1
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Hetzel M, Pezzè L, Pür C, Quensen M, Hüper A, Geng J, Kruse J, Santos L, Ertmer W, Smerzi A, Klempt C. Tomography of a Number-Resolving Detector by Reconstruction of an Atomic Many-Body Quantum State. PHYSICAL REVIEW LETTERS 2023; 131:260601. [PMID: 38215377 DOI: 10.1103/physrevlett.131.260601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/01/2022] [Accepted: 10/10/2023] [Indexed: 01/14/2024]
Abstract
The high-fidelity analysis of many-body quantum states of indistinguishable atoms requires the accurate counting of atoms. Here we report the tomographic reconstruction of an atom-number-resolving detector. The tomography is performed with an ultracold rubidium ensemble that is prepared in a coherent spin state by driving a Rabi coupling between the two hyperfine clock levels. The coupling is followed by counting the occupation number in one level. We characterize the fidelity of our detector and show that a negative-valued Wigner function is associated with it. Our results offer an exciting perspective for the high-fidelity reconstruction of entangled states and can be applied for a future demonstration of Heisenberg-limited atom interferometry.
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Affiliation(s)
- Mareike Hetzel
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - Luca Pezzè
- QSTAR and INO-CNR and LENS, Largo Enrico Fermi 2, 50125 Firenze, Italy
| | - Cebrail Pür
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - Martin Quensen
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - Andreas Hüper
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - Jiao Geng
- Key Laboratory of 3D Micro/Nano Fabrication and Characterization of Zhejiang Province, School of Engineering, Westlake University, 18 Shilongshan Road, Hangzhou 310024, Zhejiang Province, China
- Institute of Advanced Technology, Westlake Institute for Advanced Study, 18 Shilongshan Road, Hangzhou 310024, Zhejiang Province, China
| | - Jens Kruse
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - Luis Santos
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, D-30167 Hannover, Germany
| | - Wolfgang Ertmer
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - Augusto Smerzi
- QSTAR and INO-CNR and LENS, Largo Enrico Fermi 2, 50125 Firenze, Italy
| | - Carsten Klempt
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
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2
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Stitely KC, Finger F, Rosa-Medina R, Ferri F, Donner T, Esslinger T, Parkins S, Krauskopf B. Quantum Fluctuation Dynamics of Dispersive Superradiant Pulses in a Hybrid Light-Matter System. PHYSICAL REVIEW LETTERS 2023; 131:143604. [PMID: 37862667 DOI: 10.1103/physrevlett.131.143604] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/19/2023] [Accepted: 09/06/2023] [Indexed: 10/22/2023]
Abstract
We consider theoretically a driven-dissipative quantum many-body system consisting of an atomic ensemble in a single-mode optical cavity as described by the open Tavis-Cummings model. In this hybrid light-matter system, the interplay between coherent and dissipative processes leads to superradiant pulses with a buildup of strong correlations, even for systems comprising hundreds to thousands of particles. A central feature of the mean-field dynamics is a self-reversal of two spin degrees of freedom due to an underlying time-reversal symmetry, which is broken by quantum fluctuations. We demonstrate a quench protocol that can maintain highly non-Gaussian states over long timescales. This general mechanism offers interesting possibilities for the generation and control of complex fluctuation patterns, as suggested for the improvement of quantum sensing protocols for dissipative spin amplification.
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Affiliation(s)
- Kevin C Stitely
- Dodd-Walls Centre for Photonic and Quantum Technologies, New Zealand
- Department of Mathematics, University of Auckland, Auckland 1010, New Zealand
- Department of Physics, University of Auckland, Auckland 1010, New Zealand
| | - Fabian Finger
- Institute for Quantum Electronics and Quantum Center, ETH Zürich, 8093 Zürich, Switzerland
| | - Rodrigo Rosa-Medina
- Institute for Quantum Electronics and Quantum Center, ETH Zürich, 8093 Zürich, Switzerland
| | - Francesco Ferri
- Institute for Quantum Electronics and Quantum Center, ETH Zürich, 8093 Zürich, Switzerland
| | - Tobias Donner
- Institute for Quantum Electronics and Quantum Center, ETH Zürich, 8093 Zürich, Switzerland
| | - Tilman Esslinger
- Institute for Quantum Electronics and Quantum Center, ETH Zürich, 8093 Zürich, Switzerland
| | - Scott Parkins
- Dodd-Walls Centre for Photonic and Quantum Technologies, New Zealand
- Department of Physics, University of Auckland, Auckland 1010, New Zealand
| | - Bernd Krauskopf
- Dodd-Walls Centre for Photonic and Quantum Technologies, New Zealand
- Department of Mathematics, University of Auckland, Auckland 1010, New Zealand
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3
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Xin L, Barrios M, Cohen JT, Chapman MS. Long-Lived Squeezed Ground States in a Quantum Spin Ensemble. PHYSICAL REVIEW LETTERS 2023; 131:133402. [PMID: 37832022 DOI: 10.1103/physrevlett.131.133402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/16/2022] [Accepted: 09/07/2023] [Indexed: 10/15/2023]
Abstract
We generate spin squeezed ground states in an atomic spin-1 Bose-Einstein condensate tuned near the quantum-critical point separating the different spin phases of the interacting ensemble using a novel nonadiabatic technique. In contrast to typical nonequilibrium methods for preparing atomic squeezed states by quenching through a quantum phase transition, squeezed ground states are time stationary with a constant quadrature squeezing angle. A squeezed ground state with 6-8 dB of squeezing and a constant squeezing angle is demonstrated. The long-term evolution of the squeezed ground state is measured and shows gradual decrease in the degree of squeezing over 2 s that is well modeled by a slow tuning of the Hamiltonian due to the loss of atomic density. Interestingly, modeling the gradual decrease does not require additional spin decoherence models despite a loss of 75% of the atoms.
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Affiliation(s)
- Lin Xin
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - Maryrose Barrios
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - Julia T Cohen
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - Michael S Chapman
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
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4
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Li Z, Colombo S, Shu C, Velez G, Pilatowsky-Cameo S, Schmied R, Choi S, Lukin M, Pedrozo-Peñafiel E, Vuletić V. Improving metrology with quantum scrambling. Science 2023; 380:1381-1384. [PMID: 37384680 DOI: 10.1126/science.adg9500] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2023] [Accepted: 05/19/2023] [Indexed: 07/01/2023]
Abstract
Quantum scrambling describes the spreading of information into many degrees of freedom in quantum systems, such that the information is no longer accessible locally but becomes distributed throughout the system. This idea can explain how quantum systems become classical and acquire a finite temperature, or how in black holes the information about the matter falling in is seemingly erased. We probe the exponential scrambling of a multiparticle system near a bistable point in phase space and utilize it for entanglement-enhanced metrology. A time-reversal protocol is used to observe a simultaneous exponential growth of both the metrological gain and the out-of-time-order correlator, thereby experimentally verifying the relation between quantum metrology and quantum information scrambling. Our results show that rapid scrambling dynamics capable of exponentially fast entanglement generation are useful for practical metrology, resulting in a 6.8(4)-decibel gain beyond the standard quantum limit.
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Affiliation(s)
- Zeyang Li
- Department of Physics, MIT-Harvard Center for Ultracold Atoms, Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Simone Colombo
- Department of Physics, MIT-Harvard Center for Ultracold Atoms, Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Chi Shu
- Department of Physics, MIT-Harvard Center for Ultracold Atoms, Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - Gustavo Velez
- Department of Physics, MIT-Harvard Center for Ultracold Atoms, Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
- Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Saúl Pilatowsky-Cameo
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | | | - Soonwon Choi
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Mikhail Lukin
- Department of Physics, Harvard University, Cambridge, MA 02138, USA
| | - Edwin Pedrozo-Peñafiel
- Department of Physics, MIT-Harvard Center for Ultracold Atoms, Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Vladan Vuletić
- Department of Physics, MIT-Harvard Center for Ultracold Atoms, Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
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5
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Zheng W, Wang H, Schmieg R, Oesterle A, Polzik ES. Entanglement-Enhanced Magnetic Induction Tomography. PHYSICAL REVIEW LETTERS 2023; 130:203602. [PMID: 37267567 DOI: 10.1103/physrevlett.130.203602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/27/2022] [Accepted: 04/04/2023] [Indexed: 06/04/2023]
Abstract
Magnetic induction tomography (MIT) is a sensing protocol exploring conductive objects via their response to radio-frequency magnetic fields. MIT is used in nondestructive testing ranging from geophysics to medical applications. Atomic magnetometers, employed as MIT sensors, allow for significant improvement of the MIT sensitivity and for exploring its quantum limits. Here, we propose and verify a quantum-enhanced version of the atomic MIT by combining it with conditional spin squeezing and stroboscopic backaction evasion. We use this quantum enhancement to demonstrate sensitivity beyond the standard quantum limits of one-dimensional quantum MIT detecting a conductive sample.
