1
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Finger F, Rosa-Medina R, Reiter N, Christodoulou P, Donner T, Esslinger T. Spin- and Momentum-Correlated Atom Pairs Mediated by Photon Exchange and Seeded by Vacuum Fluctuations. PHYSICAL REVIEW LETTERS 2024; 132:093402. [PMID: 38489609 DOI: 10.1103/physrevlett.132.093402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/13/2023] [Revised: 10/27/2023] [Accepted: 01/23/2024] [Indexed: 03/17/2024]
Abstract
Engineering pairs of massive particles that are simultaneously correlated in their external and internal degrees of freedom is a major challenge, yet essential for advancing fundamental tests of physics and quantum technologies. In this Letter, we experimentally demonstrate a mechanism for generating pairs of atoms in well-defined spin and momentum modes. This mechanism couples atoms from a degenerate Bose gas via a superradiant photon-exchange process in an optical cavity, producing pairs via a single channel or two discernible channels. The scheme is independent of collisional interactions, fast, and tunable. We observe a collectively enhanced production of pairs and probe interspin correlations in momentum space. We characterize the emergent pair statistics and find that the observed dynamics is consistent with being primarily seeded by vacuum fluctuations in the corresponding atomic modes. Together with our observations of coherent many-body oscillations involving well-defined momentum modes, our results offer promising prospects for quantum-enhanced interferometry and quantum simulation experiments using entangled matter waves.
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Affiliation(s)
- Fabian Finger
- Institute for Quantum Electronics and Quantum Center, ETH Zürich, 8093 Zürich, Switzerland
| | - Rodrigo Rosa-Medina
- Institute for Quantum Electronics and Quantum Center, ETH Zürich, 8093 Zürich, Switzerland
| | - Nicola Reiter
- Institute for Quantum Electronics and Quantum Center, ETH Zürich, 8093 Zürich, Switzerland
| | | | - Tobias Donner
- Institute for Quantum Electronics and Quantum Center, ETH Zürich, 8093 Zürich, Switzerland
| | - Tilman Esslinger
- Institute for Quantum Electronics and Quantum Center, ETH Zürich, 8093 Zürich, Switzerland
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2
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Ren ZQ, Lu XL, Xiang ZL. Heisenberg-limited spin squeezing in a hybrid system with silicon-vacancy centers. OPTICS EXPRESS 2024; 32:4013-4026. [PMID: 38297610 DOI: 10.1364/oe.499299] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/2023] [Accepted: 01/08/2024] [Indexed: 02/02/2024]
Abstract
In this paper, we investigate the spin squeezing in a hybrid quantum system consisting of a Silicon-Vacancy (SiV) center ensemble coupled to a diamond acoustic waveguide via the strain interaction. Two sets of non-overlapping driving fields, each contains two time-dependent microwave fields, are applied to this hybrid system. By modulating these fields, the one-axis twist (OAT) interaction and two-axis two-spin (TATS) interaction can be independently realized. In the latter case the squeezing parameter scales to spin number as ξ R2∼1.61N -0.64 with the consideration of dissipation, which is very close to the Heisenberg limit. Furthermore, this hybrid system allows for the study of spin squeezing generated by the simultaneous presence of OAT and TATS interactions, which reveals sensitivity to the parity of the number of spins Ntot, whether it is even or odd. Our scheme enriches the approach for generating Heisenberg-limited spin squeezing in spin-phonon hybrid systems and offers the possibility for future applications in quantum information processing.
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3
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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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4
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Fulton J, Thenabadu M, Teh RY, Reid MD. Weak versus Deterministic Macroscopic Realism, and Einstein-Podolsky-Rosen's Elements of Reality. ENTROPY (BASEL, SWITZERLAND) 2023; 26:11. [PMID: 38275490 PMCID: PMC11154650 DOI: 10.3390/e26010011] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/24/2023] [Revised: 10/25/2023] [Accepted: 11/13/2023] [Indexed: 01/27/2024]
Abstract
The violation of a Leggett-Garg inequality confirms the incompatibility between quantum mechanics and the combined premises (called macro-realism) of macroscopic realism (MR) and noninvasive measurability (NIM). Arguments can be given that the incompatibility arises because MR fails for systems in a superposition of macroscopically distinct states-or else, that NIM fails. In this paper, we consider a strong negation of macro-realism, involving superpositions of coherent states, where the NIM premise is replaced by Bell's locality premise. We follow recent work and propose the validity of a subset of Einstein-Podolsky-Rosen (EPR) and Leggett-Garg premises, referred to as weak macroscopic realism (wMR). In finding consistency with wMR, we identify that the Leggett-Garg inequalities are violated because of failure of both MR and NIM, but also that both are valid in a weaker (less restrictive) sense. Weak MR is distinguished from deterministic macroscopic realism (dMR) by recognizing that a measurement involves a reversible unitary interaction that establishes the measurement setting. Weak MR posits that a predetermined value for the outcome of a measurement can be attributed to the system after the interaction, when the measurement setting is experimentally specified. An extended definition of wMR considers the "element of reality" defined by EPR for system A, where one can predict with certainty the outcome of a measurement on A by performing a measurement on system B. Weak MR posits that this element of reality exists once the unitary interaction determining the measurement setting at B has occurred. We demonstrate compatibility of systems violating Leggett-Garg inequalities with wMR but point out that dMR has been shown to be falsifiable. Other tests of wMR are proposed, the predictions of wMR agreeing with quantum mechanics. Finally, we compare wMR with macro-realism models discussed elsewhere. An argument in favour of wMR is presented: wMR resolves a potential contradiction pointed out by Leggett and Garg between failure of macro-realism and assumptions intrinsic to quantum measurement theory.
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Affiliation(s)
| | | | | | - Margaret D. Reid
- Centre for Quantum Science and Technology Theory, Swinburne University of Technology, Melbourne 3122, Australia; (J.F.); (M.T.); (R.Y.T.)
