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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Kubischta E, Teixeira I. Family of Quantum Codes with Exotic Transversal Gates. PHYSICAL REVIEW LETTERS 2023; 131:240601. [PMID: 38181144 DOI: 10.1103/physrevlett.131.240601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/24/2023] [Revised: 10/13/2023] [Accepted: 11/16/2023] [Indexed: 01/07/2024]
Abstract
Recently, an algorithm has been constructed that shows that the binary icosahedral group 2I together with a T-like gate forms the most efficient single-qubit universal gate set. To carry out the algorithm fault tolerantly requires a code that implements 2I transversally. However, no such code has ever been demonstrated in the literature. We fill this void by constructing a family of distance d=3 codes that all implement 2I transversally. A surprising feature of this family is that the codes can be deduced entirely from symmetry considerations that only 2I affords.
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Affiliation(s)
- Eric Kubischta
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Ian Teixeira
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
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3
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Krešić I, Robb GRM, Oppo GL, Ackemann T. Generating Multiparticle Entangled States by Self-Organization of Driven Ultracold Atoms. PHYSICAL REVIEW LETTERS 2023; 131:163602. [PMID: 37925717 DOI: 10.1103/physrevlett.131.163602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/19/2022] [Accepted: 09/07/2023] [Indexed: 11/07/2023]
Abstract
We describe a mechanism for guiding the dynamical evolution of ultracold atomic motional degrees of freedom toward multiparticle entangled Dicke-squeezed states, via nonlinear self-organization under external driving. Two examples of many-body models are investigated. In the first model, the external drive is a temporally oscillating magnetic field leading to self-organization by interatomic scattering. In the second model, the drive is a pump laser leading to transverse self-organization by photon-atom scattering in a ring cavity. We numerically demonstrate the generation of multiparticle entangled states of atomic motion and discuss prospective experimental realizations of the models. For the cavity case, the calculations with adiabatically eliminated photonic sidebands show significant momentum entanglement generation can occur even in the "bad cavity" regime. The results highlight the potential for using self-organization of atomic motion in quantum technological applications.
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Affiliation(s)
- Ivor Krešić
- Institute for Theoretical Physics, Vienna University of Technology (TU Wien), Vienna, A-1040, Austria
- Centre for Advanced Laser Techniques, Institute of Physics, Bijenička cesta 46, 10000, Zagreb, Croatia
| | - Gordon R M Robb
- SUPA and Department of Physics, University of Strathclyde, Glasgow G4 0NG, Scotland, United Kingdom
| | - Gian-Luca Oppo
- SUPA and Department of Physics, University of Strathclyde, Glasgow G4 0NG, Scotland, United Kingdom
| | - Thorsten Ackemann
- SUPA and Department of Physics, University of Strathclyde, Glasgow G4 0NG, Scotland, United Kingdom
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4
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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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5
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Chomaz L, Ferrier-Barbut I, Ferlaino F, Laburthe-Tolra B, Lev BL, Pfau T. Dipolar physics: a review of experiments with magnetic quantum gases. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2022; 86:026401. [PMID: 36583342 DOI: 10.1088/1361-6633/aca814] [Citation(s) in RCA: 20] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/2022] [Accepted: 12/02/2022] [Indexed: 06/17/2023]
Abstract
Since the achievement of quantum degeneracy in gases of chromium atoms in 2004, the experimental investigation of ultracold gases made of highly magnetic atoms has blossomed. The field has yielded the observation of many unprecedented phenomena, in particular those in which long-range and anisotropic dipole-dipole interactions (DDIs) play a crucial role. In this review, we aim to present the aspects of the magnetic quantum-gas platform that make it unique for exploring ultracold and quantum physics as well as to give a thorough overview of experimental achievements. Highly magnetic atoms distinguish themselves by the fact that their electronic ground-state configuration possesses a large electronic total angular momentum. This results in a large magnetic moment and a rich electronic transition spectrum. Such transitions are useful for cooling, trapping, and manipulating these atoms. The complex atomic structure and large dipolar moments of these atoms also lead to a dense spectrum of resonances in their two-body scattering behaviour. These resonances can be used to control the interatomic interactions and, in particular, the relative importance of contact over dipolar interactions. These features provide exquisite control knobs for exploring the few- and many-body physics of dipolar quantum gases. The study of dipolar effects in magnetic quantum gases has covered various few-body phenomena that are based on elastic and inelastic anisotropic scattering. Various many-body effects have also been demonstrated. These affect both the shape, stability, dynamics, and excitations of fully polarised repulsive Bose or Fermi gases. Beyond the mean-field instability, strong dipolar interactions competing with slightly weaker contact interactions between magnetic bosons yield new quantum-stabilised states, among which are self-bound droplets, droplet assemblies, and supersolids. Dipolar interactions also deeply affect the physics of atomic gases with an internal degree of freedom as these interactions intrinsically couple spin and atomic motion. Finally, long-range dipolar interactions can stabilise strongly correlated excited states of 1D gases and also impact the physics of lattice-confined systems, both at the spin-polarised level (Hubbard models with off-site interactions) and at the spinful level (XYZ models). In the present manuscript, we aim to provide an extensive overview of the various related experimental achievements up to the present.
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Affiliation(s)
- Lauriane Chomaz
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstrasse 25, 6020 Innsbruck, Austria
- Physikalisches Institut der Universität Heidelberg, Im Neuenheimer Feld 226, 69120 Heidelberg, Germany
| | - Igor Ferrier-Barbut
- Physikalisches Institut and Center for Integrated Quantum Science and Technology, Universität Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart, Germany
- Université Paris-Saclay, Institut d'Optique Graduate School, CNRS, Laboratoire Charles Fabry, 91127 Palaiseau, France
| | - Francesca Ferlaino
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstrasse 25, 6020 Innsbruck, Austria
- Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, 6020 Innsbruck, Austria
| | - Bruno Laburthe-Tolra
- Université Sorbonne Paris Nord, Laboratoire de Physique des Lasers, F-93430 Villetaneuse, France
- CNRS, UMR 7538, LPL, F-93430 Villetaneuse, France
| | - Benjamin L Lev
- Departments of Physics and Applied Physics and Ginzton Laboratory, Stanford University, Stanford, CA 94305, United States of America
| | - Tilman Pfau
- Physikalisches Institut and Center for Integrated Quantum Science and Technology, Universität Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart, Germany
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6
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Programmable interactions and emergent geometry in an array of atom clouds. Nature 2021; 600:630-635. [PMID: 34937894 DOI: 10.1038/s41586-021-04156-0] [Citation(s) in RCA: 28] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2021] [Accepted: 10/15/2021] [Indexed: 11/08/2022]
Abstract
Interactions govern the flow of information and the formation of correlations between constituents of many-body quantum systems, dictating phases of matter found in nature and forms of entanglement generated in the laboratory. Typical interactions decay with distance and thus produce a network of connectivity governed by geometry-such as the crystalline structure of a material or the trapping sites of atoms in a quantum simulator1,2. However, many envisioned applications in quantum simulation and computation require more complex coupling graphs including non-local interactions, which feature in models of information scrambling in black holes3-6 and mappings of hard optimization problems onto frustrated classical magnets7-11. Here we describe the realization of programmable non-local interactions in an array of atomic ensembles within an optical cavity, in which photons carry information between atomic spins12-19. By programming the distance dependence of the interactions, we access effective geometries for which the dimensionality, topology and metric are entirely distinct from the physical geometry of the array. As examples, we engineer an antiferromagnetic triangular ladder, a Möbius strip with sign-changing interactions and a treelike geometry inspired by concepts of quantum gravity5,20-22. The tree graph constitutes a toy model of holographic duality21,22, in which the quantum system lies on the boundary of a higher-dimensional geometry that emerges from measured correlations23. Our work provides broader prospects for simulating frustrated magnets and topological phases24, investigating quantum optimization paradigms10,11,25,26 and engineering entangled resource states for sensing and computation27,28.