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Affiliation(s)
- Wenqiang Zheng
- Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100 Copenhagen ø, Denmark
- Zhejiang Provincial Key Laboratory and Collaborative Innovation Center for Quantum Precision Measurement, College of Science, Zhejiang University of Technology, Hangzhou 310023, China
| | - Hengyan Wang
- Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100 Copenhagen ø, Denmark
- Department of Physics, Zhejiang University of Science and Technology, Hangzhou 310023, China
| | - Rebecca Schmieg
- Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100 Copenhagen ø, Denmark
| | - Alan Oesterle
- Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100 Copenhagen ø, Denmark
| | - Eugene S Polzik
- Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100 Copenhagen ø, Denmark
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6
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Sundar B, Barberena D, Orioli AP, Chu A, Thompson JK, Rey AM, Lewis-Swan RJ. Bosonic Pair Production and Squeezing for Optical Phase Measurements in Long-Lived Dipoles Coupled to a Cavity. PHYSICAL REVIEW LETTERS 2023; 130:113202. [PMID: 37001062 DOI: 10.1103/physrevlett.130.113202] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/30/2022] [Accepted: 02/14/2023] [Indexed: 06/19/2023]
Abstract
We propose to simulate bosonic pair creation using large arrays of long-lived dipoles with multilevel internal structure coupled to an undriven optical cavity. Entanglement between the atoms, generated by the exchange of virtual photons through a common cavity mode, grows exponentially fast and is described by two-mode squeezing of effective bosonic quadratures. The mapping between an effective bosonic model and the natural spin description of the dipoles allows us to realize the analog of optical homodyne measurements via straightforward global rotations and population measurements of the electronic states, and we propose to exploit this for quantum-enhanced sensing of an optical phase (common and differential between two ensembles). We discuss a specific implementation based on Sr atoms and show that our sensing protocol is robust to sources of decoherence intrinsic to cavity platforms. Our proposal can open unique opportunities for next-generation optical atomic clocks.
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Affiliation(s)
- Bhuvanesh Sundar
- Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
- JILA, NIST, Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - Diego Barberena
- Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
- JILA, NIST, Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - Asier Piñeiro Orioli
- Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
- JILA, NIST, Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - Anjun Chu
- Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
- JILA, NIST, Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - James K Thompson
- JILA, NIST, Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - Ana Maria Rey
- Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
- JILA, NIST, Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - Robert 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
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7
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Wang S, Zhang S, Xv B. Signal distortion awakened from optical memory estimated using a calculation method with spatiotemporal separation. OPTICS EXPRESS 2023; 31:1958-1968. [PMID: 36785219 DOI: 10.1364/oe.475872] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/15/2022] [Accepted: 11/20/2022] [Indexed: 06/18/2023]
Abstract
The fidelity of photonic storage and retrieval is an essential criterion in long-distance all-optical network nodes. However, the recovered signals from optical memories based on the photon echo (PE) protocol are accompanied by undesired waveform variation and temporal drift. In this study, we use a numerical calculation method with spatiotemporal separation to investigate the essence of signal distortion. The results show that the asynchronous evolution of the macroscopic population difference and the macroscopic dipole moment with time is responsible for echo signal real distortion caused by phase shifts at the in-phase point of the recorded information. The constructive interference of the dipoles at the moment of reaching the in-phase point induces the photon emission, and this point with a nonspecific phase will be naturally accompanied by waveform changes, a small amount of time advance and delay of the PE signal, which is actually a false signal distortion. Such radiation mechanism of the inhomogeneous broadening media provides a perspective to accurately and correctly recognize the temporal drift and waveform variation of the recovered optical signal.
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8
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Abstract
The impact of measurement imperfections on quantum metrology protocols has not been approached in a systematic manner so far. In this work, we tackle this issue by generalising firstly the notion of quantum Fisher information to account for noisy detection, and propose tractable methods allowing for its approximate evaluation. We then show that in canonical scenarios involving N probes with local measurements undergoing readout noise, the optimal sensitivity depends crucially on the control operations allowed to counterbalance the measurement imperfections—with global control operations, the ideal sensitivity (e.g., the Heisenberg scaling) can always be recovered in the asymptotic N limit, while with local control operations the quantum-enhancement of sensitivity is constrained to a constant factor. We illustrate our findings with an example of NV-centre magnetometry, as well as schemes involving spin-1/2 probes with bit-flip errors affecting their two-outcome measurements, for which we find the input states and control unitary operations sufficient to attain the ultimate asymptotic precision. The effects of detection noise on quantum metrology performances have not been rigorously investigated yet. Here, the authors fill this gap by generalising the quantum Fisher information to the case of noisy readout, and showing the consequences the imperfect measurements bring.
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9
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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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10
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Xu K, Zhang YR, Sun ZH, Li H, Song P, Xiang Z, Huang K, Li H, Shi YH, Chen CT, Song X, Zheng D, Nori F, Wang H, Fan H. Metrological Characterization of Non-Gaussian Entangled States of Superconducting Qubits. PHYSICAL REVIEW LETTERS 2022; 128:150501. [PMID: 35499907 DOI: 10.1103/physrevlett.128.150501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/2021] [Accepted: 03/15/2022] [Indexed: 06/14/2023]
Abstract
Multipartite entangled states are significant resources for both quantum information processing and quantum metrology. In particular, non-Gaussian entangled states are predicted to achieve a higher sensitivity of precision measurements than Gaussian states. On the basis of metrological sensitivity, the conventional linear Ramsey squeezing parameter (RSP) efficiently characterizes the Gaussian entangled atomic states but fails for much wider classes of highly sensitive non-Gaussian states. These complex non-Gaussian entangled states can be classified by the nonlinear squeezing parameter (NLSP), as a generalization of the RSP with respect to nonlinear observables and identified via the Fisher information. However, the NLSP has never been measured experimentally. Using a 19-qubit programmable superconducting processor, we report the characterization of multiparticle entangled states generated during its nonlinear dynamics. First, selecting ten qubits, we measure the RSP and the NLSP by single-shot readouts of collective spin operators in several different directions. Then, by extracting the Fisher information of the time-evolved state of all 19 qubits, we observe a large metrological gain of 9.89_{-0.29}^{+0.28} dB over the standard quantum limit, indicating a high level of multiparticle entanglement for quantum-enhanced phase sensitivity. Benefiting from high-fidelity full controls and addressable single-shot readouts, the superconducting processor with interconnected qubits provides an ideal platform for engineering and benchmarking non-Gaussian entangled states that are useful for quantum-enhanced metrology.
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Affiliation(s)
- Kai Xu
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Yu-Ran Zhang
- Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan
- RIKEN Center for Quantum Computing (RQC), Wako-shi, Saitama 351-0198, Japan
| | - Zheng-Hang Sun
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Hekang Li
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Pengtao Song
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Zhongcheng Xiang
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Kaixuan Huang
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Hao Li
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Yun-Hao Shi
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Chi-Tong Chen
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Xiaohui Song
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Dongning Zheng
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Franco Nori
- Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan
- RIKEN Center for Quantum Computing (RQC), Wako-shi, Saitama 351-0198, Japan
- Physics Department, University of Michigan, Ann Arbor, Michigan 48109-1040, USA
| | - H Wang
- Interdisciplinary Center for Quantum Information, State Key Laboratory of Modern Optical Instrumentation, and Zhejiang Province Key Laboratory of Quantum Technology and Device, Department of Physics, Zhejiang University, Hangzhou 310027, China
| | - Heng Fan
- Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- Beijing Academy of Quantum Information Sciences and CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
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11
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Orenes DB, Sewell RJ, Lodewyck J, Mitchell MW. Improving Short-Term Stability in Optical Lattice Clocks by Quantum Nondemolition Measurement. PHYSICAL REVIEW LETTERS 2022; 128:153201. [PMID: 35499904 DOI: 10.1103/physrevlett.128.153201] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/22/2021] [Revised: 03/20/2022] [Accepted: 03/23/2022] [Indexed: 06/14/2023]
Abstract
We propose a multimeasurement estimation protocol for quantum nondemolition (QND) measurements in a Rabi clock interferometer. The method is well suited for current state-of-the-art optical lattice clocks with QND measurement capabilities. The protocol exploits the correlations between multiple nondestructive measurements of the initially prepared coherent spin state. A suitable Gaussian estimator for the clock laser detuning is presented, and an analytic expression for the sensitivity of the protocol is derived. We use this analytic expression to optimize the protocol using available experimental parameters, achieving an improvement of 7.9 dB with respect to the standard quantum limit in terms of clock stability. We also discuss the measurement back-action effects of our protocol into the atomic state.
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Affiliation(s)
- Daniel Benedicto Orenes
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
| | - Robert J Sewell
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
| | - Jérôme Lodewyck
- LNE-SYRTE, Observatoire de Paris, Université PSL, CNRS, Sorbonne Université, 61 avenue de l'Observatoire, F-75014 Paris, France
| | - Morgan W Mitchell
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
- ICREA-Institució Catalana de Recerca i Estudis Avançats, 08010 Barcelona, Spain
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12
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Bai SY, An JH. Generating Stable Spin Squeezing by Squeezed-Reservoir Engineering. PHYSICAL REVIEW LETTERS 2021; 127:083602. [PMID: 34477431 DOI: 10.1103/physrevlett.127.083602] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/23/2021] [Revised: 07/13/2021] [Accepted: 07/26/2021] [Indexed: 06/13/2023]
Abstract
As a genuine many-body entanglement, spin squeezing (SS) can be used to realize the highly precise measurement beyond the limit constrained by classical physics. Its generation has attracted much attention recently. It was reported that N two-level systems (TLSs) located near a one-dimensional waveguide can generate SS by using the mediation effect of the waveguide. However, a coherent driving on each TLS is used to stabilize the SS, which raises a high requirement for experiments. We here propose a scheme to generate stable SS resorting to neither the spin-spin coupling nor the coherent driving on the TLSs. Incorporating the mediation role of the common waveguide and the technique of squeezed-reservoir engineering, our scheme exhibits the advantages over previous ones in the scaling relation of the SS parameter with the number of the TLSs. The long-range correlation feature of the generated SS along the waveguide in our scheme may endow it with certain superiority in quantum sensing, e.g., improving the sensing efficiency of spatially unidentified weak magnetic fields.