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5
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Leong WS, Xin M, Chen Z, Wang Y, Lan SY. Creation of Two-Mode Squeezed States in Atomic Mechanical Oscillators. PHYSICAL REVIEW LETTERS 2023; 131:193601. [PMID: 38000417 DOI: 10.1103/physrevlett.131.193601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/20/2023] [Accepted: 09/19/2023] [Indexed: 11/26/2023]
Abstract
Two-mode squeezed states, which are entangled states with bipartite quantum correlations in continuous-variable systems, are crucial in quantum information processing and metrology. Recently, continuous-variable quantum computing with the vibrational modes of trapped atoms has emerged with significant progress, featuring a high degree of control in hybridizing with spin qubits. Creating two-mode squeezed states in such a platform could enable applications that are only viable with photons. Here, we experimentally demonstrate two-mode squeezed states by employing atoms in a two-dimensional optical lattice as quantum registers. The states are generated by a controlled projection conditioned on the relative phase of two independent squeezed states. The individual squeezing is created by sudden jumps of the oscillators' frequencies, allowing generating of the two-mode squeezed states at a rate within a fraction of the oscillation frequency. We validate the states by entanglement steering criteria and Fock state analysis. Our results can be applied in other mechanical oscillators for quantum sensing and continuous-variable quantum information.
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Affiliation(s)
- Wui Seng Leong
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - Mingjie Xin
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - Zilong Chen
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - Yu Wang
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - Shau-Yu Lan
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
- Department of Physics, National Taiwan University, Taipei 10617, Taiwan
- Center for Quantum Science and Engineering, National Taiwan University, Taipei 10617, Taiwan
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6
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Gärttner M, Haas T, Noll J. General Class of Continuous Variable Entanglement Criteria. PHYSICAL REVIEW LETTERS 2023; 131:150201. [PMID: 37897784 DOI: 10.1103/physrevlett.131.150201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/12/2022] [Accepted: 08/30/2023] [Indexed: 10/30/2023]
Abstract
We present a general class of entanglement criteria for continuous variable systems. Our criteria are based on the Husimi Q distribution and allow for optimization over the set of all concave functions rendering them extremely general and versatile. We show that several entropic criteria and second moment criteria are obtained as special cases. Our criteria reveal entanglement of families of states undetected by any commonly used criteria and provide clear advantages under typical experimental constraints such as finite detector resolution and measurement statistics.
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Affiliation(s)
- Martin Gärttner
- Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany
- Physikalisches Institut, Universität Heidelberg, Im Neuenheimer Feld 226, 69120 Heidelberg, Germany
- Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
- Institute of Condensed Matter Theory and Optics, Friedrich-Schiller-University Jena, Max-Wien-Platz 1, D-07743 Jena, Germany
| | - Tobias Haas
- Centre for Quantum Information and Communication, École polytechnique de Bruxelles, CP 165, Université libre de Bruxelles, 1050 Brussels, Belgium
| | - Johannes Noll
- Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
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7
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Bilitewski T, Rey AM. Manipulating Growth and Propagation of Correlations in Dipolar Multilayers: From Pair Production to Bosonic Kitaev Models. PHYSICAL REVIEW LETTERS 2023; 131:053001. [PMID: 37595247 DOI: 10.1103/physrevlett.131.053001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/22/2022] [Accepted: 07/14/2023] [Indexed: 08/20/2023]
Abstract
We study the nonequilibrium dynamics of dipoles confined in multiple stacked two-dimensional layers realizing a long-range interacting quantum spin 1/2 XXX model. We demonstrate that strong in-plane interactions can protect a manifold of collective layer dynamics. This then allows us to map the many-body spin dynamics to bosonic models. In a bilayer configuration we show how to engineer the paradigmatic two-mode squeezing Hamiltonian known from quantum optics, resulting in exponential production of entangled pairs and generation of metrologically useful entanglement from initially prepared product states. In multilayer configurations we engineer a bosonic variant of the Kitaev model displaying chiral propagation along the layer direction. Our study illustrates how the control over interactions, lattice geometry, and state preparation in interacting dipolar systems uniquely afforded by AMO platforms such as Rydberg and magnetic atoms, polar molecules, or trapped ions allows for the control over the temporal and spatial propagation of correlations for applications in quantum sensing and quantum simulation.
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Affiliation(s)
- Thomas Bilitewski
- Department of Physics, Oklahoma State University, Stillwater, Oklahoma 74078, USA
| | - Ana Maria Rey
- JILA, National Institute of Standards and Technology and Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
- Center for Theory of Quantum Matter, University of Colorado, Boulder, Colorado 80309, USA
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8
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Ma L, Lei X, Cheng J, Yan Z, Jia X. Deterministic manipulation of steering between distant quantum network nodes. OPTICS EXPRESS 2023; 31:8257-8266. [PMID: 36859941 DOI: 10.1364/oe.479182] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/25/2022] [Accepted: 02/03/2023] [Indexed: 06/18/2023]
Abstract
Multipartite Einstein-Podolsky-Rosen (EPR) steering is a key resource in a quantum network. Although EPR steering between spatially separated regions of ultracold atomic systems has been observed, deterministic manipulation of steering between distant quantum network nodes is required for a secure quantum communication network. Here, we propose a feasible scheme to deterministically generate, store, and manipulate one-way EPR steering between distant atomic cells by a cavity-enhanced quantum memory approach. While optical cavities effectively suppress the unavoidable noises in electromagnetically induced transparency, three atomic cells are in a strong Greenberger-Horne-Zeilinger state by faithfully storing three spatially separated entangled optical modes. In this way, the strong quantum correlation of atomic cells guarantees one-to-two node EPR steering is achieved, and can perserve the stored EPR steering in these quantum nodes. Furthermore, the steerability can be actively manipulated by the temperature of the atomic cell. This scheme provides the direct reference for experimental implementation for one-way multipartite steerable states, which enables an asymmetric quantum network protocol.
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9
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Representation of nuclear magnetic moments via a Clifford algebra formulation of Bohm's hidden variables. Sci Rep 2022; 12:20674. [PMID: 36529817 PMCID: PMC9760646 DOI: 10.1038/s41598-022-24970-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2022] [Accepted: 11/22/2022] [Indexed: 12/23/2022] Open
Abstract
In this paper, we outline the research conducted by the first named author and his associates on the axiom-preserving, thus isotopic completion of quantum mechanics into hadronic mechanics according to the historical legacy by A. Einstein, B. Podolsky and N. Rosen that quantum mechanics is not a complete theory and review the ensuing exact representation of the magnetic moment and spin of the Deuteron in its ground state thanks to the isotopic completion of Pauli's matrices with an explicit and concrete content of D. Bohm's hidden variable [Formula: see text]. We then outline the independent studies conducted by the second named author on the representation of the conventional Pauli's matrices via geometric Clifford algebras. We finally show that the combination of the two studies allows a mathematically rigorous, numerically exact and time invariant geometric representation of the magnetic moment, spin and hidden variable of the Deuteron in its ground state.