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7
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Anders F, Idel A, Feldmann P, Bondarenko D, Loriani S, Lange K, Peise J, Gersemann M, Meyer-Hoppe B, Abend S, Gaaloul N, Schubert C, Schlippert D, Santos L, Rasel E, Klempt C. Momentum Entanglement for Atom Interferometry. PHYSICAL REVIEW LETTERS 2021; 127:140402. [PMID: 34652182 DOI: 10.1103/physrevlett.127.140402] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/30/2020] [Accepted: 09/03/2021] [Indexed: 06/13/2023]
Abstract
Compared to light interferometers, the flux in cold-atom interferometers is low and the associated shot noise is large. Sensitivities beyond these limitations require the preparation of entangled atoms in different momentum modes. Here, we demonstrate a source of entangled atoms that is compatible with state-of-the-art interferometers. Entanglement is transferred from the spin degree of freedom of a Bose-Einstein condensate to well-separated momentum modes, witnessed by a squeezing parameter of -3.1(8) dB. Entanglement-enhanced atom interferometers promise unprecedented sensitivities for quantum gradiometers or gravitational wave detectors.
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Affiliation(s)
- F Anders
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - A Idel
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - P Feldmann
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, D-30167 Hannover, Germany
| | - D Bondarenko
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, D-30167 Hannover, Germany
| | - S Loriani
- 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
| | - M Gersemann
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - B Meyer-Hoppe
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - S Abend
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - N Gaaloul
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - C Schubert
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
- Deutsches Zentrum für Luft- und Raumfahrt e.V. (DLR), Institut für Satellitengeodäsie und Inertialsensorik, c/o Leibniz, Universität Hannover, DLR-SI, Callinstraße 36, 30167 Hannover, Germany
| | - D Schlippert
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - L Santos
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, D-30167 Hannover, Germany
| | - E Rasel
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - C Klempt
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
- Deutsches Zentrum für Luft- und Raumfahrt e.V. (DLR), Institut für Satellitengeodäsie und Inertialsensorik, c/o Leibniz, Universität Hannover, DLR-SI, Callinstraße 36, 30167 Hannover, Germany
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8
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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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9
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Kim K, Hur J, Huh S, Choi S, Choi JY. Emission of Spin-Correlated Matter-Wave Jets from Spinor Bose-Einstein Condensates. PHYSICAL REVIEW LETTERS 2021; 127:043401. [PMID: 34355976 DOI: 10.1103/physrevlett.127.043401] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/08/2021] [Accepted: 06/16/2021] [Indexed: 06/13/2023]
Abstract
We report the observation of matter-wave jet emission in a strongly ferromagnetic spinor Bose-Einstein condensate of ^{7}Li atoms. Directional atomic beams with |F=1,m_{F}=1⟩ and |F=1,m_{F}=-1⟩ spin states are generated from |F=1,m_{F}=0⟩ state condensates or vice versa. This results from collective spin-mixing scattering events, where spontaneously produced pairs of atoms with opposite momentum facilitates additional spin-mixing collisions as they pass through the condensates. The matter-wave jets of different spin states (|F=1,m_{F}=±1⟩) can be a macroscopic Einstein-Podolsky-Rosen state with spacelike separation. Its spin-momentum correlations are studied by using the angular correlation function for each spin state. Rotating the spin axis, the inter- and intraspin-momentum correlation peaks display a high-contrast oscillation, indicating collective coherence of the atomic ensembles. We provide numerical calculations that describe the experimental results at a quantitative level. Our Letter paves the way to generating macroscopic quantum entanglement with the spin and motional degree of freedom with massive particles. It has a wide range of applications from quantum information science to the fundamental studies of quantum entanglement.
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Affiliation(s)
- Kyungtae Kim
- Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 34141, Korea
| | - Junhyeok Hur
- Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 34141, Korea
| | - SeungJung Huh
- Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 34141, Korea
| | - Soonwon Choi
- Department of Physics, University of California Berkeley, Berkeley, California 94720, USA
- Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Jae-Yoon Choi
- Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 34141, Korea
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10
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Fadel M, Usui A, Huber M, Friis N, Vitagliano G. Entanglement Quantification in Atomic Ensembles. PHYSICAL REVIEW LETTERS 2021; 127:010401. [PMID: 34270307 DOI: 10.1103/physrevlett.127.010401] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/30/2021] [Accepted: 06/02/2021] [Indexed: 06/13/2023]
Abstract
Entanglement measures quantify nonclassical correlations present in a quantum system, but can be extremely difficult to calculate, even more so, when information on its state is limited. Here, we consider broad families of entanglement criteria that are based on variances of arbitrary operators and analytically derive the lower bounds these criteria provide for two relevant entanglement measures: the best separable approximation and the generalized robustness. This yields a practical method for quantifying entanglement in realistic experimental situations, in particular, when only few measurements of simple observables are available. As a concrete application of this method, we quantify bipartite and multipartite entanglement in spin-squeezed Bose-Einstein condensates of ∼500 atoms, by lower bounding the best separable approximation and the generalized robustness only from measurements of first and second moments of the collective spin operator.
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Affiliation(s)
- Matteo Fadel
- Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
| | - Ayaka Usui
- Quantum Systems Unit, Okinawa Institute of Science and Technology Graduate University, 904-0495 Okinawa, Japan
| | - Marcus Huber
- Atominstitut, Technische Universität Wien, 1020 Vienna, Austria
- Institute for Quantum Optics and Quantum Information-IQOQI Vienna, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
| | - Nicolai Friis
- Atominstitut, Technische Universität Wien, 1020 Vienna, Austria
- Institute for Quantum Optics and Quantum Information-IQOQI Vienna, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
| | - Giuseppe Vitagliano
- Institute for Quantum Optics and Quantum Information-IQOQI Vienna, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
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11
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Evrard B, Qu A, Dalibard J, Gerbier F. From Many-Body Oscillations to Thermalization in an Isolated Spinor Gas. PHYSICAL REVIEW LETTERS 2021; 126:063401. [PMID: 33635710 DOI: 10.1103/physrevlett.126.063401] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/26/2020] [Accepted: 01/13/2021] [Indexed: 06/12/2023]
Abstract
The dynamics of a many-body system can take many forms, from a purely reversible evolution to fast thermalization. Here we show experimentally and numerically that an assembly of spin-1 atoms all in the same spatial mode allows one to explore this wide variety of behaviors. When the system can be described by a Bogoliubov analysis, the relevant energy spectrum is linear and leads to undamped oscillations of many-body observables. Outside this regime, the nonlinearity of the spectrum leads to irreversibility, characterized by a universal behavior. When the integrability of the Hamiltonian is broken, a chaotic dynamics emerges and leads to thermalization, in agreement with the eigenstate thermalization hypothesis paradigm.