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Affiliation(s)
- Si-Yuan Bai
- Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, Lanzhou 730000, China
| | - Jun-Hong An
- Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, Lanzhou 730000, China
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13
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Shumilin AV, Smirnov DS. Nuclear Spin Dynamics, Noise, Squeezing, and Entanglement in Box Model. PHYSICAL REVIEW LETTERS 2021; 126:216804. [PMID: 34114866 DOI: 10.1103/physrevlett.126.216804] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/09/2020] [Revised: 03/24/2021] [Accepted: 04/27/2021] [Indexed: 06/12/2023]
Abstract
We obtain a compact analytical solution for the nonlinear equation for the nuclear spin dynamics in the central spin box model in the limit of many nuclear spins. The total nuclear spin component along the external magnetic field is conserved and the two perpendicular components precess or oscillate depending on the electron spin polarization, with the frequency, determined by the nuclear spin polarization. As applications of our solution, we calculate the nuclear spin noise spectrum and describe the effects of nuclear spin squeezing and many body entanglement in the absence of a system excitation.
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Affiliation(s)
| | - D S Smirnov
- Ioffe Institute, 194021 St. Petersburg, Russia
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14
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Pedrozo-Peñafiel E, Colombo S, Shu C, Adiyatullin AF, Li Z, Mendez E, Braverman B, Kawasaki A, Akamatsu D, Xiao Y, Vuletić V. Entanglement on an optical atomic-clock transition. Nature 2020; 588:414-418. [PMID: 33328668 DOI: 10.1038/s41586-020-3006-1] [Citation(s) in RCA: 34] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2020] [Accepted: 10/21/2020] [Indexed: 11/09/2022]
Abstract
State-of-the-art atomic clocks are based on the precise detection of the energy difference between two atomic levels, which is measured in terms of the quantum phase accumulated over a given time interval1-4. The stability of optical-lattice clocks (OLCs) is limited both by the interrupted interrogation of the atomic system by the local-oscillator laser (Dick noise5) and by the standard quantum limit (SQL) that arises from the quantum noise associated with discrete measurement outcomes. Although schemes for removing the Dick noise have been recently proposed and implemented4,6-8, performance beyond the SQL by engineering quantum correlations (entanglement) between atoms9-20 has been demonstrated only in proof-of-principle experiments with microwave clocks of limited stability. The generation of entanglement on an optical-clock transition and operation of an OLC beyond the SQL represent important goals in quantum metrology, but have not yet been demonstrated experimentally16. Here we report the creation of a many-atom entangled state on an OLC transition, and use it to demonstrate a Ramsey sequence with an Allan deviation below the SQL after subtraction of the local-oscillator noise. We achieve a metrological gain of [Formula: see text] decibels over the SQL by using an ensemble consisting of a few hundred ytterbium-171 atoms, corresponding to a reduction of the averaging time by a factor of 2.8 ± 0.3. Our results are currently limited by the phase noise of the local oscillator and Dick noise, but demonstrate the possible performance improvement in state-of-the-art OLCs1-4 through the use of entanglement. This will enable further advances in timekeeping precision and accuracy, with many scientific and technological applications, including precision tests of the fundamental laws of physics21-23, geodesy24-26 and gravitational-wave detection27.
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Affiliation(s)
- Edwin Pedrozo-Peñafiel
- Department of Physics, MIT-Harvard Center for Ultracold Atoms and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Simone Colombo
- Department of Physics, MIT-Harvard Center for Ultracold Atoms and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Chi Shu
- Department of Physics, MIT-Harvard Center for Ultracold Atoms and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA.,Department of Physics, Harvard University, Cambridge, MA, USA
| | - Albert F Adiyatullin
- Department of Physics, MIT-Harvard Center for Ultracold Atoms and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Zeyang Li
- Department of Physics, MIT-Harvard Center for Ultracold Atoms and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Enrique Mendez
- Department of Physics, MIT-Harvard Center for Ultracold Atoms and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Boris Braverman
- Department of Physics, MIT-Harvard Center for Ultracold Atoms and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA.,Department of Physics and Max Planck Centre for Extreme and Quantum Photonics, University of Ottawa, Ottawa, Ontario, Canada
| | - Akio Kawasaki
- Department of Physics, MIT-Harvard Center for Ultracold Atoms and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA.,W. W. Hansen Experimental Physics Laboratory and Department of Physics, Stanford University, Stanford, CA, USA
| | - Daisuke Akamatsu
- Department of Physics, MIT-Harvard Center for Ultracold Atoms and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA.,National Metrology Institute of Japan (NMIJ), National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Japan
| | - Yanhong Xiao
- Department of Physics, MIT-Harvard Center for Ultracold Atoms and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA.,State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, and Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, China
| | - Vladan Vuletić
- Department of Physics, MIT-Harvard Center for Ultracold Atoms and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA.
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15
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Pezzè L, Smerzi A. Heisenberg-Limited Noisy Atomic Clock Using a Hybrid Coherent and Squeezed State Protocol. PHYSICAL REVIEW LETTERS 2020; 125:210503. [PMID: 33274961 DOI: 10.1103/physrevlett.125.210503] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2020] [Accepted: 09/29/2020] [Indexed: 06/12/2023]
Abstract
We propose a hybrid quantum-classical atomic clock where the interrogation of atoms prepared in a spin-coherent (or weakly squeezed) state is used to feed back one or more highly spin-squeezed atomic states toward their optimal phase-sensitivity point. The hybrid clock overcomes the stability of a single Ramsey clock using coherent or optimal spin-squeezed states and reaches a Heisenberg-limited stability while avoiding nondestructive measurements. When optimized with respect to the total number of particles, the protocol surpasses the state-of-the-art proposals that use Greenberger-Horne-Zeilinger or NOON states. We compare analytical predictions with numerical simulations of clock operations, including correlated 1/f local oscillator noise.
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Affiliation(s)
- Luca Pezzè
- QSTAR, INO-CNR and LENS, Largo Enrico Fermi 2, 50125 Firenze, Italy
| | - Augusto Smerzi
- QSTAR, INO-CNR and LENS, Largo Enrico Fermi 2, 50125 Firenze, Italy
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16
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Rossi MAC, Albarelli F, Tamascelli D, Genoni MG. Noisy Quantum Metrology Enhanced by Continuous Nondemolition Measurement. PHYSICAL REVIEW LETTERS 2020; 125:200505. [PMID: 33258625 DOI: 10.1103/physrevlett.125.200505] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/07/2020] [Accepted: 10/19/2020] [Indexed: 06/12/2023]
Abstract
We show that continuous quantum nondemolition (QND) measurement of an atomic ensemble is able to improve the precision of frequency estimation even in the presence of independent dephasing acting on each atom. We numerically simulate the dynamics of an ensemble with up to N=150 atoms initially prepared in a (classical) spin coherent state, and we show that, thanks to the spin squeezing dynamically generated by the measurement, the information obtainable from the continuous photocurrent scales superclassically with respect to the number of atoms N. We provide evidence that such superclassical scaling holds for different values of dephasing and monitoring efficiency. We moreover calculate the extra information obtainable via a final strong measurement on the conditional states generated during the dynamics and show that the corresponding ultimate limit is nearly achieved via a projective measurement of the spin-squeezed collective spin operator. We also briefly discuss the difference between our protocol and standard estimation schemes, where the state preparation time is neglected.
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Affiliation(s)
- Matteo A C Rossi
- QTF Centre of Excellence, Turku Centre for Quantum Physics, Department of Physics and Astronomy, University of Turku, FI-20014 Turun Yliopisto, Finland
| | - Francesco Albarelli
- Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warszawa, Poland
| | - Dario Tamascelli
- Dipartimento di Fisica "Aldo Pontremoli," Università degli Studi di Milano, I-20133 Milano, Italy
| | - Marco G Genoni
- Dipartimento di Fisica "Aldo Pontremoli," Università degli Studi di Milano, I-20133 Milano, Italy
- INFN - Sezione di Milano, I-20133 Milano, Italy
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17
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Retrodiction beyond the Heisenberg uncertainty relation. Nat Commun 2020; 11:5658. [PMID: 33168831 PMCID: PMC7652952 DOI: 10.1038/s41467-020-19495-1] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/28/2020] [Accepted: 10/14/2020] [Indexed: 11/23/2022] Open
Abstract
In quantum mechanics, the Heisenberg uncertainty relation presents an ultimate limit to the precision by which one can predict the outcome of position and momentum measurements on a particle. Heisenberg explicitly stated this relation for the prediction of “hypothetical future measurements”, and it does not describe the situation where knowledge is available about the system both earlier and later than the time of the measurement. Here, we study what happens under such circumstances with an atomic ensemble containing 1011 rubidium atoms, initiated nearly in the ground state in the presence of a magnetic field. The collective spin observables of the atoms are then well described by canonical position and momentum observables, \documentclass[12pt]{minimal}
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\begin{document}$$[{\hat{x}}_{\text{A}},{\hat{p}}_{\text{A}}]=i\hslash$$\end{document}[x^A,p^A]=iℏ. Quantum non-demolition measurements of \documentclass[12pt]{minimal}
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\begin{document}$${\hat{p}}_{\text{A}}$$\end{document}p^A before and of \documentclass[12pt]{minimal}
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\begin{document}$${\hat{x}}_{\text{A}}$$\end{document}x^A after time t allow precise estimates of both observables at time t. By means of the past quantum state formalism, we demonstrate that outcomes of measurements of both the \documentclass[12pt]{minimal}
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\begin{document}$${\hat{p}}_{A}$$\end{document}p^A observables can be inferred with errors below the standard quantum limit. The capability of assigning precise values to multiple observables and to observe their variation during physical processes may have implications in quantum state estimation and sensing. If we have access to information about a quantum system both before and after a measurement, we are not in the usual remit of the Heisenberg uncertainty principle anymore. Here, the authors demonstrate that, in such a scenario, one can retrodict position and momentum measurements without being limited by HUR.