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10
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Distributed quantum sensing with mode-entangled spin-squeezed atomic states. Nature 2022; 612:661-665. [PMID: 36418400 DOI: 10.1038/s41586-022-05363-z] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/12/2022] [Accepted: 08/16/2022] [Indexed: 11/25/2022]
Abstract
Quantum sensors are used for precision timekeeping, field sensing and quantum communication1-3. Comparisons among a distributed network of these sensors are capable of, for example, synchronizing clocks at different locations4-8. The performance of a sensor network is limited by technical challenges as well as the inherent noise associated with the quantum states used to realize the network9. For networks with only spatially localized entanglement at each node, the noise performance of the network improves at best with the square root of the number of nodes10. Here we demonstrate that spatially distributed entanglement between network nodes offers better scaling with network size. A shared quantum nondemolition measurement entangles a clock network with up to four nodes. This network provides up to 4.5 decibels better precision than one without spatially distributed entanglement, and 11.6 decibels improvement as compared to a network of sensors operating at the quantum projection noise limit. We demonstrate the generality of the approach with atomic clock and atomic interferometer protocols, in scientific and technologically relevant configurations optimized for intrinsically differential comparisons of sensor outputs.
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11
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Entanglement-enhanced matter-wave interferometry in a high-finesse cavity. Nature 2022; 610:472-477. [PMID: 36261551 PMCID: PMC9581775 DOI: 10.1038/s41586-022-05197-9] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/26/2021] [Accepted: 08/05/2022] [Indexed: 11/30/2022]
Abstract
An ensemble of atoms can operate as a quantum sensor by placing atoms in a superposition of two different states. Upon measurement of the sensor, each atom is individually projected into one of the two states. Creating quantum correlations between the atoms, that is entangling them, could lead to resolutions surpassing the standard quantum limit1–3 set by projections of individual atoms. Large amounts of entanglement4–6 involving the internal degrees of freedom of laser-cooled atomic ensembles4–16 have been generated in collective cavity quantum-electrodynamics systems, in which many atoms simultaneously interact with a single optical cavity mode. Here we report a matter-wave interferometer in a cavity quantum-electrodynamics system of 700 atoms that are entangled in their external degrees of freedom. In our system, each individual atom falls freely under gravity and simultaneously traverses two paths through space while entangled with the other atoms. We demonstrate both quantum non-demolition measurements and cavity-mediated spin interactions for generating squeezed momentum states with directly observed sensitivity \documentclass[12pt]{minimal}
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\begin{document}$$3\,.\,{4}_{-0.9}^{+1.1}$$\end{document}3.4−0.9+1.1 dB and \documentclass[12pt]{minimal}
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\begin{document}$$2\,.\,{5}_{-0.6}^{+0.6}$$\end{document}2.5−0.6+0.6 dB below the standard quantum limit, respectively. We successfully inject an entangled state into a Mach–Zehnder light-pulse interferometer with directly observed sensitivity \documentclass[12pt]{minimal}
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\begin{document}$$1\,.\,{7}_{-0.5}^{+0.5}$$\end{document}1.7−0.5+0.5 dB below the standard quantum limit. The combination of particle delocalization and entanglement in our approach may influence developments of enhanced inertial sensors17,18, searches for new physics, particles and fields19–23, future advanced gravitational wave detectors24,25 and accessing beyond mean-field quantum many-body physics26–30. A matter-wave interferometer is demonstrated with an interferometric phase noise below the standard quantum limit, combining two core concepts of quantum mechanics, that a particle can simultaneously be in two places at once and entanglement between distinct particles.
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12
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Hernández Yanes T, Płodzień M, Mackoit Sinkevičienė M, Žlabys G, Juzeliūnas G, Witkowska E. One- and Two-Axis Squeezing via Laser Coupling in an Atomic Fermi-Hubbard Model. PHYSICAL REVIEW LETTERS 2022; 129:090403. [PMID: 36083675 DOI: 10.1103/physrevlett.129.090403] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/14/2022] [Revised: 07/05/2022] [Accepted: 07/28/2022] [Indexed: 06/15/2023]
Abstract
Generation, storage, and utilization of correlated many-body quantum states are crucial objectives of future quantum technologies and metrology. Such states can be generated by the spin-squeezing protocols, i.e., one-axis twisting and two-axis countertwisting. In this Letter, we show activation of these two squeezing mechanisms in a system composed of ultracold atomic fermions in the Mott insulating phase by a position-dependent laser coupling of atomic internal states. Realization of both the squeezing protocols is feasible in the current state-of-the-art experiments.
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Affiliation(s)
- T Hernández Yanes
- Institute of Physics PAS, Aleja Lotnikow 32/46, 02-668 Warszawa, Poland
| | - M Płodzień
- ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Av. Carl Friedrich Gauss 3, 08860 Castelldefels (Barcelona), Spain
| | - M Mackoit Sinkevičienė
- Institute of Theoretical Physics and Astronomy, Vilnius University, Saulėtekio 3, LT-10257, Vilnius, Lithuania
| | - G Žlabys
- Institute of Theoretical Physics and Astronomy, Vilnius University, Saulėtekio 3, LT-10257, Vilnius, Lithuania
| | - G Juzeliūnas
- Institute of Theoretical Physics and Astronomy, Vilnius University, Saulėtekio 3, LT-10257, Vilnius, Lithuania
| | - E Witkowska
- Institute of Physics PAS, Aleja Lotnikow 32/46, 02-668 Warszawa, Poland
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13
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Bhattacharjee A, Joshi MK, Karan S, Leach J, Jha AK. Propagation-induced revival of entanglement in the angle-OAM bases. SCIENCE ADVANCES 2022; 8:eabn7876. [PMID: 35930646 PMCID: PMC9355354 DOI: 10.1126/sciadv.abn7876] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/21/2021] [Accepted: 06/21/2022] [Indexed: 06/15/2023]
Abstract
Although the continuous-variable position-momentum entanglement of photon pairs produced by parametric down-conversion has applicability in several quantum information applications, it is not suitable for applications involving long-distance propagation. This is because entanglement in the position-momentum bases, as seen through Einstein-Podolsky-Rosen (EPR)-correlation measurements, decays very rapidly with photons propagating away from the source. In contrast, in this article, we show that in the continuous-variable bases of angle-orbital angular momentum (OAM), the entanglement, as seen through EPR-correlation measurements, exhibits a remarkably different behavior. As with the position-momentum bases, initially, the entanglement in the angle-OAM bases also decays with propagation, and after a few centimeters of propagation, there is no angle-OAM entanglement left. However, as the photons continue to travel further away from the source, the entanglement in the angle-OAM bases revives. We theoretically and experimentally demonstrate this behavior and show that angle-OAM entanglement revives even in the presence of strong turbulence.