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Affiliation(s)
- Bertrand Evrard
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL Research University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - An Qu
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL Research University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - Jean Dalibard
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL Research University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - Fabrice Gerbier
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL Research University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
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12
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Guo SF, Chen F, Liu Q, Xue M, Chen JJ, Cao JH, Mao TW, Tey MK, You L. Faster State Preparation across Quantum Phase Transition Assisted by Reinforcement Learning. PHYSICAL REVIEW LETTERS 2021; 126:060401. [PMID: 33635691 DOI: 10.1103/physrevlett.126.060401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/19/2020] [Accepted: 01/12/2021] [Indexed: 06/12/2023]
Abstract
An energy gap develops near quantum critical point of quantum phase transition in a finite many-body (MB) system, facilitating the ground state transformation by adiabatic parameter change. In real application scenarios, however, the efficacy for such a protocol is compromised by the need to balance finite system lifetime with adiabaticity, as exemplified in a recent experiment that prepares three-mode balanced Dicke state near deterministically [Y.-Q. Zou et al., Proc. Natl. Acad. Sci. U.S.A. 115, 6381 (2018)PNASA60027-842410.1073/pnas.1715105115]. Instead of tracking the instantaneous ground state as unanimously required for most adiabatic crossing, this work reports a faster sweeping policy taking advantage of excited level dynamics. It is obtained based on deep reinforcement learning (DRL) from a multistep training scheme we develop. In the absence of loss, a fidelity ≥99% between prepared and the target Dicke state is achieved over a small fraction of the adiabatically required time. When loss is included, training is carried out according to an operational benchmark, the interferometric sensitivity of the prepared state instead of fidelity, leading to better sensitivity in about half of the previously reported time. Implemented in a Bose-Einstein condensate of ∼10^{4} ^{87}Rb atoms, the balanced three-mode Dicke state exhibiting an improved number squeezing of 13.02±0.20 dB is observed within 766 ms, highlighting the potential of DRL for quantum dynamics control and quantum state preparation in interacting MB systems.
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Affiliation(s)
- Shuai-Feng Guo
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Feng Chen
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Qi Liu
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Ming Xue
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Jun-Jie Chen
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Jia-Hao Cao
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Tian-Wei Mao
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
| | - Meng Khoon Tey
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
- Frontier Science Center for Quantum Information, Beijing, China
| | - Li You
- State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China
- Frontier Science Center for Quantum Information, Beijing, China
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13
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Gabardos L, Zhu B, Lepoutre S, Rey AM, Laburthe-Tolra B, Vernac L. Relaxation of the Collective Magnetization of a Dense 3D Array of Interacting Dipolar S=3 Atoms. PHYSICAL REVIEW LETTERS 2020; 125:143401. [PMID: 33064529 DOI: 10.1103/physrevlett.125.143401] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/26/2020] [Accepted: 08/14/2020] [Indexed: 06/11/2023]
Abstract
We report on measurements of the dynamics of the total magnetization and spin populations in an almost unit-filled lattice system comprising about 10^{4} spin S=3 chromium atoms, under the effect of dipolar interactions. The observed spin population dynamics is unaffected by the use of a spin echo and fully consistent with numerical simulations of the S=3 XXZ spin model. On the contrary, the observed magnetization decays slower than in simulations and, surprisingly, reaches a small but nonzero asymptotic value within the longest timescale. Our findings show that spin coherences are sensitive probes to systematic effects affecting quantum many-body behavior that cannot be diagnosed by merely measuring spin populations.
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Affiliation(s)
- Lucas Gabardos
- Laboratoire de Physique des Lasers, Université Paris 13, F-93430 Villetaneuse, France
- CNRS, UMR 7538, LPL, F-93430 Villetaneuse, France
| | - Bihui Zhu
- ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138, USA
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Steven Lepoutre
- Laboratoire de Physique des Lasers, Université Paris 13, F-93430 Villetaneuse, France
- Université Paris-Saclay, CNRS, Laboratoire Aimé Cotton, 91405, Orsay, France
| | - Ana Maria Rey
- JILA, NIST and Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
- Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
| | - Bruno Laburthe-Tolra
- Laboratoire de Physique des Lasers, Université Paris 13, F-93430 Villetaneuse, France
- CNRS, UMR 7538, LPL, F-93430 Villetaneuse, France
| | - Laurent Vernac
- Laboratoire de Physique des Lasers, Université Paris 13, F-93430 Villetaneuse, France
- CNRS, UMR 7538, LPL, F-93430 Villetaneuse, France
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14
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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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15
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Qu A, Evrard B, Dalibard J, Gerbier F. Probing Spin Correlations in a Bose-Einstein Condensate Near the Single-Atom Level. PHYSICAL REVIEW LETTERS 2020; 125:033401. [PMID: 32745434 DOI: 10.1103/physrevlett.125.033401] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/23/2020] [Accepted: 06/26/2020] [Indexed: 06/11/2023]
Abstract
Using parametric conversion induced by a Shapiro-type resonance, we produce and characterize a two-mode squeezed vacuum state in a sodium spin 1 Bose-Einstein condensate. Spin-changing collisions generate correlated pairs of atoms in the m=±1 Zeeman states out of a condensate with initially all atoms in m=0. A novel fluorescence imaging technique with sensitivity ΔN∼1.6 atom enables us to demonstrate the role of quantum fluctuations in the initial dynamics and to characterize the full distribution of the final state. Assuming that all atoms share the same spatial wave function, we infer a squeezing parameter of 15.3 dB.
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Affiliation(s)
- An Qu
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL Research University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - Bertrand Evrard
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL Research University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - Jean Dalibard
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL Research University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
| | - Fabrice Gerbier
- Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-PSL Research University, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, France
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16
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17
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Bondarenko D, Feldmann P. Quantum Autoencoders to Denoise Quantum Data. PHYSICAL REVIEW LETTERS 2020; 124:130502. [PMID: 32302195 DOI: 10.1103/physrevlett.124.130502] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/12/2019] [Accepted: 02/24/2020] [Indexed: 06/11/2023]
Abstract
Entangled states are an important resource for quantum computation, communication, metrology, and the simulation of many-body systems. However, noise limits the experimental preparation of such states. Classical data can be efficiently denoised by autoencoders-neural networks trained in unsupervised manner. We develop a novel quantum autoencoder that successfully denoises Greenberger-Horne-Zeilinger, W, Dicke, and cluster states subject to spin-flip errors and random unitary noise. Various emergent quantum technologies could benefit from the proposed unsupervised quantum neural networks.