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18
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Guan Q, Highman M, Meier EJ, Williams GR, Scarola V, DeMarco B, Kotochigova S, Gadway B. Nondestructive dispersive imaging of rotationally excited ultracold molecules. Phys Chem Chem Phys 2020; 22:20531-20544. [PMID: 32966419 DOI: 10.1039/d0cp03419c] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
A barrier to realizing the potential of molecules for quantum information science applications is a lack of high-fidelity, single-molecule imaging techniques. Here, we present and theoretically analyze a general scheme for dispersive imaging of electronic ground-state molecules. Our technique relies on the intrinsic anisotropy of excited molecular rotational states to generate optical birefringence, which can be detected through polarization rotation of an off-resonant probe laser beam. Using 23Na87Rb and 87Rb133Cs as examples, we construct a formalism for choosing the molecular state to be imaged and the excited electronic states involved in off-resonant coupling. Our proposal establishes the relevant parameters for achieving degree-level polarization rotations for bulk molecular gases, thus enabling high-fidelity nondestructive imaging. We additionally outline requirements for the high-fidelity imaging of individually trapped molecules.
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Affiliation(s)
- Qingze Guan
- Department of Physics, Temple University, Philadelphia, PA 19122, USA.
| | - Michael Highman
- Department of Physics and IQUIST, University of Illinois at Urbana-Champaign, Urbana, IL 61801-3080, USA.
| | - Eric J Meier
- Department of Physics and IQUIST, University of Illinois at Urbana-Champaign, Urbana, IL 61801-3080, USA.
| | - Garrett R Williams
- Department of Physics and IQUIST, University of Illinois at Urbana-Champaign, Urbana, IL 61801-3080, USA.
| | - Vito Scarola
- Department of Physics, Virginia Tech, Blacksburg, VA 24061, USA.
| | - Brian DeMarco
- Department of Physics and IQUIST, University of Illinois at Urbana-Champaign, Urbana, IL 61801-3080, USA.
| | | | - Bryce Gadway
- Department of Physics and IQUIST, University of Illinois at Urbana-Champaign, Urbana, IL 61801-3080, USA.
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19
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Ma X, Zhang X, Huang K, Lu X. Noise-suppressing and lock-free optical interferometer for cold atom experiments. OPTICS EXPRESS 2020; 28:28584-28589. [PMID: 32988125 DOI: 10.1364/oe.400356] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/15/2020] [Accepted: 08/28/2020] [Indexed: 06/11/2023]
Abstract
A novel noise-suppressing and lock-free interferometer is proposed and experimentally demonstrated in the study of the quantum non-destructive (QND) interaction of cold atoms. A QND measurement based on far-off resonant dispersive probing is usually carried out by a Mach-Zehnder type interferometer. It is an experimental challenge in its own right to reduce the classical noise, such as acoustic noise, phase noise and amplitude noise of lasers, and to lock the interferometer at the white-light position that corresponds to a nearly zero path-length difference. Here, we report an interferometer with an inserted acousto-optic modulator (AOM). It is noise immune and lock-free in principle. The experiments show that the new interferometer is able to measure cold atoms for more than 30 minutes and reduce the phase noise by about 30 dB.
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20
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Szigeti SS, Nolan SP, Close JD, Haine SA. High-Precision Quantum-Enhanced Gravimetry with a Bose-Einstein Condensate. PHYSICAL REVIEW LETTERS 2020; 125:100402. [PMID: 32955338 DOI: 10.1103/physrevlett.125.100402] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/01/2020] [Accepted: 07/27/2020] [Indexed: 06/11/2023]
Abstract
We show that the inherently large interatomic interactions of a Bose-Einstein condensate (BEC) can enhance the sensitivity of a high precision cold-atom gravimeter beyond the shot-noise limit (SNL). Through detailed numerical simulation, we demonstrate that our scheme produces spin-squeezed states with variances up to 14 dB below the SNL, and that absolute gravimetry measurement sensitivities between two and five times below the SNL are achievable with BECs between 10^{4} and 10^{6} in atom number. Our scheme is robust to phase diffusion, imperfect atom counting, and shot-to-shot variations in atom number and laser intensity. Our proposal is immediately achievable in current laboratories, since it needs only a small modification to existing state-of-the-art experiments and does not require additional guiding potentials or optical cavities.
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Affiliation(s)
- Stuart S Szigeti
- Department of Quantum Science, Research School of Physics, The Australian National University, Canberra 2601, Australia
| | - Samuel P Nolan
- QSTAR, INO-CNR and LENS, Largo Enrico Fermi 2, Firenze 50125, Italy
| | - John D Close
- Department of Quantum Science, Research School of Physics, The Australian National University, Canberra 2601, Australia
| | - Simon A Haine
- Department of Quantum Science, Research School of Physics, The Australian National University, Canberra 2601, Australia
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21
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Bao H, Duan J, Jin S, Lu X, Li P, Qu W, Wang M, Novikova I, Mikhailov EE, Zhao KF, Mølmer K, Shen H, Xiao Y. Spin squeezing of 10 11 atoms by prediction and retrodiction measurements. Nature 2020; 581:159-163. [PMID: 32405021 DOI: 10.1038/s41586-020-2243-7] [Citation(s) in RCA: 28] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/11/2019] [Accepted: 02/26/2020] [Indexed: 11/09/2022]
Abstract
The measurement sensitivity of quantum probes using N uncorrelated particles is restricted by the standard quantum limit1, which is proportional to [Formula: see text]. This limit, however, can be overcome by exploiting quantum entangled states, such as spin-squeezed states2. Here we report the measurement-based generation of a quantum state that exceeds the standard quantum limit for probing the collective spin of 1011 rubidium atoms contained in a macroscopic vapour cell. The state is prepared and verified by sequences of stroboscopic quantum non-demolition (QND) measurements. We then apply the theory of past quantum states3,4 to obtain spin state information from the outcomes of both earlier and later QND measurements. Rather than establishing a physically squeezed state in the laboratory, the past quantum state represents the combined system information from these prediction and retrodiction measurements. This information is equivalent to a noise reduction of 5.6 decibels and a metrologically relevant squeezing of 4.5 decibels relative to the coherent spin state. The past quantum state yields tighter constraints on the spin component than those obtained by conventional QND measurements. Our measurement uses 1,000 times more atoms than previous squeezing experiments5-10, with a corresponding angular variance of the squeezed collective spin of 4.6 × 10-13 radians squared. Although this work is rooted in the foundational theory of quantum measurements, it may find practical use in quantum metrology and quantum parameter estimation, as we demonstrate by applying our protocol to quantum enhanced atomic magnetometry.
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Affiliation(s)
- Han Bao
- Department of Physics, State Key Laboratory of Surface Physics and Key Laboratory of Micro and Nano Photonic Structures, Ministry of Education, Fudan University, Shanghai, China
| | - Junlei Duan
- Department of Physics, State Key Laboratory of Surface Physics and Key Laboratory of Micro and Nano Photonic Structures, Ministry of Education, Fudan University, Shanghai, China
| | - Shenchao Jin
- Department of Physics, State Key Laboratory of Surface Physics and Key Laboratory of Micro and Nano Photonic Structures, Ministry of Education, Fudan University, Shanghai, China
| | - Xingda Lu
- Department of Physics, State Key Laboratory of Surface Physics and Key Laboratory of Micro and Nano Photonic Structures, Ministry of Education, Fudan University, Shanghai, China
| | - Pengxiong Li
- Department of Physics, State Key Laboratory of Surface Physics and Key Laboratory of Micro and Nano Photonic Structures, Ministry of Education, Fudan University, Shanghai, China
| | - Weizhi Qu
- Department of Physics, State Key Laboratory of Surface Physics and Key Laboratory of Micro and Nano Photonic Structures, Ministry of Education, Fudan University, Shanghai, China
| | - Mingfeng Wang
- Department of Physics, State Key Laboratory of Surface Physics and Key Laboratory of Micro and Nano Photonic Structures, Ministry of Education, Fudan University, Shanghai, China.,Department of Physics, Wenzhou University, Zhejiang, China
| | - Irina Novikova
- Department of Physics, College of William and Mary, Williamsburg, VA, USA
| | | | - Kai-Feng Zhao
- Applied Ion Beam Physics Laboratory, Key Laboratory of the Ministry of Education, and Institute of Modern Physics, Fudan University, Shanghai, China
| | - Klaus Mølmer
- Department of Physics and Astronomy, Aarhus University, Aarhus, Denmark.
| | - Heng Shen
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Shanxi University, Taiyuan, China. .,Clarendon Laboratory, University of Oxford, Oxford, UK.
| | - Yanhong Xiao
- Department of Physics, State Key Laboratory of Surface Physics and Key Laboratory of Micro and Nano Photonic Structures, Ministry of Education, Fudan University, Shanghai, China. .,State Key Laboratory of Quantum Optics and Quantum Optics Devices, Shanxi University, Taiyuan, China.