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Affiliation(s)
| | - Mritunjay K. Joshi
- Department of Physics, Indian Institute of Technology Kanpur, Kanpur UP 208016, India
| | - Suman Karan
- Department of Physics, Indian Institute of Technology Kanpur, Kanpur UP 208016, India
| | - Jonathan Leach
- School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK
| | - Anand K. Jha
- Department of Physics, Indian Institute of Technology Kanpur, Kanpur UP 208016, India
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14
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Alaoui YA, Zhu B, Muleady SR, Dubosclard W, Roscilde T, Rey AM, Laburthe-Tolra B, Vernac L. Measuring Correlations from the Collective Spin Fluctuations of a Large Ensemble of Lattice-Trapped Dipolar Spin-3 Atoms. PHYSICAL REVIEW LETTERS 2022; 129:023401. [PMID: 35867449 DOI: 10.1103/physrevlett.129.023401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/18/2022] [Revised: 03/23/2022] [Accepted: 05/12/2022] [Indexed: 06/15/2023]
Abstract
We perform collective spin measurements to study the buildup of two-body correlations between ≈10^{4} spin s=3 chromium atoms pinned in a 3D optical lattice. The spins interact via long range and anisotropic dipolar interactions. From the fluctuations of total magnetization, measured at the standard quantum limit, we estimate the dynamical growth of the connected pairwise correlations associated with magnetization. The quantum nature of the correlations is assessed by comparisons with analytical short- and long-time expansions and numerical simulations. Our Letter shows that measuring fluctuations of spin populations for s>1/2 spins provides new ways to characterize correlations in quantum many-body systems.
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Affiliation(s)
- Youssef Aziz Alaoui
- Université Paris 13, Laboratoire de Physique des Lasers, F-93430 Villetaneuse, France
- CNRS, UMR 7538, LPL, F-93430 Villetaneuse, France
| | - Bihui Zhu
- Homer L. Dodge Department of Physics and Astronomy, The University of Oklahoma, Norman, Oklahoma 73019, USA and Center for Quantum Research and Technology, The University of Oklahoma, Norman, Oklahoma 73019, USA
| | - Sean Robert Muleady
- 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
| | - William Dubosclard
- Université Paris 13, Laboratoire de Physique des Lasers, F-93430 Villetaneuse, France
- CNRS, UMR 7538, LPL, F-93430 Villetaneuse, France
| | - Tommaso Roscilde
- Université Lyon, Ens de Lyon, CNRS, Laboratoire de Physique, F-69342 Lyon, 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
- Université Paris 13, Laboratoire de Physique des Lasers, F-93430 Villetaneuse, France
- CNRS, UMR 7538, LPL, F-93430 Villetaneuse, France
| | - Laurent Vernac
- Université Paris 13, Laboratoire de Physique des Lasers, F-93430 Villetaneuse, France
- CNRS, UMR 7538, LPL, F-93430 Villetaneuse, France
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15
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Kunkel P, Prüfer M, Lannig S, Strohmaier R, Gärttner M, Strobel H, Oberthaler MK. Detecting Entanglement Structure in Continuous Many-Body Quantum Systems. PHYSICAL REVIEW LETTERS 2022; 128:020402. [PMID: 35089742 DOI: 10.1103/physrevlett.128.020402] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/21/2021] [Accepted: 12/06/2021] [Indexed: 06/14/2023]
Abstract
A prerequisite for the comprehensive understanding of many-body quantum systems is a characterization in terms of their entanglement structure. The experimental detection of entanglement in spatially extended many-body systems describable by quantum fields still presents a major challenge. We develop a general scheme for certifying entanglement and demonstrate it by revealing entanglement between distinct subsystems of a spinor Bose-Einstein condensate. Our scheme builds on the spatially resolved simultaneous detection of the quantum field in two conjugate observables which allows the experimental confirmation of quantum correlations between local as well as nonlocal partitions of the system. The detection of squeezing in Bogoliubov modes in a multimode setting illustrates its potential to boost the capabilities of quantum simulations to study entanglement in spatially extended many-body systems.
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Affiliation(s)
- Philipp Kunkel
- Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Maximilian Prüfer
- Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Stefan Lannig
- Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Robin Strohmaier
- Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Martin Gärttner
- Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
- Physikalisches Institut, Universität Heidelberg, Im Neuenheimer Feld 226, 69120 Heidelberg, Germany
- Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany
| | - Helmut Strobel
- Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Markus K Oberthaler
- Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
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16
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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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17
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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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18
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Chen CA, Khlebnikov S, Hung CL. Observation of Quasiparticle Pair Production and Quantum Entanglement in Atomic Quantum Gases Quenched to an Attractive Interaction. PHYSICAL REVIEW LETTERS 2021; 127:060404. [PMID: 34420342 DOI: 10.1103/physrevlett.127.060404] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/23/2021] [Accepted: 07/08/2021] [Indexed: 06/13/2023]
Abstract
We report observations of quasiparticle pair production by a modulational instability in an atomic superfluid and present a measurement technique that enables direct characterization of quasiparticle quantum entanglement. By quenching the atomic interaction to attractive and then back to weakly repulsive, we produce correlated quasiparticles and monitor their evolution in a superfluid through evaluating the in situ density noise power spectrum, which essentially measures a "homodyne" interference between ground-state atoms and quasiparticles of opposite momenta. We observe large amplitude growth in the power spectrum and subsequent coherent oscillations in a wide spatial frequency band within our resolution limit, demonstrating coherent quasiparticle generation and evolution. The spectrum is observed to oscillate below a quantum limit set by the Peres-Horodecki separability criterion of continuous-variable states, thereby confirming quantum entanglement between interaction quench-induced quasiparticles.