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Affiliation(s)
- Dmytro Bondarenko
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstr. 2, DE-30167 Hannover, Germany
| | - Polina Feldmann
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstr. 2, DE-30167 Hannover, Germany
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18
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Aloy A, Tura J, Baccari F, Acín A, Lewenstein M, Augusiak R. Device-Independent Witnesses of Entanglement Depth from Two-Body Correlators. PHYSICAL REVIEW LETTERS 2019; 123:100507. [PMID: 31573313 DOI: 10.1103/physrevlett.123.100507] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/27/2019] [Indexed: 06/10/2023]
Abstract
We consider the characterization of entanglement depth in a quantum many-body system from the device-independent perspective; that is, we aim at certifying how many particles are genuinely entangled without relying on assumptions on the system itself nor on the measurements performed. We obtain device-independent witnesses of entanglement depth (DIWEDs) using the Bell inequalities introduced in [J. Tura et al., Science 344, 1256 (2014)SCIEAS0036-807510.1126/science.1247715] and compute their k-producibility bounds. To this end, we exploit two complementary methods: first, a variational one, yielding a possibly optimal k-producible state; second, a certificate of optimality via a semidefinite program, based on a relaxation of the quantum marginal problem. Numerical results suggest a clear pattern on k-producible bounds for large system sizes, which we then tackle analytically in the thermodynamic limit. Contrary to existing DIWEDs, the ones we present here can be effectively measured by accessing only collective measurements and second moments thereof. These technical requirements are met in current experiments, which have already been performed in the context of detecting Bell correlations in quantum many-body systems of 5×10^{2}-5×10^{5} atoms.
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Affiliation(s)
- A Aloy
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
| | - J Tura
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany
| | - F Baccari
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
| | - A Acín
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
- ICREA, Pg. Lluis Companys 23, 08010 Barcelona, Spain
| | - M Lewenstein
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
- ICREA, Pg. Lluis Companys 23, 08010 Barcelona, Spain
| | - R Augusiak
- Center for Theoretical Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland
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19
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Zhao YY, Xiang GY, Hu XM, Liu BH, Li CF, Guo GC, Schwonnek R, Wolf R. Entanglement Detection by Violations of Noisy Uncertainty Relations: A Proof of Principle. PHYSICAL REVIEW LETTERS 2019; 122:220401. [PMID: 31283283 DOI: 10.1103/physrevlett.122.220401] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/22/2018] [Indexed: 06/09/2023]
Abstract
It is well known that the violation of a local uncertainty relation can be used as an indicator for the presence of entanglement. Unfortunately, the practical use of these nonlinear witnesses has been limited to few special cases in the past. However, new methods for computing uncertainty bounds have become available. Here we report on an experimental implementation of uncertainty-based entanglement witnesses, benchmarked in a regime dominated by strong local noise. We combine the new computational method with a local noise tomography in order to design noise-adapted entanglement witnesses. This proof-of-principle experiment shows that quantum noise can be successfully handled by a fully quantum model in order to enhance the ability to detect entanglement.
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Affiliation(s)
- Yuan-Yuan Zhao
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China
- School of Physics and Astronomy, Sun Yat-Sen University, Zhuhai, Guangdong 519082, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Guo-Yong Xiang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Xiao-Min Hu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Bi-Heng Liu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Chuan-Feng Li
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Guang-Can Guo
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - René Schwonnek
- Institut für Theoretische Physik, Leibniz Universität Hannover, 30167, Hannover, Germany
- Department of Electrical and Computer Engineering, National University of Singapore, 117583, Singapore
| | - Ramona Wolf
- Institut für Theoretische Physik, Leibniz Universität Hannover, 30167, Hannover, Germany
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20
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Sompet P, Szigeti SS, Schwartz E, Bradley AS, Andersen MF. Thermally robust spin correlations between two 85Rb atoms in an optical microtrap. Nat Commun 2019; 10:1889. [PMID: 31015406 PMCID: PMC6478867 DOI: 10.1038/s41467-019-09420-6] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2018] [Accepted: 03/11/2019] [Indexed: 11/21/2022] Open
Abstract
The complex collisional properties of atoms fundamentally limit investigations into a range of processes in many-atom ensembles. In contrast, the bottom-up assembly of few- and many-body systems from individual atoms offers a controlled approach to isolating and studying such collisional processes. Here, we use optical tweezers to individually assemble pairs of trapped 85Rb atoms, and study the spin dynamics of the two-body system in a thermal state. The spin-2 atoms show strong pair correlation between magnetic sublevels on timescales exceeding one second, with measured relative number fluctuations 11.9 ± 0.3 dB below quantum shot noise, limited only by detection efficiency. Spin populations display relaxation dynamics consistent with simulations and theoretical predictions for 85Rb spin interactions, and contrary to the coherent spin waves witnessed in finite-temperature many-body experiments and zero-temperature two-body experiments. Our experimental approach offers a versatile platform for studying two-body quantum dynamics and may provide a route to thermally robust entanglement generation. Spin-changing atomic collisions are important for thermally robust entanglement generation with applications in quantum information. Here the authors demonstrate record high spin state correlations and long spin relaxation times in the collision of two Rb atoms at relatively warm temperatures.
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Affiliation(s)
- Pimonpan Sompet
- The Dodd-Walls Centre for Photonic and Quantum Technologies, Department of Physics, University of Otago, Dunedin, New Zealand.,Max-Planck-Institut für Quantenoptik, 85748, Garching, Germany
| | - Stuart S Szigeti
- The Dodd-Walls Centre for Photonic and Quantum Technologies, Department of Physics, University of Otago, Dunedin, New Zealand.,Department of Quantum Science, Research School of Physics and Engineering, The Australian National University, Canberra, ACT, 2601, Australia
| | - Eyal Schwartz
- The Dodd-Walls Centre for Photonic and Quantum Technologies, Department of Physics, University of Otago, Dunedin, New Zealand
| | - Ashton S Bradley
- The Dodd-Walls Centre for Photonic and Quantum Technologies, Department of Physics, University of Otago, Dunedin, New Zealand
| | - Mikkel F Andersen
- The Dodd-Walls Centre for Photonic and Quantum Technologies, Department of Physics, University of Otago, Dunedin, New Zealand.
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21
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Davis EJ, Bentsen G, Homeier L, Li T, Schleier-Smith MH. Photon-Mediated Spin-Exchange Dynamics of Spin-1 Atoms. PHYSICAL REVIEW LETTERS 2019; 122:010405. [PMID: 31012698 DOI: 10.1103/physrevlett.122.010405] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/06/2018] [Indexed: 06/09/2023]
Abstract
We report direct observations of photon-mediated spin-exchange interactions in an atomic ensemble. Interactions extending over a distance of 500 μm are generated within a cloud of cold rubidium atoms coupled to a single mode of light in an optical resonator. We characterize the system via quench dynamics and imaging of the local magnetization, verifying the coherence of the interactions and demonstrating optical control of their strength and sign. Furthermore, by initializing the spin-1 system in the m_{f}=0 Zeeman state, we observe correlated pair creation in the m_{f}=±1 states, a process analogous to spontaneous parametric down-conversion and to spin mixing in Bose-Einstein condensates. Our work opens new opportunities in quantum simulation with long-range interactions and in entanglement-enhanced metrology.