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22
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Muñoz-Arias MH, Poggi PM, Jessen PS, Deutsch IH. Simulating Nonlinear Dynamics of Collective Spins via Quantum Measurement and Feedback. PHYSICAL REVIEW LETTERS 2020; 124:110503. [PMID: 32242733 DOI: 10.1103/physrevlett.124.110503] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/05/2019] [Accepted: 03/03/2020] [Indexed: 06/11/2023]
Abstract
We study a method to simulate quantum many-body dynamics of spin ensembles using measurement-based feedback. By performing a weak collective measurement on a large ensemble of two-level quantum systems and applying global rotations conditioned on the measurement outcome, one can simulate the dynamics of a mean-field quantum kicked top, a standard paradigm of quantum chaos. We analytically show that there exists a regime in which individual quantum trajectories adequately recover the classical limit, and show the transition between noisy quantum dynamics to full deterministic chaos described by classical Lyapunov exponents. We also analyze the effects of decoherence, and show that the proposed scheme represents a robust method to explore the emergence of chaos from complex quantum dynamics in a realistic experimental platform based on an atom-light interface.
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Affiliation(s)
- Manuel H Muñoz-Arias
- Center for Quantum Information and Control, CQuIC, Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131, USA
| | - Pablo M Poggi
- Center for Quantum Information and Control, CQuIC, Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131, USA
| | - Poul S Jessen
- Center for Quantum Information and Control, CQuIC, College of Optical Sciences and Department of Physics, University of Arizona, Tucson, Arizona 85721, USA
| | - Ivan H Deutsch
- Center for Quantum Information and Control, CQuIC, Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico 87131, USA
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23
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Ma X, Zhang X, Huang K, Lu X. Low noise measurement method based on differential optical interferometer for cold atom experiments. OPTICS EXPRESS 2020; 28:175-183. [PMID: 32118948 DOI: 10.1364/oe.381560] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/11/2019] [Accepted: 12/13/2019] [Indexed: 06/10/2023]
Abstract
We proposed and realized a low noise measurement method based on differential optical interferometer to measure trapped cold atoms in a magneto-optical trap (MOT). The configuration is based on a Mach-Zehnder type interferometer, which is composed of two beams of different frequencies. A long-term stability in phase monitor has been obtained by use of the vibration immune mechanism through subtraction of the interferograms imaged on the two photodetectors. With this new configuration, the noise caused by environmental perturbation is greatly reduced at low frequency while the signal of phase shift keeps a good long-term stability.
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24
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Kaubruegger R, Silvi P, Kokail C, van Bijnen R, Rey AM, Ye J, Kaufman AM, Zoller P. Variational Spin-Squeezing Algorithms on Programmable Quantum Sensors. PHYSICAL REVIEW LETTERS 2019; 123:260505. [PMID: 31951449 DOI: 10.1103/physrevlett.123.260505] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/02/2019] [Indexed: 06/10/2023]
Abstract
Arrays of atoms trapped in optical tweezers combine features of programmable analog quantum simulators with atomic quantum sensors. Here we propose variational quantum algorithms, tailored for tweezer arrays as programmable quantum sensors, capable of generating entangled states on demand for precision metrology. The scheme is designed to generate metrological enhancement by optimizing it in a feedback loop on the quantum device itself, thus preparing the best entangled states given the available quantum resources. We apply our ideas to the generation of spin-squeezed states on Sr atom tweezer arrays, where finite-range interactions are generated through Rydberg dressing. The complexity of experimental variational optimization of our quantum circuits is expected to scale favorably with system size. We numerically show our approach to be robust to noise, and surpassing known protocols.
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Affiliation(s)
- Raphael Kaubruegger
- Center for Quantum Physics, University of Innsbruck, Innsbruck A-6020, Austria
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck A-6020, Austria
| | - Pietro Silvi
- Center for Quantum Physics, University of Innsbruck, Innsbruck A-6020, Austria
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck A-6020, Austria
| | - Christian Kokail
- Center for Quantum Physics, University of Innsbruck, Innsbruck A-6020, Austria
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck A-6020, Austria
| | - Rick van Bijnen
- Center for Quantum Physics, University of Innsbruck, Innsbruck A-6020, Austria
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck A-6020, Austria
| | - Ana Maria Rey
- JILA, National Institute of Standards and Technology and University of Colorado and Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
- Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
| | - Jun Ye
- JILA, National Institute of Standards and Technology and University of Colorado and Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - Adam M Kaufman
- JILA, National Institute of Standards and Technology and University of Colorado and Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - Peter Zoller
- Center for Quantum Physics, University of Innsbruck, Innsbruck A-6020, Austria
- Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, Innsbruck A-6020, Austria
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25
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Compact chip-scale guided cold atom gyrometers for inertial navigation: Enabling technologies and design study. ACTA ACUST UNITED AC 2019. [DOI: 10.1116/1.5120348] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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26
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Braverman B, Kawasaki A, Pedrozo-Peñafiel E, Colombo S, Shu C, Li Z, Mendez E, Yamoah M, Salvi L, Akamatsu D, Xiao Y, Vuletić V. Near-Unitary Spin Squeezing in ^{171}Yb. PHYSICAL REVIEW LETTERS 2019; 122:223203. [PMID: 31283296 DOI: 10.1103/physrevlett.122.223203] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2019] [Indexed: 06/09/2023]
Abstract
Spin squeezing can improve atomic precision measurements beyond the standard quantum limit (SQL), and unitary spin squeezing is essential for improving atomic clocks. We report substantial and nearly unitary spin squeezing in ^{171}Yb, an optical lattice clock atom. The collective nuclear spin of ∼10^{3} atoms is squeezed by cavity feedback, using light detuned from the system's resonances to attain unitarity. The observed precision gain over the SQL is limited by state readout to 6.5(4) dB, while the generated states offer a gain of 12.9(6) dB, limited by the curvature of the Bloch sphere. Using a squeezed state within 30% of unitarity, we demonstrate an interferometer that improves the averaging time over the SQL by a factor of 3.7(2). In the future, the squeezing can be simply transferred onto the optical-clock transition of ^{171}Yb.
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Affiliation(s)
- Boris Braverman
- Department of Physics, MIT-Harvard Center for Ultracold Atoms and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Akio Kawasaki
- Department of Physics, MIT-Harvard Center for Ultracold Atoms and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Edwin Pedrozo-Peñafiel
- Department of Physics, MIT-Harvard Center for Ultracold Atoms and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Simone Colombo
- Department of Physics, MIT-Harvard Center for Ultracold Atoms and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Chi Shu
- Department of Physics, MIT-Harvard Center for Ultracold Atoms and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Zeyang Li
- Department of Physics, MIT-Harvard Center for Ultracold Atoms and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Enrique Mendez
- Department of Physics, MIT-Harvard Center for Ultracold Atoms and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Megan Yamoah
- Department of Physics, MIT-Harvard Center for Ultracold Atoms and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Leonardo Salvi
- Department of Physics, MIT-Harvard Center for Ultracold Atoms and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Dipartimento di Fisica e Astronomia and LENS-Università di Firenze, INFN-Sezione di Firenze, Via Sansone 1, 50019 Sesto Fiorentino, Italy
| | - Daisuke Akamatsu
- Department of Physics, MIT-Harvard Center for Ultracold Atoms and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- National Metrology Institute of Japan (NMIJ), National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1 Umezono, Tsukuba, Ibaraki 305-8563, Japan
| | - Yanhong Xiao
- Department of Physics, MIT-Harvard Center for Ultracold Atoms and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Department of Physics, State Key Laboratory of Surface Physics and Key Laboratory of Micro and Nano Photonic Structures (Ministry of Education), Fudan University, Shanghai 200433, China
| | - Vladan Vuletić
- Department of Physics, MIT-Harvard Center for Ultracold Atoms and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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27
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Gietka K, Mivehvar F, Ritsch H. Supersolid-Based Gravimeter in a Ring Cavity. PHYSICAL REVIEW LETTERS 2019; 122:190801. [PMID: 31144935 DOI: 10.1103/physrevlett.122.190801] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/14/2018] [Indexed: 06/09/2023]
Abstract
We propose a novel type of composite light-matter interferometer based on a supersolidlike phase of a driven Bose-Einstein condensate coupled to a pair of degenerate counterpropagating electromagnetic modes of an optical ring cavity. The supersolidlike condensate under the influence of the gravity drags the cavity optical potential with itself, thereby changing the relative phase of the two cavity electromagnetic fields. Monitoring the phase evolution of the cavity output fields thus allows for a nondestructive measurement of the gravitational acceleration. We show that the sensitivity of the proposed gravimeter exhibits Heisenberg-like scaling with respect to the atom number. As the relative phase of the cavity fields is insensitive to photon losses, the gravimeter is robust against these deleterious effects. For state-of-the-art experimental parameters, the relative sensitivity Δg/g of such a gravimeter could be of the order of 10^{-10}-10^{-8} for a condensate of a half a million atoms and interrogation time of the order of a few seconds.
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Affiliation(s)
- Karol Gietka
- Faculty of Physics, University of Warsaw, ul. Pasteura 5, 02-093 Warsaw, Poland
| | - Farokh Mivehvar
- Institut für Theoretische Physik, Universität Innsbruck, A-6020 Innsbruck, Austria
| | - Helmut Ritsch
- Institut für Theoretische Physik, Universität Innsbruck, A-6020 Innsbruck, Austria
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28
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Evrard A, Makhalov V, Chalopin T, Sidorenkov LA, Dalibard J, Lopes R, Nascimbene S. Enhanced Magnetic Sensitivity with Non-Gaussian Quantum Fluctuations. PHYSICAL REVIEW LETTERS 2019; 122:173601. [PMID: 31107084 DOI: 10.1103/physrevlett.122.173601] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/18/2019] [Indexed: 06/09/2023]
Abstract
The precision of a quantum sensor can overcome its classical counterpart when its constituents are entangled. In Gaussian squeezed states, quantum correlations lead to a reduction of the quantum projection noise below the shot noise limit. However, the most sensitive states involve complex non-Gaussian quantum fluctuations, making the required measurement protocol challenging. Here we measure the sensitivity of nonclassical states of the electronic spin J=8 of dysprosium atoms, created using light-induced nonlinear spin coupling. Magnetic sublevel resolution enables us to reach the optimal sensitivity of non-Gaussian (oversqueezed) states, well above the capability of squeezed states and about half the Heisenberg limit.