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Affiliation(s)
- Cheng-An Chen
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
| | - Sergei Khlebnikov
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
- Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, USA
| | - Chen-Lung Hung
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
- Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, USA
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19
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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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20
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Bergh B, Gärttner M. Experimentally Accessible Bounds on Distillable Entanglement from Entropic Uncertainty Relations. PHYSICAL REVIEW LETTERS 2021; 126:190503. [PMID: 34047593 DOI: 10.1103/physrevlett.126.190503] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/21/2021] [Accepted: 04/01/2021] [Indexed: 06/12/2023]
Abstract
Entanglement is not only the resource that fuels many quantum technologies but also plays a key role for some of the most profound open questions of fundamental physics. Experiments controlling quantum systems at the single quantum level may shed light on these puzzles. However, measuring, or even bounding, entanglement experimentally has proven to be an outstanding challenge, especially when the prepared quantum states are mixed. We use entropic uncertainty relations for bipartite systems to derive measurable lower bounds on distillable entanglement. We showcase these bounds by applying them to physical models realizable in cold-atom experiments. The derived entanglement bounds rely on measurements in only two different bases and are generically applicable to any quantum simulation platform.
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Affiliation(s)
- Bjarne Bergh
- Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Martin Gärttner
- Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
- Physikalisches Institut, Universität Heidelberg, Im Neuenheimer Feld 226, 69120 Heidelberg, Germany
- Institut für Theoretische Physik, Ruprecht-Karls-Universität Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany
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21
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Yadin B, Fadel M, Gessner M. Metrological complementarity reveals the Einstein-Podolsky-Rosen paradox. Nat Commun 2021; 12:2410. [PMID: 33893281 PMCID: PMC8065158 DOI: 10.1038/s41467-021-22353-3] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2020] [Accepted: 03/11/2021] [Indexed: 02/02/2023] Open
Abstract
The Einstein-Podolsky-Rosen (EPR) paradox plays a fundamental role in our understanding of quantum mechanics, and is associated with the possibility of predicting the results of non-commuting measurements with a precision that seems to violate the uncertainty principle. This apparent contradiction to complementarity is made possible by nonclassical correlations stronger than entanglement, called steering. Quantum information recognises steering as an essential resource for a number of tasks but, contrary to entanglement, its role for metrology has so far remained unclear. Here, we formulate the EPR paradox in the framework of quantum metrology, showing that it enables the precise estimation of a local phase shift and of its generating observable. Employing a stricter formulation of quantum complementarity, we derive a criterion based on the quantum Fisher information that detects steering in a larger class of states than well-known uncertainty-based criteria. Our result identifies useful steering for quantum-enhanced precision measurements and allows one to uncover steering of non-Gaussian states in state-of-the-art experiments.
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Affiliation(s)
- Benjamin Yadin
- grid.4563.40000 0004 1936 8868School of Mathematical Sciences and Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham, UK ,grid.4991.50000 0004 1936 8948Wolfson College, University of Oxford, Oxford, UK
| | - Matteo Fadel
- grid.6612.30000 0004 1937 0642Department of Physics, University of Basel, Basel, Switzerland
| | - Manuel Gessner
- grid.462844.80000 0001 2308 1657Laboratoire Kastler Brossel, ENS-Université PSL, CNRS, Sorbonne Université, Collège de France, Paris, France
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22
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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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23
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Wang M, Xiang Y, Kang H, Han D, Liu Y, He Q, Gong Q, Su X, Peng K. Deterministic Distribution of Multipartite Entanglement and Steering in a Quantum Network by Separable States. PHYSICAL REVIEW LETTERS 2020; 125:260506. [PMID: 33449714 DOI: 10.1103/physrevlett.125.260506] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2020] [Accepted: 12/09/2020] [Indexed: 06/12/2023]
Abstract
As two valuable quantum resources, Einstein-Podolsky-Rosen entanglement and steering play important roles in quantum-enhanced communication protocols. Distributing such quantum resources among multiple remote users in a network is a crucial precondition underlying various quantum tasks. We experimentally demonstrate the deterministic distribution of two- and three-mode Gaussian entanglement and steering by transmitting separable states in a network consisting of a quantum server and multiple users. In our experiment, entangled states are not prepared solely by the quantum server, but are created among independent users during the distribution process. More specifically, the quantum server prepares separable squeezed states and applies classical displacements on them before spreading out, and users simply perform local beam-splitter operations and homodyne measurements after they receive separable states. We show that the distributed Gaussian entanglement and steerability are robust against channel loss. Furthermore, one-way Gaussian steering is achieved among users that is useful for further directional or highly asymmetric quantum information processing.