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Affiliation(s)
- Emily J Davis
- Department of Physics, Stanford University, Stanford, California 94305, USA
| | - Gregory Bentsen
- Department of Physics, Stanford University, Stanford, California 94305, USA
| | - Lukas Homeier
- Department of Physics, Stanford University, Stanford, California 94305, USA
| | - Tracy Li
- Department of Physics, Stanford University, Stanford, California 94305, USA
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22
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Quantum-enhanced sensing using non-classical spin states of a highly magnetic atom. Nat Commun 2018; 9:4955. [PMID: 30470745 PMCID: PMC6251866 DOI: 10.1038/s41467-018-07433-1] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2018] [Accepted: 10/26/2018] [Indexed: 11/08/2022] Open
Abstract
Coherent superposition states of a mesoscopic quantum object play a major role in our understanding of the quantum to classical boundary, as well as in quantum-enhanced metrology and computing. However, their practical realization and manipulation remains challenging, requiring a high degree of control of the system and its coupling to the environment. Here, we use dysprosium atoms-the most magnetic element in its ground state-to realize coherent superpositions between electronic spin states of opposite orientation, with a mesoscopic spin size J = 8. We drive coherent spin states to quantum superpositions using non-linear light-spin interactions, observing a series of collapses and revivals of quantum coherence. These states feature highly non-classical behavior, with a sensitivity to magnetic fields enhanced by a factor 13.9(1.1) compared to coherent spin states-close to the Heisenberg limit 2J = 16-and an intrinsic fragility to environmental noise.
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23
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Beating the classical precision limit with spin-1 Dicke states of more than 10,000 atoms. Proc Natl Acad Sci U S A 2018; 115:6381-6385. [PMID: 29858344 DOI: 10.1073/pnas.1715105115] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Interferometry is a paradigm for most precision measurements. Using N uncorrelated particles, the achievable precision for a two-mode (two-path) interferometer is bounded by the standard quantum limit (SQL), [Formula: see text], due to the discrete (quanta) nature of individual measurements. Despite being a challenging benchmark, the two-mode SQL has been approached in a number of systems, including the Laser Interferometer Gravitational-Wave Observatory and today's best atomic clocks. For multimode interferometry, the SQL becomes [Formula: see text] using M modes. Higher precision can also be achieved using entangled particles such that quantum noises from individual particles cancel out. In this work, we demonstrate an interferometric precision of [Formula: see text] dB beyond the three-mode SQL, using balanced spin-1 (three-mode) Dicke states containing thousands of entangled atoms. The input quantum states are deterministically generated by controlled quantum phase transition and exhibit close to ideal quality. Our work shines light on the pursuit of quantum metrology beyond SQL.
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24
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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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25
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Lange K, Peise J, Lücke B, Kruse I, Vitagliano G, Apellaniz I, Kleinmann M, Tóth G, Klempt C. Entanglement between two spatially separated atomic modes. Science 2018; 360:416-418. [PMID: 29700263 DOI: 10.1126/science.aao2035] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2017] [Accepted: 03/22/2018] [Indexed: 02/15/2024]
Abstract
Modern quantum technologies in the fields of quantum computing, quantum simulation, and quantum metrology require the creation and control of large ensembles of entangled particles. In ultracold ensembles of neutral atoms, nonclassical states have been generated with mutual entanglement among thousands of particles. The entanglement generation relies on the fundamental particle-exchange symmetry in ensembles of identical particles, which lacks the standard notion of entanglement between clearly definable subsystems. Here, we present the generation of entanglement between two spatially separated clouds by splitting an ensemble of ultracold identical particles prepared in a twin Fock state. Because the clouds can be addressed individually, our experiments open a path to exploit the available entangled states of indistinguishable particles for quantum information applications.
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Affiliation(s)
- Karsten Lange
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - Jan Peise
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - Bernd Lücke
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - Ilka Kruse
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
| | - Giuseppe Vitagliano
- Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria
- Department of Theoretical Physics, University of the Basque Country UPV/EHU, Post Office Box 644, E-48080 Bilbao, Spain
| | - Iagoba Apellaniz
- Department of Theoretical Physics, University of the Basque Country UPV/EHU, Post Office Box 644, E-48080 Bilbao, Spain
| | - Matthias Kleinmann
- Department of Theoretical Physics, University of the Basque Country UPV/EHU, Post Office Box 644, E-48080 Bilbao, Spain
- Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, D-57068 Siegen, Germany
| | - Géza Tóth
- Department of Theoretical Physics, University of the Basque Country UPV/EHU, Post Office Box 644, E-48080 Bilbao, Spain
- Ikerbasque, Basque Foundation for Science, E-48013 Bilbao, Spain
- Wigner Research Centre for Physics, Hungarian Academy of Sciences, Post Office Box 49, H-1525 Budapest, Hungary
| | - Carsten Klempt
- Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany.
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26
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Eldredge Z, Foss-Feig M, Gross JA, Rolston SL, Gorshkov AV. Optimal and secure measurement protocols for quantum sensor networks. PHYSICAL REVIEW. A 2018; 97:10.1103/PhysRevA.97.042337. [PMID: 31093589 PMCID: PMC6513338 DOI: 10.1103/physreva.97.042337] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Studies of quantum metrology have shown that the use of many-body entangled states can lead to an enhancement in sensitivity when compared with unentangled states. In this paper, we quantify the metrological advantage of entanglement in a setting where the measured quantity is a linear function of parameters individually coupled to each qubit. We first generalize the Heisenberg limit to the measurement of nonlocal observables in a quantum network, deriving a bound based on the multiparameter quantum Fisher information. We then propose measurement protocols that can make use of Greenberger-Horne-Zeilinger (GHZ) states or spin-squeezed states and show that in the case of GHZ states the protocol is optimal, i.e., it saturates our bound. We also identify nanoscale magnetic resonance imaging as a promising setting for this technology.
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Affiliation(s)
- Zachary Eldredge
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Michael Foss-Feig
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
- United States Army Research Laboratory, Adelphi, Maryland 20783, USA
| | - Jonathan A Gross
- Center for Quantum Information and Control, University of New Mexico, Albuquerque, New Mexico 87131, USA
| | - S L Rolston
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - Alexey V Gorshkov
- Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
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27
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Schwonnek R, Dammeier L, Werner RF. State-Independent Uncertainty Relations and Entanglement Detection in Noisy Systems. PHYSICAL REVIEW LETTERS 2017; 119:170404. [PMID: 29219466 DOI: 10.1103/physrevlett.119.170404] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/31/2017] [Indexed: 06/07/2023]
Abstract
Quantifying quantum mechanical uncertainty is vital for the increasing number of experiments that reach the uncertainty limited regime. We present a method for computing tight variance uncertainty relations, i.e., the optimal state-independent lower bound for the sum of the variances for any set of two or more measurements. The bounds come with a guaranteed error estimate, so results of preassigned accuracy can be obtained straightforwardly. Our method also works for postive-operator-valued measurements. Therefore, it can be used for detecting entanglement in noisy environments, even in cases where conventional spin squeezing criteria fail because of detector noise.
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Affiliation(s)
- René Schwonnek
- Leibniz Universität Hannover-Institut für Theoretische Physik, Hannover 30167, Germany
| | - Lars Dammeier
- Leibniz Universität Hannover-Institut für Theoretische Physik, Hannover 30167, Germany
| | - Reinhard F Werner
- Leibniz Universität Hannover-Institut für Theoretische Physik, Hannover 30167, Germany
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28
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Wagner S, Schmied R, Fadel M, Treutlein P, Sangouard N, Bancal JD. Bell Correlations in a Many-Body System with Finite Statistics. PHYSICAL REVIEW LETTERS 2017; 119:170403. [PMID: 29219453 DOI: 10.1103/physrevlett.119.170403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/10/2017] [Indexed: 06/07/2023]
Abstract
A recent experiment reported the first violation of a Bell correlation witness in a many-body system [Science 352, 441 (2016)]. Following discussions in this Letter, we address here the question of the statistics required to witness Bell correlated states, i.e., states violating a Bell inequality, in such experiments. We start by deriving multipartite Bell inequalities involving an arbitrary number of measurement settings, two outcomes per party and one- and two-body correlators only. Based on these inequalities, we then build up improved witnesses able to detect Bell correlated states in many-body systems using two collective measurements only. These witnesses can potentially detect Bell correlations in states with an arbitrarily low amount of spin squeezing. We then establish an upper bound on the statistics needed to convincingly conclude that a measured state is Bell correlated.
