abstract
Quantum sensors outperform their classical counterparts in their estimation precision, given the same amount of resources. So far, quantum-enhanced sensitivity has been achieved by exploiting the superposition principle. This enhancement has been obtained for particular forms of entangled states, adaptive measurement basis change, critical many-body systems, and steady state of periodically driven systems. Here, we introduce a different approach to obtain quantum-enhanced sensitivity in a many-body probe through utilizing the nature of quantum measurement and its subsequent wave function collapse without demanding prior entanglement. Our protocol consists of a sequence of local measurements, without reinitialization, performed regularly during the evolution of a many-body probe. As the number of sequences increases, the sensing precision is enhanced beyond the standard limit, reaching the Heisenberg bound asymptotically. The benefits of the protocol are multifold as it uses a product initial state and avoids complex initialization (e.g., prior entangled states or critical ground states) and allows for remote quantum sensing.
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Affiliation(s)
- Victor Montenegro
- Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610051, China
| | - Gareth Siôn Jones
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
| | - Sougato Bose
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
| | - Abolfazl Bayat
- Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610051, China
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Sarkar S, Mukhopadhyay C, Alase A, Bayat A. Free-Fermionic Topological Quantum Sensors. PHYSICAL REVIEW LETTERS 2022; 129:090503. [PMID: 36083659 DOI: 10.1103/physrevlett.129.090503] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/21/2022] [Accepted: 08/05/2022] [Indexed: 06/15/2023]
Abstract
Second order quantum phase transitions, with well-known features such as long-range entanglement, symmetry breaking, and gap closing, exhibit quantum enhancement for sensing at criticality. However, it is unclear which of these features are responsible for this enhancement. To address this issue, we investigate phase transitions in free-fermionic topological systems that exhibit neither symmetry-breaking nor long-range entanglement. We analytically demonstrate that quantum enhanced sensing is possible using topological edge states near the phase boundary. Remarkably, such enhancement also endures for ground states of such models that are accessible in solid state experiments. We illustrate the results with 1D Su-Schrieffer-Heeger chain and a 2D Chern insulator which are both experimentally accessible. While neither symmetry-breaking nor long-range entanglement are essential, gap closing remains as the major candidate for the ultimate source of quantum enhanced sensing. In addition, we also provide a fixed and simple measurement strategy that achieves near-optimal precision for sensing using generic edge states irrespective of the parameter value. This paves the way for development of topological quantum sensors which are expected to also be robust against local perturbations.
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Affiliation(s)
- Saubhik Sarkar
- Institute for Quantum Science and Technology and Department of Physics and Astronomy, University of Calgary, Calgary, Alberta T2N 1N4, Canada
| | - Chiranjib Mukhopadhyay
- RCQI, Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta 9, 84511 Bratislava, Slovakia
- Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610051, China
| | - Abhijeet Alase
- Institute for Quantum Science and Technology and Department of Physics and Astronomy, University of Calgary, Calgary, Alberta T2N 1N4, Canada
| | - Abolfazl Bayat
- Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610051, China
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Ying ZJ, Felicetti S, Liu G, Braak D. Critical Quantum Metrology in the Non-Linear Quantum Rabi Model. ENTROPY (BASEL, SWITZERLAND) 2022; 24:1015. [PMID: 35892995 PMCID: PMC9330817 DOI: 10.3390/e24081015] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/16/2022] [Revised: 07/17/2022] [Accepted: 07/19/2022] [Indexed: 02/01/2023]
Abstract
The quantum Rabi model (QRM) with linear coupling between light mode and qubit exhibits the analog of a second-order phase transition for vanishing mode frequency which allows for criticality-enhanced quantum metrology in a few-body system. We show that the QRM including a nonlinear coupling term exhibits much higher measurement precisions due to its first-order-like phase transition at finite frequency, avoiding the detrimental slowing-down effect close to the critical point of the linear QRM. When a bias term is added to the Hamiltonian, the system can be used as a fluxmeter or magnetometer if implemented in circuit QED platforms.
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Affiliation(s)
- Zu-Jian Ying
- School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China
| | - Simone Felicetti
- Institute for Complex Systems, National Research Council (ISC-CNR), 00185 Rome, Italy
| | - Gang Liu
- School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China
| | - Daniel Braak
- EP VI and Center for Electronic Correlations and Magnetism, University of Augsburg, 86135 Augsburg, Germany
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Mukherjee V, Divakaran U. Many-body quantum thermal machines. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 33:454001. [PMID: 34359061 DOI: 10.1088/1361-648x/ac1b60] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/22/2021] [Accepted: 08/06/2021] [Indexed: 06/13/2023]
Abstract
Thermodynamics of quantum systems and quantum thermal machines are rapidly developing fields, which have already delivered several promising results, as well as raised many intriguing questions. Many-body quantum machines present new opportunities stemming from many-body effects. At the same time, they pose new challenges related to many-body physics. In this short review we discuss some of the recent developments on technologies based on many-body quantum systems. We mainly focus on many-body effects in quantum thermal machines. We also briefly address the role played by many-body systems in the development of quantum batteries and quantum probes.
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Affiliation(s)
- Victor Mukherjee
- Department of Physical Sciences, IISER Berhampur, Berhampur 760010, India
| | - Uma Divakaran
- Department of Physics, Indian Institute of Technology Palakkad, Palakkad, 678557, India
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