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Affiliation(s)
- Meihong Wang
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Yu Xiang
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
- State Key Laboratory for Mesoscopic Physics, School of Physics, Frontiers Science Center for Nano-optoelectronics & Collaborative Innovation Center of Quantum Matter, Peking University, Beijing 100871, China
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
| | - Haijun Kang
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Dongmei Han
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Yang Liu
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Qiongyi He
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
- State Key Laboratory for Mesoscopic Physics, School of Physics, Frontiers Science Center for Nano-optoelectronics & Collaborative Innovation Center of Quantum Matter, Peking University, Beijing 100871, China
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
| | - Qihuang Gong
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
- State Key Laboratory for Mesoscopic Physics, School of Physics, Frontiers Science Center for Nano-optoelectronics & Collaborative Innovation Center of Quantum Matter, Peking University, Beijing 100871, China
- Beijing Academy of Quantum Information Sciences, Beijing 100193, China
| | - Xiaolong Su
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
| | - Kunchi Peng
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China
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24
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Chen CA, Hung CL. Observation of Universal Quench Dynamics and Townes Soliton Formation from Modulational Instability in Two-Dimensional Bose Gases. PHYSICAL REVIEW LETTERS 2020; 125:250401. [PMID: 33416392 DOI: 10.1103/physrevlett.125.250401] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/10/2019] [Accepted: 11/16/2020] [Indexed: 06/12/2023]
Abstract
We experimentally study universal nonequilibrium dynamics of two-dimensional atomic Bose gases quenched from repulsive to attractive interactions. We observe the manifestation of modulational instability that, instead of causing collapse, fragments a large two-dimensional superfluid into multiple wave packets universally around a threshold atom number necessary for the formation of Townes solitons. We confirm that the density distributions of quench-induced solitary waves are in excellent agreement with the stationary Townes profiles. Furthermore, our density measurements in the space and time domain reveal detailed information about this dynamical process, from the hyperbolic growth of density waves, the formation of solitons, to the subsequent collision and collapse dynamics, demonstrating multiple universal behaviors in an attractive many-body system in association with the formation of a quasistationary state.
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Affiliation(s)
- Cheng-An Chen
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
| | - Chen-Lung Hung
- Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana 47907, USA
- Purdue Quantum Science and Engineering Institute, Purdue University, West Lafayette, Indiana 47907, USA
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25
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Becher JH, Sindici E, Klemt R, Jochim S, Daley AJ, Preiss PM. Measurement of Identical Particle Entanglement and the Influence of Antisymmetrization. PHYSICAL REVIEW LETTERS 2020; 125:180402. [PMID: 33196275 DOI: 10.1103/physrevlett.125.180402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/27/2020] [Accepted: 09/25/2020] [Indexed: 06/11/2023]
Abstract
We explore the relationship between symmetrization and entanglement through measurements on few-particle systems in a multiwell potential. In particular, considering two or three trapped atoms, we measure and distinguish correlations arising from two different physical origins: antisymmetrization of the fermionic wave function and interaction between particles. We quantify this through the entanglement negativity of states, and the introduction of an antisymmetric negativity, which allows us to understand the role that symmetrization plays in the measured entanglement properties. We apply this concept both to pure theoretical states and to experimentally reconstructed density matrices of two or three mobile particles in an array of optical tweezers.
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Affiliation(s)
- J H Becher
- Physics Institute, Heidelberg University, Im Neuenheimer Feld 226, 69120 Heidelberg, Germany
| | - E Sindici
- Department of Physics and SUPA, University of Strathclyde, Glasgow G4 0NG, United Kingdom
| | - R Klemt
- Physics Institute, Heidelberg University, Im Neuenheimer Feld 226, 69120 Heidelberg, Germany
| | - S Jochim
- Physics Institute, Heidelberg University, Im Neuenheimer Feld 226, 69120 Heidelberg, Germany
| | - A J Daley
- Department of Physics and SUPA, University of Strathclyde, Glasgow G4 0NG, United Kingdom
| | - P M Preiss
- Physics Institute, Heidelberg University, Im Neuenheimer Feld 226, 69120 Heidelberg, Germany
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26
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Li Y, Pawłowski K, Décamps B, Colciaghi P, Fadel M, Treutlein P, Zibold T. Fundamental Limit of Phase Coherence in Two-Component Bose-Einstein Condensates. PHYSICAL REVIEW LETTERS 2020; 125:123402. [PMID: 33016728 DOI: 10.1103/physrevlett.125.123402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/09/2020] [Accepted: 08/24/2020] [Indexed: 06/11/2023]
Abstract
We experimentally and theoretically study phase coherence in two-component Bose-Einstein condensates of ^{87}Rb atoms on an atom chip. Using Ramsey interferometry we determine the temporal decay of coherence between the |F=1,m_{F}=-1⟩ and |F=2,m_{F}=+1⟩ hyperfine ground states. We observe that the coherence is limited by random collisional phase shifts due to the stochastic nature of atom loss. The mechanism is confirmed quantitatively by a quantum trajectory method based on a master equation which takes into account collisional interactions, atom number fluctuations, and losses in the system. This decoherence process can be slowed down by reducing the density of the condensate. Our findings are relevant for experiments on quantum metrology and many-particle entanglement with Bose-Einstein condensates and the development of chip-based atomic clocks.
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Affiliation(s)
- Yifan Li
- Department of Physics, University of Basel, 4056 Basel, Switzerland
- Department of Engineering Physics, Tsinghua University, Beijing 100084, China
| | - Krzysztof Pawłowski
- Center for Theoretical Physics, Polish Academy of Sciences, 02-668 Warsaw, Poland
| | - Boris Décamps
- Department of Physics, University of Basel, 4056 Basel, Switzerland
| | - Paolo Colciaghi
- Department of Physics, University of Basel, 4056 Basel, Switzerland
| | - Matteo Fadel
- Department of Physics, University of Basel, 4056 Basel, Switzerland
| | | | - Tilman Zibold
- Department of Physics, University of Basel, 4056 Basel, Switzerland
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27
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Gessner M, Smerzi A, Pezzè L. Multiparameter squeezing for optimal quantum enhancements in sensor networks. Nat Commun 2020; 11:3817. [PMID: 32733031 PMCID: PMC7393128 DOI: 10.1038/s41467-020-17471-3] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2020] [Accepted: 06/12/2020] [Indexed: 11/09/2022] Open
Abstract
Squeezing currently represents the leading strategy for quantum enhanced precision measurements of a single parameter in a variety of continuous- and discrete-variable settings and technological applications. However, many important physical problems including imaging and field sensing require the simultaneous measurement of multiple unknown parameters. The development of multiparameter quantum metrology is yet hindered by the intrinsic difficulty in finding saturable sensitivity bounds and feasible estimation strategies. Here, we derive the general operational concept of multiparameter squeezing, identifying metrologically useful states and optimal estimation strategies. When applied to spin- or continuous-variable systems, our results generalize widely-used spin- or quadrature-squeezing parameters. Multiparameter squeezing provides a practical and versatile concept that paves the way to the development of quantum-enhanced estimation of multiple phases, gradients, and fields, and for the efficient characterization of multimode quantum states in atomic and optical sensor networks.