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Affiliation(s)
- Sebastian Wagner
- Quantum Optics Theory Group, Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
| | - Roman Schmied
- Quantum Atom Optics Lab, Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
| | - Matteo Fadel
- Quantum Atom Optics Lab, Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
| | - Philipp Treutlein
- Quantum Atom Optics Lab, Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
| | - Nicolas Sangouard
- Quantum Optics Theory Group, Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
| | - Jean-Daniel Bancal
- Quantum Optics Theory Group, Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
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29
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Entanglement between more than two hundred macroscopic atomic ensembles in a solid. Nat Commun 2017; 8:906. [PMID: 29030556 PMCID: PMC5640660 DOI: 10.1038/s41467-017-00897-7] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2017] [Accepted: 08/03/2017] [Indexed: 11/24/2022] Open
Abstract
There are both fundamental and practical motivations for studying whether quantum entanglement can exist in macroscopic systems. However, multiparty entanglement is generally fragile and difficult to quantify. Dicke states are multiparty entangled states where a single excitation is delocalized over many systems. Building on previous work on quantum memories for photons, we create a Dicke state in a solid by storing a single photon in a crystal that contains many large atomic ensembles with distinct resonance frequencies. The photon is re-emitted at a well-defined time due to an interference effect analogous to multi-slit diffraction. We derive a lower bound for the number of entangled ensembles based on the contrast of the interference and the single-photon character of the input, and we experimentally demonstrate entanglement between over two hundred ensembles, each containing a billion atoms. We also illustrate the fact that each individual ensemble contains further entanglement. Multipartite entanglement is of both fundamental and practical interest, but is notoriously difficult to witness and characterise. Here, Zarkeshian et al. demonstrate multipartite entanglement in an atomic frequency comb storing a single photon in a Dicke state spread over a macroscopic ensemble.
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30
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Experimental certification of millions of genuinely entangled atoms in a solid. Nat Commun 2017; 8:907. [PMID: 29030544 PMCID: PMC5640624 DOI: 10.1038/s41467-017-00898-6] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2017] [Accepted: 08/04/2017] [Indexed: 11/08/2022] Open
Abstract
Quantum theory predicts that entanglement can also persist in macroscopic physical systems, albeit difficulties to demonstrate it experimentally remain. Recently, significant progress has been achieved and genuine entanglement between up to 2900 atoms was reported. Here, we demonstrate 16 million genuinely entangled atoms in a solid-state quantum memory prepared by the heralded absorption of a single photon. We develop an entanglement witness for quantifying the number of genuinely entangled particles based on the collective effect of directed emission combined with the non-classical nature of the emitted light. The method is applicable to a wide range of physical systems and is effective even in situations with significant losses. Our results clarify the role of multipartite entanglement in ensemble-based quantum memories and demonstrate the accessibility to certain classes of multipartite entanglement with limited experimental control.The presence of entanglement in macroscopic systems is notoriously difficult to observe. Here, the authors develop a witness which allow them to demonstrate entanglement between millions of atoms in a solid-state quantum memory prepared by the heralded absorption of a single photon.
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31
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Tasgin ME. Many-Particle Entanglement Criterion for Superradiantlike States. PHYSICAL REVIEW LETTERS 2017; 119:033601. [PMID: 28777590 DOI: 10.1103/physrevlett.119.033601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/29/2016] [Indexed: 06/07/2023]
Abstract
We derive a many-particle entanglement criterion for mixed states using a relation between single-mode and many-particle nonclassicalities. The criterion relies on the measurement of collective spin observables. It works very well not only in the vicinity of the Dicke states, but also for the superpositions of Dicke states: superradiant ground states of finite or infinite number of particles and time evolution of single-photon superradiance from an extended sample where random phases appear. We also obtain a criterion for ensemble-field entanglement, which is successful for such kinds of states. We also observe an interesting phenomenon: even though the collective excitation of this many-particle system has a sub-Poissonian character, which results in entanglement, the wave function displays bunching.
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Affiliation(s)
- Mehmet Emre Tasgin
- Institute of Nuclear Sciences, Hacettepe University, 06800 Ankara, Turkey
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32
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Engelsen NJ, Krishnakumar R, Hosten O, Kasevich MA. Bell Correlations in Spin-Squeezed States of 500 000 Atoms. PHYSICAL REVIEW LETTERS 2017; 118:140401. [PMID: 28430469 DOI: 10.1103/physrevlett.118.140401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/23/2016] [Indexed: 06/07/2023]
Abstract
Bell correlations, indicating nonlocality in composite quantum systems, were until recently only seen in small systems. Here, we demonstrate Bell correlations in squeezed states of 5×10^{5} ^{87}Rb atoms. The correlations are inferred using collective measurements as witnesses and are statistically significant to 124 standard deviations. The states are both generated and characterized using optical-cavity aided measurements.
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Affiliation(s)
- Nils J Engelsen
- Department of Physics, Stanford University, Stanford, California 94305, USA
| | - Rajiv Krishnakumar
- Department of Physics, Stanford University, Stanford, California 94305, USA
| | - Onur Hosten
- Department of Physics, Stanford University, Stanford, California 94305, USA
| | - Mark A Kasevich
- Department of Physics, Stanford University, Stanford, California 94305, USA
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33
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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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34
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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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35
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Bohnet JG, Sawyer BC, Britton JW, Wall ML, Rey AM, Foss-Feig M, Bollinger JJ. Quantum spin dynamics and entanglement generation with hundreds of trapped ions. Science 2016; 352:1297-301. [PMID: 27284189 DOI: 10.1126/science.aad9958] [Citation(s) in RCA: 103] [Impact Index Per Article: 12.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2015] [Accepted: 05/04/2016] [Indexed: 11/03/2022]
Abstract
Quantum simulation of spin models can provide insight into problems that are difficult or impossible to study with classical computers. Trapped ions are an established platform for quantum simulation, but only systems with fewer than 20 ions have demonstrated quantum correlations. We studied quantum spin dynamics arising from an engineered, homogeneous Ising interaction in a two-dimensional array of (9)Be(+) ions in a Penning trap. We verified entanglement in spin-squeezed states of up to 219 ions, directly observing 4.0 ± 0.9 decibels of spectroscopic enhancement, and observed states with non-Gaussian statistics consistent with oversqueezed states. The good agreement with ab initio theory that includes interactions and decoherence lays the groundwork for simulations of the transverse-field Ising model with variable-range interactions, which are generally intractable with classical methods.