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Affiliation(s)
- Alexandre Evrard
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - Vasiliy Makhalov
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - Thomas Chalopin
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - Leonid A Sidorenkov
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - Jean Dalibard
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - Raphael Lopes
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - Sylvain Nascimbene
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
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29
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Lewis-Swan RJ, Norcia MA, Cline JRK, Thompson JK, Rey AM. Robust Spin Squeezing via Photon-Mediated Interactions on an Optical Clock Transition. PHYSICAL REVIEW LETTERS 2018; 121:070403. [PMID: 30169094 DOI: 10.1103/physrevlett.121.070403] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/23/2018] [Indexed: 06/08/2023]
Abstract
Cavity QED is a promising avenue for the deterministic generation of entangled and spin-squeezed states for quantum metrology. One archetypal scheme generates squeezing via collective one-axis twisting interactions. However, we show that in implementations using optical transitions in long-lived atoms the achievable squeezing is fundamentally limited by collectively enhanced emission into the cavity mode which is generated in parallel with the cavity-mediated spin-spin interactions. We propose an alternative scheme which generates a squeezed state that is protected from collective emission, and investigate its sensitivity to realistic sources of experimental noise and imperfections.
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Affiliation(s)
- Robert J Lewis-Swan
- JILA, NIST, and Department of Physics, University of Colorado, 440 UCB, Boulder, Colorado 80309, USA
- Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
| | - Matthew A Norcia
- JILA, NIST, and Department of Physics, University of Colorado, 440 UCB, Boulder, Colorado 80309, USA
| | - Julia R K Cline
- JILA, NIST, and Department of Physics, University of Colorado, 440 UCB, Boulder, Colorado 80309, USA
| | - James K Thompson
- JILA, NIST, and Department of Physics, University of Colorado, 440 UCB, Boulder, Colorado 80309, USA
| | - Ana Maria Rey
- JILA, NIST, and Department of Physics, University of Colorado, 440 UCB, Boulder, Colorado 80309, USA
- Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
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30
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Blair EP, Tóth G, Lent CS. Entanglement loss in molecular quantum-dot qubits due to interaction with the environment. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:195602. [PMID: 29578454 DOI: 10.1088/1361-648x/aab98d] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We study quantum entanglement loss due to environmental interaction in a condensed matter system with a complex geometry relevant to recent proposals for computing with single electrons at the nanoscale. We consider a system consisting of two qubits, each realized by an electron in a double quantum dot, which are initially in an entangled Bell state. The qubits are widely separated and each interacts with its own environment. The environment for each is modeled by surrounding double quantum dots placed at random positions with random orientations. We calculate the unitary evolution of the joint system and environment. The global state remains pure throughout. We examine the time dependence of the expectation value of the bipartite Clauser-Horne-Shimony-Holt (CHSH) and Brukner-Paunković-Rudolph-Vedral (BPRV) Bell operators and explore the emergence of correlations consistent with local realism. Though the details of this transition depend on the specific environmental geometry, we show how the results can be mapped on to a universal behavior with appropriate scaling. We determine the relevant disentanglement times based on realistic physical parameters for molecular double-dots.
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Affiliation(s)
- Enrique P Blair
- Electrical and Computer Engineering Department, Baylor University, Waco, TX, United States of America
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31
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Salvi L, Poli N, Vuletić V, Tino GM. Squeezing on Momentum States for Atom Interferometry. PHYSICAL REVIEW LETTERS 2018; 120:033601. [PMID: 29400516 DOI: 10.1103/physrevlett.120.033601] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/07/2017] [Revised: 11/06/2017] [Indexed: 06/07/2023]
Abstract
We propose and analyze a method that allows for the production of squeezed states of the atomic center-of-mass motion that can be injected into an atom interferometer. Our scheme employs dispersive probing in a ring resonator on a narrow transition in order to provide a collective measurement of the relative population of two momentum states. We show that this method is applicable to a Bragg diffraction-based strontium atom interferometer with large diffraction orders. This technique can be extended also to small diffraction orders and large atom numbers N by inducing atomic transparency at the frequency of the probe field, reaching an interferometer phase resolution scaling Δϕ∼N^{-3/4}. We show that for realistic parameters it is possible to obtain a 20 dB gain in interferometer phase estimation compared to the standard quantum limit. Our method is applicable to other atomic species where a narrow transition is available or can be synthesized.
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Affiliation(s)
- Leonardo Salvi
- Dipartimento di Fisica e Astronomia and LENS-Università di Firenze, INFN-Sezione di Firenze, Via Sansone 1, 50019 Sesto Fiorentino, Italy
| | - Nicola Poli
- Dipartimento di Fisica e Astronomia and LENS-Università di Firenze, INFN-Sezione di Firenze, Via Sansone 1, 50019 Sesto Fiorentino, Italy
| | - Vladan Vuletić
- Department of Physics, Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Guglielmo M Tino
- Dipartimento di Fisica e Astronomia and LENS-Università di Firenze, INFN-Sezione di Firenze, Via Sansone 1, 50019 Sesto Fiorentino, Italy
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32
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Nolan SP, Szigeti SS, Haine SA. Optimal and Robust Quantum Metrology Using Interaction-Based Readouts. PHYSICAL REVIEW LETTERS 2017; 119:193601. [PMID: 29219523 DOI: 10.1103/physrevlett.119.193601] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/12/2017] [Indexed: 06/07/2023]
Abstract
Useful quantum metrology requires nonclassical states with a high particle number and (close to) the optimal exploitation of the state's quantum correlations. Unfortunately, the single-particle detection resolution demanded by conventional protocols, such as spin squeezing via one-axis twisting, places severe limits on the particle number. Additionally, the challenge of finding optimal measurements (that saturate the quantum Cramér-Rao bound) for an arbitrary nonclassical state limits most metrological protocols to only moderate levels of quantum enhancement. "Interaction-based readout" protocols have been shown to allow optimal interferometry or to provide robustness against detection noise at the expense of optimality. In this Letter, we prove that one has great flexibility in constructing an optimal protocol, thereby allowing it to also be robust to detection noise. This requires the full probability distribution of outcomes in an optimal measurement basis, which is typically easily accessible and can be determined from specific criteria we provide. Additionally, we quantify the robustness of several classes of interaction-based readouts under realistic experimental constraints. We determine that optimal and robust quantum metrology is achievable in current spin-squeezing experiments.
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Affiliation(s)
- Samuel P Nolan
- School of Mathematics and Physics, University of Queensland, Brisbane, Queensland 4072, Australia
| | - Stuart S Szigeti
- School of Mathematics and Physics, University of Queensland, Brisbane, Queensland 4072, Australia
- ARC Centre of Excellence for Engineered Quantum Systems, University of Queensland, Brisbane, Queensland 4072, Australia
- Department of Physics, Centre for Quantum Science, and Dodd-Walls Centre for Photonic and Quantum Technologies, University of Otago, Dunedin 9010, New Zealand
| | - Simon A Haine
- Department of Physics and Astronomy, University of Sussex, Brighton BN1 9QH, United Kingdom
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33
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Song W, Yang W, An J, Feng M. Dissipation-assisted spin squeezing of nitrogen-vacancy centers coupled to a rectangular hollow metallic waveguide. OPTICS EXPRESS 2017; 25:19226-19235. [PMID: 29041116 DOI: 10.1364/oe.25.019226] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/24/2017] [Accepted: 06/10/2017] [Indexed: 06/07/2023]
Abstract
Spin squeezing has received much attention due to the interesting physics and important applications such as quantum metrology and quantum information processing. We here present a scheme to engineer stable spin squeezing in an array of nitrogen vacancy centers (NVCs) coupled to a rectangular hollow metallic waveguide. The remarkable feature of the waveguide as the common environment media is that one can switch on/off either the waveguide induced dipole-dipole interactions or correlated spontaneous emissions among the NVCs by designing their spatial separation. It permits us to achieve a dissipative Dicke model after the dipole-dipole interactions vanish due to destructive interference. With the external driving lasers on each NVC, a second-order phase transition is triggered, separating the steady state into two phases with and without collective spin squeezing. Supplying a physical realization of the dissipative Dicke model, our study gives a bridge between the generation of the stable spin squeezing and the phase transition physics.
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34
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Martin Ciurana F, Colangelo G, Slodička L, Sewell RJ, Mitchell MW. Entanglement-Enhanced Radio-Frequency Field Detection and Waveform Sensing. PHYSICAL REVIEW LETTERS 2017; 119:043603. [PMID: 29341778 DOI: 10.1103/physrevlett.119.043603] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/25/2017] [Indexed: 06/07/2023]
Abstract
We demonstrate a new technique for detecting the amplitude of arbitrarily chosen components of radio-frequency waveforms based on stroboscopic backaction evading measurements. We combine quantum nondemolition measurements and stroboscopic probing to detect waveform components with magnetic sensitivity beyond the standard quantum limit. Using an ensemble of 1.5×10^{6} cold rubidium atoms, we demonstrate entanglement-enhanced sensing of sinusoidal and linearly chirped waveforms, with 1.0(2) and 0.8(3) dB metrologically relevant noise reduction, respectively. We achieve volume-adjusted sensitivity of δBsqrt[V]≈3.96 fTsqrt[cm^{3}/Hz], comparable to the best rf magnetometers.
