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Simplified quantum optical Stokes observables and Bell's theorem. Sci Rep 2022; 12:10101. [PMID: 35710579 PMCID: PMC9203794 DOI: 10.1038/s41598-022-14232-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2021] [Accepted: 05/11/2022] [Indexed: 11/09/2022] Open
Abstract
We discuss a simplified form of Stokes operators for quantum optical fields that involve the known concept of binning. Behind polarization analyzer photon numbers (more generally intensities) are measured. We have two outputs, say, for horizontal and vertical polarization. If the value obtained in horizontal output is greater than in vertical one we put 1. Otherwise, we put − 1. For equal photon numbers, we put 0. Such observables do not have all properties of the Stokes operators, but can be employed in Bell type measurements, involving polarization analyzers. They are especially handy for states of undefined number of photons, e.g. squeezed vacuum and their realisation is intuitive. We show that our observables can lead to quite robust violations of associated Bell inequalities. We formulate a strongly supported numerically conjecture that one can observe with this approach violations of local realism for the four mode squeezed vacuum for all pumping powers (i.e. gain values).
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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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Huang Y, Xiong HN, Yang Y, Hu ZD, Xi Z. Quantum control of spin-nematic squeezing in a dipolar spin-1 condensate. Sci Rep 2017; 7:43159. [PMID: 28233786 PMCID: PMC5324127 DOI: 10.1038/srep43159] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/04/2016] [Accepted: 01/20/2017] [Indexed: 11/09/2022] Open
Abstract
Versatile controllability of interactions and magnetic field in ultracold atomic gases ha now reached an era where spin mixing dynamics and spin-nematic squeezing can be studied. Recent experiments have realized spin-nematic squeezed vacuum and dynamic stabilization following a quench through a quantum phase transition. Here we propose a scheme for storage of maximal spin-nematic squeezing, with its squeezing angle maintained in a fixed direction, in a dipolar spin-1 condensate by applying a microwave pulse at a time that maximal squeezing occurs. The dynamic stabilization of the system is achieved by manipulating the external periodic microwave pulses. The stability diagram for the range of pulse periods and phase shifts that stabilize the dynamics is numerical simulated and agrees with a stability analysis. Moreover, the stability range coincides well with the spin-nematic vacuum squeezed region which indicates that the spin-nematic squeezed vacuum will never disappear as long as the spin dynamics are stabilized.
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Affiliation(s)
- Yixiao Huang
- School of Science, Zhejiang University of Science and Technology, Hangzhou, Zhejiang, 310023, China.,College of Computer Science, Shaanxi Normal University, Xi'an 710062, China
| | - Heng-Na Xiong
- Department of Applied Physics, Zhejiang University of Technology, Hangzhou 310023, China
| | - Yang Yang
- Department of Applied Physics, Zhejiang University of Technology, Hangzhou 310023, China
| | - Zheng-Da Hu
- Jiangsu Provincial Research Center of Light Industrial Optoelectronic Engineering and Technology, School of Science, Jiangnan University, Wuxi 214122, China
| | - Zhengjun Xi
- College of Computer Science, Shaanxi Normal University, Xi'an 710062, China
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Auccaise R, Araujo-Ferreira AG, Sarthour RS, Oliveira IS, Bonagamba TJ, Roditi I. Spin squeezing in a quadrupolar nuclei NMR system. PHYSICAL REVIEW LETTERS 2015; 114:043604. [PMID: 25679893 DOI: 10.1103/physrevlett.114.043604] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/21/2014] [Indexed: 06/04/2023]
Abstract
We have produced and characterized spin-squeezed states at a temperature of 26 °C in a nuclear magnetic resonance quadrupolar system. The experiment was carried out on 133Cs nuclei of spin I=7/2 in a sample of lyotropic liquid crystal. The source of spin squeezing was identified as the interaction between the quadrupole moment of the nuclei and the electric field gradients present within the molecules. We use the spin angular momentum representation to describe formally the nonlinear operators that produce the spin squeezing on a Hilbert space of dimension 2I+1=8. The quantitative and qualitative characterization of this spin-squeezing phenomenon is expressed by a squeezing parameter and squeezing angle developed for the two-mode Bose-Einstein condensate system, as well as by the Wigner quasiprobability distribution function. The generality of the present experimental scheme points to potential applications in solid-state physics.