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Affiliation(s)
- Justin G Bohnet
- National Institute of Standards and Technology (NIST), Boulder, CO 80305, USA.
| | - Brian C Sawyer
- National Institute of Standards and Technology (NIST), Boulder, CO 80305, USA. Georgia Tech Research Institute, Atlanta, GA 30332, USA
| | - Joseph W Britton
- National Institute of Standards and Technology (NIST), Boulder, CO 80305, USA. Army Research Lab, Adelphi, MD 20783, USA
| | - Michael L Wall
- JILA, NIST, and University of Colorado, Boulder, CO 80309, USA
| | - Ana Maria Rey
- JILA, NIST, and Department of Physics, University of Colorado, Boulder, CO 80309, USA
| | - Michael Foss-Feig
- Army Research Lab, Adelphi, MD 20783, USA. Joint Quantum Institute and NIST, Gaithersburg, MD 20899, USA
| | - John J Bollinger
- National Institute of Standards and Technology (NIST), Boulder, CO 80305, USA.
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36
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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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37
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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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38
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Marty O, Cramer M, Plenio MB. Practical Entanglement Estimation for Spin-System Quantum Simulators. PHYSICAL REVIEW LETTERS 2016; 116:105301. [PMID: 27015489 DOI: 10.1103/physrevlett.116.105301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2015] [Indexed: 06/05/2023]
Abstract
We present practical methods to measure entanglement for quantum simulators that can be realized with trapped ions, cold atoms, and superconducting qubits. Focusing on long- and short-range Ising-type Hamiltonians, we introduce schemes that are applicable under realistic experimental conditions including mixedness due to, e.g., noise or temperature. In particular, we identify a single observable whose expectation value serves as a lower bound to entanglement and that may be obtained by a simple quantum circuit. As such circuits are not (yet) available for every platform, we investigate the performance of routinely measured observables as quantitative entanglement witnesses. Possible applications include experimental studies of entanglement scaling in critical systems and the reliable benchmarking of quantum simulators.
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Affiliation(s)
- O Marty
- Institut für Theoretische Physik & IQST, Albert-Einstein-Allee 11, Universität Ulm, Germany
| | - M Cramer
- Institut für Theoretische Physik & IQST, Albert-Einstein-Allee 11, Universität Ulm, Germany
| | - M B Plenio
- Institut für Theoretische Physik & IQST, Albert-Einstein-Allee 11, Universität Ulm, Germany
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39
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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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40
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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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41
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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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42
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Liang YC, Rosset D, Bancal JD, Pütz G, Barnea TJ, Gisin N. Family of Bell-like Inequalities as Device-Independent Witnesses for Entanglement Depth. PHYSICAL REVIEW LETTERS 2015; 114:190401. [PMID: 26024153 DOI: 10.1103/physrevlett.114.190401] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/08/2014] [Indexed: 06/04/2023]
Abstract
We present a simple family of Bell inequalities applicable to a scenario involving arbitrarily many parties, each of which performs two binary-outcome measurements. We show that these inequalities are members of the complete set of full-correlation Bell inequalities discovered by Werner-Wolf-Żukowski-Brukner. For scenarios involving a small number of parties, we further verify that these inequalities are facet defining for the convex set of Bell-local correlations. Moreover, we show that the amount of quantum violation of these inequalities naturally manifests the extent to which the underlying system is genuinely many-body entangled. In other words, our Bell inequalities, when supplemented with the appropriate quantum bounds, naturally serve as device-independent witnesses for entanglement depth, allowing one to certify genuine k-partite entanglement in an arbitrary n≥k-partite scenario without relying on any assumption about the measurements being performed, or the dimension of the underlying physical system. A brief comparison is made between our witnesses and those based on some other Bell inequalities, as well as quantum Fisher information. A family of witnesses for genuine k-partite nonlocality applicable to an arbitrary n≥k-partite scenario based on our Bell inequalities is also presented.
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Affiliation(s)
- Yeong-Cherng Liang
- Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland
- Department of Physics, National Cheng Kung University, Tainan 701, Taiwan
| | - Denis Rosset
- Group of Applied Physics, University of Geneva, CH-1211 Geneva 4, Switzerland
| | - Jean-Daniel Bancal
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore
| | - Gilles Pütz
- Group of Applied Physics, University of Geneva, CH-1211 Geneva 4, Switzerland
| | - Tomer Jack Barnea
- Group of Applied Physics, University of Geneva, CH-1211 Geneva 4, Switzerland
| | - Nicolas Gisin
- Group of Applied Physics, University of Geneva, CH-1211 Geneva 4, Switzerland
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43
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Schwemmer C, Knips L, Tran MC, de Rosier A, Laskowski W, Paterek T, Weinfurter H. Genuine Multipartite Entanglement without Multipartite Correlations. PHYSICAL REVIEW LETTERS 2015; 114:180501. [PMID: 26000990 DOI: 10.1103/physrevlett.114.180501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/09/2014] [Indexed: 06/04/2023]
Abstract
Nonclassical correlations between measurement results make entanglement the essence of quantum physics and the main resource for quantum information applications. Surprisingly, there are n-particle states which do not exhibit n-partite correlations at all but still are genuinely n-partite entangled. We introduce a general construction principle for such states, implement them in a multiphoton experiment and analyze their properties in detail. Remarkably, even without multipartite correlations, these states do violate Bell inequalities showing that there is no classical, i.e., local realistic model describing their properties.
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Affiliation(s)
- Christian Schwemmer
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany
- Department für Physik, Ludwig-Maximilians-Universität, 80797 München, Germany
| | - Lukas Knips
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany
- Department für Physik, Ludwig-Maximilians-Universität, 80797 München, Germany
| | - Minh Cong Tran
- School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, 637371 Singapore
| | - Anna de Rosier
- Institute of Theoretical Physics and Astrophysics, University of Gdańsk, PL-80-952 Gdańsk, Poland
| | - Wiesław Laskowski
- Institute of Theoretical Physics and Astrophysics, University of Gdańsk, PL-80-952 Gdańsk, Poland
| | - Tomasz Paterek
- School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, 637371 Singapore
- Center for Quantum Technologies, National University of Singapore, Singapore, 117543 Singapore
- MajuLab, CNRS-UNS-NUS-NTU International Joint Research Unit, Singapore, UMI 3654 Singapore
| | - Harald Weinfurter
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany
- Department für Physik, Ludwig-Maximilians-Universität, 80797 München, Germany
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44
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Interaction-free measurements by quantum Zeno stabilization of ultracold atoms. Nat Commun 2015; 6:6811. [PMID: 25869121 PMCID: PMC4403339 DOI: 10.1038/ncomms7811] [Citation(s) in RCA: 32] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2014] [Accepted: 03/02/2015] [Indexed: 11/09/2022] Open
Abstract
Quantum mechanics predicts that our physical reality is influenced by events that can potentially happen but factually do not occur. Interaction-free measurements (IFMs) exploit this counterintuitive influence to detect the presence of an object without requiring any interaction with it. Here we propose and realize an IFM concept based on an unstable many-particle system. In our experiments, we employ an ultracold gas in an unstable spin configuration, which can undergo a rapid decay. The object—realized by a laser beam—prevents this decay because of the indirect quantum Zeno effect and thus, its presence can be detected without interacting with a single atom. Contrary to existing proposals, our IFM does not require single-particle sources and is only weakly affected by losses and decoherence. We demonstrate confidence levels of 90%, well beyond previous optical experiments. The inherent strangeness of quantum mechanics means it is possible to detect objects using single-quantum particles even if they do not interact directly. Peise et al. realize such an ‘interaction-free measurement' by exploiting the quantum Zeno effect in a BEC, obviating the need for single-particle sources.