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Affiliation(s)
- Manuel Gessner
- Laboratoire Kastler Brossel, ENS-PSL Université, CNRS, Sorbonne Université, Collège de France, 24 Rue Lhomond, 75005, Paris, France.
| | - Augusto Smerzi
- QSTAR, CNR-INO and LENS, Largo Enrico Fermi 2, 50125, Firenze, Italy
| | - Luca Pezzè
- QSTAR, CNR-INO and LENS, Largo Enrico Fermi 2, 50125, Firenze, Italy
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28
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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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29
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Benavides-Riveros CL, Wolff J, Marques MAL, Schilling C. Reduced Density Matrix Functional Theory for Bosons. PHYSICAL REVIEW LETTERS 2020; 124:180603. [PMID: 32441966 DOI: 10.1103/physrevlett.124.180603] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/16/2020] [Accepted: 04/21/2020] [Indexed: 06/11/2023]
Abstract
Based on a generalization of Hohenberg-Kohn's theorem, we propose a ground state theory for bosonic quantum systems. Since it involves the one-particle reduced density matrix γ as a variable but still recovers quantum correlations in an exact way it is particularly well suited for the accurate description of Bose-Einstein condensates. As a proof of principle we study the building block of optical lattices. The solution of the underlying v-representability problem is found and its peculiar form identifies the constrained search formalism as the ideal starting point for constructing accurate functional approximations: The exact functionals F[γ] for this N-boson Hubbard dimer and general Bogoliubov-approximated systems are determined. For Bose-Einstein condensates with N_{BEC}≈N condensed bosons, the respective gradient forces are found to diverge, ∇_{γ}F∝1/sqrt[1-N_{BEC}/N], providing a comprehensive explanation for the absence of complete condensation in nature.
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Affiliation(s)
- Carlos L Benavides-Riveros
- Institut für Physik, Martin-Luther-Universität Halle-Wittenberg, 06120 Halle (Saale), Germany
- NR-ISM, Division of Ultrafast Processes in Materials (FLASHit), Area della Ricerca di Roma 1, Via Salaria Km 29.3, I-00016 Monterotondo Scalo, Italy
| | - Jakob Wolff
- Institut für Physik, Martin-Luther-Universität Halle-Wittenberg, 06120 Halle (Saale), Germany
| | - Miguel A L Marques
- Institut für Physik, Martin-Luther-Universität Halle-Wittenberg, 06120 Halle (Saale), Germany
| | - Christian Schilling
- Department of Physics, Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, 80333 München, Germany
- Wolfson College, University of Oxford, Linton Rd, Oxford OX2 6UD, United Kingdom
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30
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Experimental demonstration of Einstein-Podolsky-Rosen entanglement in rotating coordinate space. Sci Bull (Beijing) 2020; 65:280-285. [PMID: 36659092 DOI: 10.1016/j.scib.2019.11.011] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/17/2019] [Revised: 10/22/2019] [Accepted: 10/31/2019] [Indexed: 01/21/2023]
Abstract
Einstein-Podolsky-Rosen (EPR) entanglement involving a pair of particles entangled in their positions and momenta is of special interest in the field of quantum information. Previously, EPR entanglement has been studied in different physical systems but in fixed coordinate spaces. Here, we demonstrate an experiment of ghost imaging and ghost interference in rotated position-momentum spaces by using position-momentum entangled photons generated from a hot atomic ensemble. By using different image objects, the measured position-momentum correlations exhibit intriguing dynamics, including gradual decrease and axis-independent EPR entanglement. The reported results on manipulating the EPR entanglement in rotating coordinate spaces hold promise in quantum communication and distant quantum image processing.
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31
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Kale SS, Ding Y, Chen YP, Friedrich B, Kais S. Spin-momentum entanglement in a Bose–Einstein condensate. Phys Chem Chem Phys 2020; 22:25669-25674. [DOI: 10.1039/d0cp03945d] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Mechanisms including two types of Raman laser coupling (Ω1 & Ω2) and rf field coupling (Ωrf) are applied to drive transitions between different hyperfine spin states. We investigated the entanglement between the spin and momentum degrees of freedom.
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Affiliation(s)
| | - Yijue Ding
- Department of Chemistry
- Purdue University
- USA
| | - Yong P. Chen
- Purdue Quantum Science and Engineering Institute
- Purdue University
- West Lafayette
- USA
- Department of Physics and Astronomy
| | | | - Sabre Kais
- Department of Chemistry
- Purdue University
- USA
- Purdue Quantum Science and Engineering Institute
- Purdue University
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32
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Bell correlations between spatially separated pairs of atoms. Nat Commun 2019; 10:4447. [PMID: 31575860 PMCID: PMC6773866 DOI: 10.1038/s41467-019-12192-8] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2019] [Accepted: 08/27/2019] [Indexed: 11/16/2022] Open
Abstract
Bell correlations are a foundational demonstration of how quantum entanglement contradicts the classical notion of local realism. Rigorous validation of quantum nonlocality have only been achieved between solid-state electron spins, internal states of trapped atoms, and photon polarisations, all weakly coupling to gravity. Bell tests with freely propagating massive particles, which could provide insights into the link between gravity and quantum mechanics, have proven to be much more challenging to realise. Here we use a collision between two Bose-Einstein condensates to generate spin entangled pairs of ultracold helium atoms, and measure their spin correlations along uniformly rotated bases. We show that correlations in the pairs agree with the theoretical prediction of a Bell triplet state, and observe a quantum mechanical witness of Bell correlations with \documentclass[12pt]{minimal}
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\begin{document}$$6\sigma$$\end{document}6σ significance. Extensions to this scheme could find promising applications in quantum metrology, as well as for investigating the interplay between quantum mechanics and gravity. Entangled particles some distance apart can be used to show the strikingly nonlocal nature of quantum mechanics. Here the authors generate spatially separated pairs of helium atoms by colliding Bose-Einstein condensates and show that they are entangled by observing nonlocal correlations.