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Affiliation(s)
- R Auccaise
- Departamento de Física, Universidade Estadual de Ponta Grossa, Av. Carlos Cavalcanti, 4748, 84030-900 Ponta Grossa, Paraná, Brazil
| | - A G Araujo-Ferreira
- Instituto de Física de São Carlos, Universidade de São Paulo, Caixa Postal 369, 13560-970 São Carlos, São Paulo, Brazil
| | - R S Sarthour
- Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, 22290-180 Rio de Janeiro, Rio de Janeiro, Brazil
| | - I S Oliveira
- Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, 22290-180 Rio de Janeiro, Rio de Janeiro, Brazil
| | - T J Bonagamba
- Instituto de Física de São Carlos, Universidade de São Paulo, Caixa Postal 369, 13560-970 São Carlos, São Paulo, Brazil
| | - I Roditi
- Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, 22290-180 Rio de Janeiro, Rio de Janeiro, Brazil
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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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Killoran N, Cramer M, Plenio MB. Extracting entanglement from identical particles. PHYSICAL REVIEW LETTERS 2014; 112:150501. [PMID: 24785015 DOI: 10.1103/physrevlett.112.150501] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/22/2014] [Indexed: 06/03/2023]
Abstract
Identical particles and entanglement are both fundamental components of quantum mechanics. However, when identical particles are condensed in a single spatial mode, the standard notions of entanglement, based on clearly identifiable subsystems, break down. This has led many to conclude that such systems have limited value for quantum information tasks, compared to distinguishable particle systems. To the contrary, we show that any entanglement formally appearing amongst the identical particles, including entanglement due purely to symmetrization, can be extracted into an entangled state of independent modes, which can then be applied to any task. In fact, the entanglement of the mode system is in one-to-one correspondence with the entanglement between the inaccessible identical particles. This settles the long-standing debate about the resource capabilities of such states, in particular spin-squeezed states of Bose-Einstein condensates, while also revealing a new perspective on how and when entanglement is generated in passive optical networks. Our results thus reveal new fundamental connections between entanglement, squeezing, and indistinguishability.
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Affiliation(s)
- N Killoran
- Institut für Theoretische Physik, Albert-Einstein-Allee 11, Universität Ulm, D-89069 Ulm, Germany
| | - M Cramer
- Institut für Theoretische Physik, Albert-Einstein-Allee 11, Universität Ulm, D-89069 Ulm, Germany
| | - M B Plenio
- Institut für Theoretische Physik, Albert-Einstein-Allee 11, Universität Ulm, D-89069 Ulm, Germany
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Gerritsma R, Negretti A, Doerk H, Idziaszek Z, Calarco T, Schmidt-Kaler F. Bosonic Josephson junction controlled by a single trapped ion. PHYSICAL REVIEW LETTERS 2012; 109:080402. [PMID: 23002726 DOI: 10.1103/physrevlett.109.080402] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/16/2011] [Indexed: 06/01/2023]
Abstract
We theoretically investigate the properties of a double-well bosonic Josephson junction coupled to a single trapped ion. We find that the coupling between the wells can be controlled by the internal state of the ion, which can be used for studying mesoscopic entanglement between the two systems and to measure their interaction with high precision. As a particular example we consider a single ^{87}Rb atom and a small Bose-Einstein condensate controlled by a single 171Yb+ ion. We calculate interwell coupling rates reaching hundreds of Hz, while the state dependence amounts to tens of Hz for plausible values of the currently unknown s-wave scattering length between the atom and the ion. The analysis shows that it is possible to induce either the self-trapping or the tunneling regime, depending on the internal state of the ion. This enables the generation of large scale ion-atomic wave packet entanglement within current technology.
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Affiliation(s)
- R Gerritsma
- Institut für Physik, Johannes Gutenberg-Universität Mainz, D-55099 Mainz, Germany.
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Bar-Gill N, Gross C, Mazets I, Oberthaler M, Kurizki G. Einstein-Podolsky-Rosen correlations of ultracold atomic gases. PHYSICAL REVIEW LETTERS 2011; 106:120404. [PMID: 21517287 DOI: 10.1103/physrevlett.106.120404] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/07/2010] [Indexed: 05/30/2023]
Abstract
We demonstrate that collective continuous variables of two species of trapped ultracold bosonic gases can be Einstein-Podolsky-Rosen-correlated (entangled) via inherent interactions between the species. We propose two different schemes for creating these correlations--a dynamical scheme and a static scheme analogous to two-mode squeezing in quantum optics. We quantify the correlations by using known measures of entanglement and study the effect of finite temperature on these quantum correlations.
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