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45
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Aolita L, de Melo F, Davidovich L. Open-system dynamics of entanglement: a key issues review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2015; 78:042001. [PMID: 25811809 DOI: 10.1088/0034-4885/78/4/042001] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
One of the greatest challenges in the fields of quantum information processing and quantum technologies is the detailed coherent control over each and every constituent of quantum systems with an ever increasing number of particles. Within this endeavor, harnessing of many-body entanglement against the detrimental effects of the environment is a major pressing issue. Besides being an important concept from a fundamental standpoint, entanglement has been recognized as a crucial resource for quantum speed-ups or performance enhancements over classical methods. Understanding and controlling many-body entanglement in open systems may have strong implications in quantum computing, quantum simulations of many-body systems, secure quantum communication or cryptography, quantum metrology, our understanding of the quantum-to-classical transition, and other important questions of quantum foundations.In this paper we present an overview of recent theoretical and experimental efforts to underpin the dynamics of entanglement under the influence of noise. Entanglement is thus taken as a dynamic quantity on its own, and we survey how it evolves due to the unavoidable interaction of the entangled system with its surroundings. We analyze several scenarios, corresponding to different families of states and environments, which render a very rich diversity of dynamical behaviors.In contrast to single-particle quantities, like populations and coherences, which typically vanish only asymptotically in time, entanglement may disappear at a finite time. In addition, important classes of entanglement display an exponential decay with the number of particles when subject to local noise, which poses yet another threat to the already-challenging scaling of quantum technologies. Other classes, however, turn out to be extremely robust against local noise. Theoretical results and recent experiments regarding the difference between local and global decoherence are summarized. Control and robustness-enhancement techniques, scaling laws, statistical and geometrical aspects of multipartite-entanglement decay are also reviewed; all in order to give a broad picture of entanglement dynamics in open quantum systems addressed to both theorists and experimentalists inside and outside the field of quantum information.
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Affiliation(s)
- Leandro Aolita
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
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46
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McConnell R, Zhang H, Hu J, Ćuk S, Vuletić V. Entanglement with negative Wigner function of almost 3,000 atoms heralded by one photon. Nature 2015; 519:439-42. [DOI: 10.1038/nature14293] [Citation(s) in RCA: 148] [Impact Index Per Article: 16.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/28/2014] [Accepted: 01/27/2015] [Indexed: 11/09/2022]
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47
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Thompson JK. Atomic doughnuts from single photons. Nature 2015; 519:420-2. [DOI: 10.1038/519420b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
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48
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Drut JE, Porter WJ. Convexity of the entanglement entropy of SU(2N)-symmetric fermions with attractive interactions. PHYSICAL REVIEW LETTERS 2015; 114:050402. [PMID: 25699423 DOI: 10.1103/physrevlett.114.050402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/10/2014] [Indexed: 06/04/2023]
Abstract
The positivity of the probability measure of attractively interacting systems of 2N-component fermions enables the derivation of an exact convexity property for the ground-state energy of such systems. Using analogous arguments, applied to path-integral expressions for the entanglement entropy derived recently, we prove nonperturbative analytic relations for the Rényi entropies of those systems. These relations are valid for all subsystem sizes, particle numbers, and dimensions, and in arbitrary external trapping potentials.
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Affiliation(s)
- Joaquín E Drut
- Department of Physics and Astronomy, University of North Carolina, Chapel Hill, North Carolina 27599, USA
| | - William J Porter
- Department of Physics and Astronomy, University of North Carolina, Chapel Hill, North Carolina 27599, USA
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Behbood N, Martin Ciurana F, Colangelo G, Napolitano M, Tóth G, Sewell RJ, Mitchell MW. Generation of macroscopic singlet states in a cold atomic ensemble. PHYSICAL REVIEW LETTERS 2014; 113:093601. [PMID: 25215981 DOI: 10.1103/physrevlett.113.093601] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/02/2014] [Indexed: 06/03/2023]
Abstract
We report the generation of a macroscopic singlet state in a cold atomic sample via quantum nondemolition measurement-induced spin squeezing. We observe 3 dB of spin squeezing and detect entanglement with 5σ statistical significance using a generalized spin-squeezing inequality. The degree of squeezing implies at least 50% of the atoms have formed singlets.
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Affiliation(s)
- N Behbood
- ICFO-Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain
| | - F Martin Ciurana
- ICFO-Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain
| | - G Colangelo
- ICFO-Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain
| | - M Napolitano
- ICFO-Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain
| | - Géza Tóth
- Department of Theoretical Physics, University of the Basque Country UPV/EHU, P.O. Box 644, E-48080 Bilbao, Spain and IKERBASQUE, Basque Foundation for Science, E-48011 Bilbao, Spain and Wigner Research Centre for Physics, Hungarian Academy of Sciences, P.O. Box 49, H-1525 Budapest, Hungary
| | - R J Sewell
- ICFO-Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain
| | - M W Mitchell
- ICFO-Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain and ICREA-Institució Catalana de Recerca i Estudis Avançats, 08015 Barcelona, Spain
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Herdman CM, Inglis S, Roy PN, Melko RG, Del Maestro A. Path-integral Monte Carlo method for Rényi entanglement entropies. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:013308. [PMID: 25122411 DOI: 10.1103/physreve.90.013308] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/06/2014] [Indexed: 06/03/2023]
Abstract
We introduce a quantum Monte Carlo algorithm to measure the Rényi entanglement entropies in systems of interacting bosons in the continuum. This approach is based on a path-integral ground state method that can be applied to interacting itinerant bosons in any spatial dimension with direct relevance to experimental systems of quantum fluids. We demonstrate how it may be used to compute spatial mode entanglement, particle partitioned entanglement, and the entanglement of particles, providing insights into quantum correlations generated by fluctuations, indistinguishability, and interactions. We present proof-of-principle calculations and benchmark against an exactly soluble model of interacting bosons in one spatial dimension. As this algorithm retains the fundamental polynomial scaling of quantum Monte Carlo when applied to sign-problem-free models, future applications should allow for the study of entanglement entropy in large-scale many-body systems of interacting bosons.
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Affiliation(s)
- C M Herdman
- Department of Physics, University of Vermont, Burlington, Vermont 05405, USA
| | - Stephen Inglis
- Department of Physics, Arnold Sommerfeld Center for Theoretical Physics, and Center for Nanoscience, Ludwig-Maximilians-Universität München, Theresienstraße 37, 80333 Munich, Germany and Department of Physics and Astronomy, University of Waterloo, Ontario, Canada N2L 3G1
| | - P-N Roy
- Department of Chemistry, University of Waterloo, Ontario, Canada N2L 3G1
| | - R G Melko
- Department of Physics and Astronomy, University of Waterloo, Ontario, Canada N2L 3G1 and Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada N2L 2Y5
| | - A Del Maestro
- Department of Physics, University of Vermont, Burlington, Vermont 05405, USA and Vermont Complex Systems Center, University of Vermont, Burlington, Vermont 05405, USA
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