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33
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Reid MD, He QY. Quantifying the Mesoscopic Nature of Einstein-Podolsky-Rosen Nonlocality. PHYSICAL REVIEW LETTERS 2019; 123:120402. [PMID: 31633988 DOI: 10.1103/physrevlett.123.120402] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/05/2018] [Revised: 05/21/2019] [Indexed: 06/10/2023]
Abstract
Evidence for Bell's nonlocality is so far mainly restricted to microscopic systems, where the elements of reality that are negated predetermine results of measurements to within one spin unit. Any observed nonlocal effect (or lack of classical predetermination) is then limited to no more than the difference of a single photon or electron being detected or not (at a given detector). In this paper, we analyze experiments that report the Einstein-Podolsky-Rosen (EPR) steering form of nonlocality for mesoscopic photonic or Bose-Einstein condensate systems. Using an EPR steering parameter, we show how the EPR nonlocalities involved can be quantified for four-mode states, to give evidence of EPR-nonlocal effects corresponding to a two-mode number difference of 10^{5} photons, or of several tens of atoms (at a given site). Applying to experiments, we also show how the variance criterion of Duan, Giedke, Cirac and Zoller for EPR entanglement can be used to determine a lower bound on the number of particles in a pure two-mode EPR-entangled or steerable state.
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Affiliation(s)
- M D Reid
- Centre for Quantum and Optical Science, Swinburne University of Technology, Melbourne, Victoria 3122, Australia
- Institute of Theoretical Atomic, Molecular and Optical Physics (ITAMP), Harvard University, Cambridge, Massachusetts 02138, USA
| | - Q Y He
- State Key Laboratory of Mesoscopic Physics, School of Physics, Peking University, Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
- Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
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34
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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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35
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Zhen YZ, Xu XY, Li L, Liu NL, Chen K. The Einstein-Podolsky-Rosen Steering and Its Certification. ENTROPY 2019; 21:e21040422. [PMID: 33267136 PMCID: PMC7514909 DOI: 10.3390/e21040422] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/17/2019] [Revised: 04/03/2019] [Accepted: 04/16/2019] [Indexed: 11/16/2022]
Abstract
The Einstein–Podolsky–Rosen (EPR) steering is a subtle intermediate correlation between entanglement and Bell nonlocality. It not only theoretically completes the whole picture of non-local effects but also practically inspires novel quantum protocols in specific scenarios. However, a verification of EPR steering is still challenging due to difficulties in bounding unsteerable correlations. In this survey, the basic framework to study the bipartite EPR steering is discussed, and general techniques to certify EPR steering correlations are reviewed.
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Affiliation(s)
- Yi-Zheng Zhen
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
- Institute for Quantum Science and Engineering, Southern University of Science and Technology (SUSTech), Shenzhen 518055, China
| | - Xin-Yu Xu
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Li Li
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
- Correspondence: (L.L.); (N.-L.L.); (K.C.)
| | - Nai-Le Liu
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
- Correspondence: (L.L.); (N.-L.L.); (K.C.)
| | - Kai Chen
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
- Correspondence: (L.L.); (N.-L.L.); (K.C.)
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36
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Gessner M, Smerzi A, Pezzè L. Metrological Nonlinear Squeezing Parameter. PHYSICAL REVIEW LETTERS 2019; 122:090503. [PMID: 30932524 DOI: 10.1103/physrevlett.122.090503] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/29/2018] [Indexed: 06/09/2023]
Abstract
The well-known metrological linear squeezing parameters (such as quadrature or spin squeezing) efficiently quantify the sensitivity of Gaussian states. Yet, these parameters are insufficient to characterize the much wider class of highly sensitive non-Gaussian states. Here, we introduce a class of metrological nonlinear squeezing parameters obtained by analytical optimization of measurement observables among a given set of accessible (possibly nonlinear) operators. This allows for the metrological characterization of non-Gaussian quantum states of discrete and continuous variables. Our results lead to optimized and experimentally feasible recipes for a high-precision moment-based estimation of a phase parameter and can be used to systematically construct multipartite entanglement and nonclassicality witnesses for complex quantum states.
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Affiliation(s)
- Manuel Gessner
- QSTAR, CNR-INO and LENS, Largo Enrico Fermi 2, 50125 Firenze, Italy
- Département de Physique, École Normale Supérieure, PSL Université, CNRS, 24 Rue Lhomond, 75005 Paris, France
| | - Augusto Smerzi
- Département de Physique, École Normale Supérieure, PSL Université, CNRS, 24 Rue Lhomond, 75005 Paris, France
| | - Luca Pezzè
- Département de Physique, École Normale Supérieure, PSL Université, CNRS, 24 Rue Lhomond, 75005 Paris, France
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37
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Abstract
Entanglement survives between spatially separated atoms of an atomic cloud after it expands
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Affiliation(s)
- Daniel Cavalcanti
- Institut de Ciències Fotòniques (ICFO), The Barcelona Institute of Science and Technology, 08860 Castelldefels, Barcelona, Spain.
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38
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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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39
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Kunkel P, Prüfer M, Strobel H, Linnemann D, Frölian A, Gasenzer T, Gärttner M, Oberthaler MK. Spatially distributed multipartite entanglement enables EPR steering of atomic clouds. Science 2018; 360:413-416. [DOI: 10.1126/science.aao2254] [Citation(s) in RCA: 125] [Impact Index Per Article: 20.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2017] [Accepted: 02/16/2018] [Indexed: 11/02/2022]
Abstract
A key resource for distributed quantum-enhanced protocols is entanglement between spatially separated modes. However, the robust generation and detection of entanglement between spatially separated regions of an ultracold atomic system remain a challenge. We used spin mixing in a tightly confined Bose-Einstein condensate to generate an entangled state of indistinguishable particles in a single spatial mode. We show experimentally that this entanglement can be spatially distributed by self-similar expansion of the atomic cloud. We used spatially resolved spin read-out to reveal a particularly strong form of quantum correlations known as Einstein-Podolsky-Rosen (EPR) steering between distinct parts of the expanded cloud. Based on the strength of EPR steering, we constructed a witness, which confirmed genuine 5-partite entanglement.
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Affiliation(s)
- Philipp Kunkel
- Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Maximilian Prüfer
- Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Helmut Strobel
- Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Daniel Linnemann
- Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Anika Frölian
- Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Thomas Gasenzer
- Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Martin Gärttner
- Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Markus K. Oberthaler
- Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
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