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Affiliation(s)
- F Martin Ciurana
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain
| | - G Colangelo
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain
| | - L Slodička
- Department of Optics, Palacký University, 17. listopadu 1192/12, 771 46 Olomouc, Czech Republic
| | - R J Sewell
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain
| | - M W Mitchell
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain
- ICREA-Institució Catalana de Recerca i Estudis Avançats, 08010 Barcelona, Spain
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35
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Ma L, Slattery O, Tang X. Optical quantum memory based on electromagnetically induced transparency. JOURNAL OF OPTICS (2010) 2017; 19:043001. [PMID: 28828172 PMCID: PMC5562294 DOI: 10.1088/2040-8986/19/4/043001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Electromagnetically induced transparency (EIT) is a promising approach to implement quantum memory in quantum communication and quantum computing applications. In this paper, following a brief overview of the main approaches to quantum memory, we provide details of the physical principle and theory of quantum memory based specifically on EIT. We discuss the key technologies for implementing quantum memory based on EIT and review important milestones, from the first experimental demonstration to current applications in quantum information systems.
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Affiliation(s)
- Lijun Ma
- Information Technology Laboratory, National Institute of Standards and Technology, 100 Bureau Dr, Gaithersburg, MD 20899, United States of America
| | - Oliver Slattery
- Information Technology Laboratory, National Institute of Standards and Technology, 100 Bureau Dr, Gaithersburg, MD 20899, United States of America
| | - Xiao Tang
- Information Technology Laboratory, National Institute of Standards and Technology, 100 Bureau Dr, Gaithersburg, MD 20899, United States of America
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36
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Colangelo G, Ciurana FM, Bianchet LC, Sewell RJ, Mitchell MW. Simultaneous tracking of spin angle and amplitude beyond classical limits. Nature 2017; 543:525-528. [PMID: 28332519 PMCID: PMC5407441 DOI: 10.1038/nature21434] [Citation(s) in RCA: 48] [Impact Index Per Article: 6.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/08/2016] [Accepted: 01/19/2017] [Indexed: 11/09/2022]
Abstract
Measurement of spin precession is central to extreme sensing in physics, geophysics, chemistry, nanotechnology and neuroscience, and underlies magnetic resonance spectroscopy. Because there is no spin-angle operator, any measurement of spin precession is necessarily indirect, for example, it may be inferred from spin projectors at different times. Such projectors do not commute, and so quantum measurement back-action-the random change in a quantum state due to measurement-necessarily enters the spin measurement record, introducing errors and limiting sensitivity. Here we show that this disturbance in the spin projector can be reduced below N1/2-the classical limit for N spins-by directing the quantum measurement back-action almost entirely into an unmeasured spin component. This generates a planar squeezed state that, because spins obey non-Heisenberg uncertainty relations, enables simultaneous precise knowledge of spin angle and spin amplitude. We use high-dynamic-range optical quantum non-demolition measurements applied to a precessing magnetic spin ensemble to demonstrate spin tracking with steady-state angular sensitivity 2.9 decibels below the standard quantum limit, simultaneously with amplitude sensitivity 7.0 decibels below the Poissonian variance. The standard quantum limit and Poissonian variance indicate the best possible sensitivity with independent particles. Our method surpasses these limits in non-commuting observables, enabling orders-of-magnitude improvements in sensitivity for state-of-the-art sensing and spectroscopy.
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Affiliation(s)
- Giorgio Colangelo
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain
| | - Ferran Martin Ciurana
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain
| | - Lorena C. Bianchet
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain
| | - Robert J. Sewell
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain
| | - Morgan W. Mitchell
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain
- ICREA – Institució Catalana de Recerca i Estudis Avançats, 08015 Barcelona, Spain
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37
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Luo XY, Zou YQ, Wu LN, Liu Q, Han MF, Tey MK, You L. Deterministic entanglement generation from driving through quantum phase transitions. Science 2017; 355:620-623. [DOI: 10.1126/science.aag1106] [Citation(s) in RCA: 143] [Impact Index Per Article: 20.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2016] [Accepted: 01/12/2017] [Indexed: 11/02/2022]
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38
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Proposal and proof-of-principle demonstration of non-destructive detection of photonic qubits using a Tm:LiNbO 3 waveguide. Nat Commun 2016; 7:13454. [PMID: 27853153 PMCID: PMC5118539 DOI: 10.1038/ncomms13454] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2016] [Accepted: 10/06/2016] [Indexed: 11/19/2022] Open
Abstract
Non-destructive detection of photonic qubits is an enabling technology for quantum information processing and quantum communication. For practical applications, such as quantum repeaters and networks, it is desirable to implement such detection in a way that allows some form of multiplexing as well as easy integration with other components such as solid-state quantum memories. Here, we propose an approach to non-destructive photonic qubit detection that promises to have all the mentioned features. Mediated by an impurity-doped crystal, a signal photon in an arbitrary time-bin qubit state modulates the phase of an intense probe pulse that is stored during the interaction. Using a thulium-doped waveguide in LiNbO3, we perform a proof-of-principle experiment with macroscopic signal pulses, demonstrating the expected cross-phase modulation as well as the ability to preserve the coherence between temporal modes. Our findings open the path to a new key component of quantum photonics based on rare-earth-ion-doped crystals. Rare-earth doped crystals are a promising platform for developing quantum devices. Here, Sinclair et al. propose and demonstrate a concept for non-destructive detection of photonic qubits using solid-state waveguides, which could help reduce signal losses in quantum information processing.
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39
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Abstract
Quantum mechanics predicts the existence of correlations between composite systems that, although puzzling to our physical intuition, enable technologies not accessible in a classical world. Notwithstanding, there is still no efficient general method to theoretically quantify and experimentally detect entanglement of many qubits. Here we propose to detect entanglement by measuring the statistical response of a quantum system to an arbitrary nonlocal parametric evolution. We witness entanglement without relying on the tomographic reconstruction of the quantum state, or the realization of witness operators. The protocol requires two collective settings for any number of parties and is robust against noise and decoherence occurring after the implementation of the parametric transformation. To illustrate its user friendliness we demonstrate multipartite entanglement in different experiments with ions and photons by analyzing published data on fidelity visibilities and variances of collective observables.
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40
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Kruse I, Lange K, Peise J, Lücke B, Pezzè L, Arlt J, Ertmer W, Lisdat C, Santos L, Smerzi A, Klempt C. Improvement of an Atomic Clock using Squeezed Vacuum. PHYSICAL REVIEW LETTERS 2016; 117:143004. [PMID: 27740781 DOI: 10.1103/physrevlett.117.143004] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/25/2016] [Indexed: 06/06/2023]
Abstract
Since the pioneering work of Ramsey, atom interferometers are employed for precision metrology, in particular to measure time and to realize the second. In a classical interferometer, an ensemble of atoms is prepared in one of the two input states, whereas the second one is left empty. In this case, the vacuum noise restricts the precision of the interferometer to the standard quantum limit (SQL). Here, we propose and experimentally demonstrate a novel clock configuration that surpasses the SQL by squeezing the vacuum in the empty input state. We create a squeezed vacuum state containing an average of 0.75 atoms to improve the clock sensitivity of 10000 atoms by 2.05_{-0.37}^{+0.34} dB. The SQL poses a significant limitation for today's microwave fountain clocks, which serve as the main time reference. We evaluate the major technical limitations and challenges for devising a next generation of fountain clocks based on atomic squeezed vacuum.
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Affiliation(s)
- I Kruse
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - K Lange
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - J Peise
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - B Lücke
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - L Pezzè
- QSTAR, INO-CNR and LENS, Largo Enrico Fermi 2, I-50125 Firenze, Italy
| | - J Arlt
- Institut for Fysik og Astronomi, Aarhus Universitet, Ny Munkegade 120, DK-8000 Århus C, Denmark
| | - W Ertmer
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - C Lisdat
- Physikalisch-Technische Bundesanstalt, Bundesallee 100, D-38116 Braunschweig, Germany
| | - L Santos
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, D-30167 Hannover, Germany
| | - A Smerzi
- QSTAR, INO-CNR and LENS, Largo Enrico Fermi 2, I-50125 Firenze, Italy
| | - C Klempt
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
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41
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McConnell R, Zhang H, Hu J, Ćuk S, Vuletić V. Entanglement with negative Wigner function of three thousand atoms heralded by one photon. ACTA ACUST UNITED AC 2016. [DOI: 10.1088/1742-6596/723/1/012054] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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42
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Martin Ciurana F, Colangelo G, Sewell RJ, Mitchell MW. Real-time shot-noise-limited differential photodetection for atomic quantum control. OPTICS LETTERS 2016; 41:2946-2949. [PMID: 27367072 DOI: 10.1364/ol.41.002946] [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 demonstrate high-efficiency, shot-noise-limited differential photodetection with real-time signal conditioning, suitable for feedback-based quantum control of atomic systems. The detector system has quantum efficiency of 0.92, is shot-noise-limited from 7.4×105 to 3.7×108 photons per pulse, and provides real-time voltage-encoded output at up to 2.3 M pulses per second.
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43
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Hosten O, Krishnakumar R, Engelsen NJ, Kasevich MA. Quantum phase magnification. Science 2016; 352:1552-5. [DOI: 10.1126/science.aaf3397] [Citation(s) in RCA: 104] [Impact Index Per Article: 13.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2016] [Accepted: 05/17/2016] [Indexed: 11/02/2022]
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44
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Cox KC, Greve GP, Weiner JM, Thompson JK. Deterministic Squeezed States with Collective Measurements and Feedback. PHYSICAL REVIEW LETTERS 2016; 116:093602. [PMID: 26991175 DOI: 10.1103/physrevlett.116.093602] [Citation(s) in RCA: 45] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/07/2015] [Indexed: 06/05/2023]
Abstract
We demonstrate the creation of entangled, spin-squeezed states using a collective, or joint, measurement and real-time feedback. The pseudospin state of an ensemble of N=5×10^{4} laser-cooled ^{87}Rb atoms is deterministically driven to a specified population state with angular resolution that is a factor of 5.5(8) [7.4(6) dB] in variance below the standard quantum limit for unentangled atoms-comparable to the best enhancements using only unitary evolution. Without feedback, conditioning on the outcome of the joint premeasurement, we directly observe up to 59(8) times [17.7(6) dB] improvement in quantum phase variance relative to the standard quantum limit for N=4×10^{5} atoms. This is one of the largest reported entanglement enhancements to date in any system.
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Affiliation(s)
- Kevin C Cox
- JILA, NIST, and University of Colorado, 440 UCB, Boulder, Colorado 80309, USA
| | - Graham P Greve
- JILA, NIST, and University of Colorado, 440 UCB, Boulder, Colorado 80309, USA
| | - Joshua M Weiner
- JILA, NIST, and University of Colorado, 440 UCB, Boulder, Colorado 80309, USA
| | - James K Thompson
- JILA, NIST, and University of Colorado, 440 UCB, Boulder, Colorado 80309, USA
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45
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Measurement noise 100 times lower than the quantum-projection limit using entangled atoms. Nature 2016; 529:505-8. [DOI: 10.1038/nature16176] [Citation(s) in RCA: 282] [Impact Index Per Article: 35.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2015] [Accepted: 10/22/2015] [Indexed: 11/08/2022]
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46
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Chen W, Hu J, Duan Y, Braverman B, Zhang H, Vuletić V. Carving Complex Many-Atom Entangled States by Single-Photon Detection. PHYSICAL REVIEW LETTERS 2015; 115:250502. [PMID: 26722909 DOI: 10.1103/physrevlett.115.250502] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/10/2015] [Indexed: 06/05/2023]
Abstract
We propose a versatile and efficient method to generate a broad class of complex entangled states of many atoms via the detection of a single photon. For an atomic ensemble contained in a strongly coupled optical cavity illuminated by weak single- or multifrequency light, the atom-light interaction entangles the frequency spectrum of a transmitted photon with the collective spin of the atomic ensemble. Simple time-resolved detection of the transmitted photon then projects the atomic ensemble into a desired pure entangled state. This method can be implemented with existing technology, yields high success probability per trial, and can generate complex entangled states such as mesoscopic superposition states of coherent spin states with high fidelity.
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Affiliation(s)
- Wenlan Chen
- Department of Physics and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Jiazhong Hu
- Department of Physics and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Yiheng Duan
- Department of Physics and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Boris Braverman
- Department of Physics and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Hao Zhang
- Department of Physics and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Vladan Vuletić
- Department of Physics and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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47
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Satisfying the Einstein-Podolsky-Rosen criterion with massive particles. Nat Commun 2015; 6:8984. [PMID: 26612105 PMCID: PMC4674826 DOI: 10.1038/ncomms9984] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/09/2015] [Accepted: 10/23/2015] [Indexed: 11/11/2022] Open
Abstract
In 1935, Einstein, Podolsky and Rosen (EPR) questioned the completeness of quantum mechanics by devising a quantum state of two massive particles with maximally correlated space and momentum coordinates. The EPR criterion qualifies such continuous-variable entangled states, where a measurement of one subsystem seemingly allows for a prediction of the second subsystem beyond the Heisenberg uncertainty relation. Up to now, continuous-variable EPR correlations have only been created with photons, while the demonstration of such strongly correlated states with massive particles is still outstanding. Here we report on the creation of an EPR-correlated two-mode squeezed state in an ultracold atomic ensemble. The state shows an EPR entanglement parameter of 0.18(3), which is 2.4 s.d. below the threshold 1/4 of the EPR criterion. We also present a full tomographic reconstruction of the underlying many-particle quantum state. The state presents a resource for tests of quantum nonlocality and a wide variety of applications in the field of continuous-variable quantum information and metrology. Continuous-variables EPR states present a resource for applications to quantum information processing and metrology, but these states have been created until now only with photon pairs. Here, the authors report the creation of an EPR-correlated two-mode squeezed states in an ultracold atomic ensemble.
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48
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Gabbrielli M, Pezzè L, Smerzi A. Spin-Mixing Interferometry with Bose-Einstein Condensates. PHYSICAL REVIEW LETTERS 2015; 115:163002. [PMID: 26550872 DOI: 10.1103/physrevlett.115.163002] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2015] [Indexed: 06/05/2023]
Abstract
Unstable spinor Bose-Einstein condensates are ideal candidates to create nonlinear three-mode interferometers. Our analysis goes beyond the standard SU(1,1) parametric approach and therefore provides the regime of parameters where sub-shot-noise sensitivities can be reached with respect to the input total average number of particles. Decoherence due to particle losses and finite detection efficiency are also considered.
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Affiliation(s)
- Marco Gabbrielli
- Dipartimento di Fisica e Astronomia, Università degli Studi di Firenze, via Sansone 1, I-50019, Sesto Fiorentino, Italy
- QSTAR, INO-CNR and LENS, Largo Enrico Fermi 2, I-50125 Firenze, Italy
| | - Luca Pezzè
- QSTAR, INO-CNR and LENS, Largo Enrico Fermi 2, I-50125 Firenze, Italy
| | - Augusto Smerzi
- QSTAR, INO-CNR and LENS, Largo Enrico Fermi 2, I-50125 Firenze, Italy
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49
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Barontini G, Hohmann L, Haas F, Esteve J, Reichel J. Deterministic generation of multiparticle entanglement by quantum Zeno dynamics. Science 2015; 349:1317-21. [DOI: 10.1126/science.aaa0754] [Citation(s) in RCA: 78] [Impact Index Per Article: 8.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
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50
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Nicholson T, Campbell S, Hutson R, Marti G, Bloom B, McNally R, Zhang W, Barrett M, Safronova M, Strouse G, Tew W, Ye J. Systematic evaluation of an atomic clock at 2 × 10(-18) total uncertainty. Nat Commun 2015; 6:6896. [PMID: 25898253 PMCID: PMC4411304 DOI: 10.1038/ncomms7896] [Citation(s) in RCA: 141] [Impact Index Per Article: 15.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2015] [Accepted: 03/11/2015] [Indexed: 11/24/2022] Open
Abstract
The pursuit of better atomic clocks has advanced many research areas, providing better quantum state control, new insights in quantum science, tighter limits on fundamental constant variation and improved tests of relativity. The record for the best stability and accuracy is currently held by optical lattice clocks. Here we take an important step towards realizing the full potential of a many-particle clock with a state-of-the-art stable laser. Our (87)Sr optical lattice clock now achieves fractional stability of 2.2 × 10(-16) at 1 s. With this improved stability, we perform a new accuracy evaluation of our clock, reducing many systematic uncertainties that limited our previous measurements, such as those in the lattice ac Stark shift, the atoms' thermal environment and the atomic response to room-temperature blackbody radiation. Our combined measurements have reduced the total uncertainty of the JILA Sr clock to 2.1 × 10(-18) in fractional frequency units.
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Affiliation(s)
- T.L. Nicholson
- JILA, National Institute of Standards and Technology and University of Colorado, Boulder, Colorado 80309-0440, USA
- Department of Physics, University of Colorado, Boulder, Colorado 80309-0390, USA
| | - S.L. Campbell
- JILA, National Institute of Standards and Technology and University of Colorado, Boulder, Colorado 80309-0440, USA
- Department of Physics, University of Colorado, Boulder, Colorado 80309-0390, USA
| | - R.B. Hutson
- JILA, National Institute of Standards and Technology and University of Colorado, Boulder, Colorado 80309-0440, USA
- Department of Physics, University of Colorado, Boulder, Colorado 80309-0390, USA
| | - G.E. Marti
- JILA, National Institute of Standards and Technology and University of Colorado, Boulder, Colorado 80309-0440, USA
- Department of Physics, University of Colorado, Boulder, Colorado 80309-0390, USA
| | - B.J. Bloom
- JILA, National Institute of Standards and Technology and University of Colorado, Boulder, Colorado 80309-0440, USA
- Department of Physics, University of Colorado, Boulder, Colorado 80309-0390, USA
| | - R.L. McNally
- JILA, National Institute of Standards and Technology and University of Colorado, Boulder, Colorado 80309-0440, USA
- Department of Physics, University of Colorado, Boulder, Colorado 80309-0390, USA
| | - W. Zhang
- JILA, National Institute of Standards and Technology and University of Colorado, Boulder, Colorado 80309-0440, USA
- Department of Physics, University of Colorado, Boulder, Colorado 80309-0390, USA
| | - M.D. Barrett
- JILA, National Institute of Standards and Technology and University of Colorado, Boulder, Colorado 80309-0440, USA
- Centre for Quantum Technologies, 3 Science Drive 2, Singapore 117543, Singapore
| | - M.S. Safronova
- University of Delaware, Newark, Delaware 19716, USA
- Joint Quantum Institute, NIST and the University of Maryland, College Park, Maryland 20899, USA
| | - G.F. Strouse
- National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - W.L. Tew
- National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - J. Ye
- JILA, National Institute of Standards and Technology and University of Colorado, Boulder, Colorado 80309-0440, USA
- Department of Physics, University of Colorado, Boulder, Colorado 80309-0390, USA
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