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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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Viermann C, Sparn M, Liebster N, Hans M, Kath E, Parra-López Á, Tolosa-Simeón M, Sánchez-Kuntz N, Haas T, Strobel H, Floerchinger S, Oberthaler MK. Quantum field simulator for dynamics in curved spacetime. Nature 2022; 611:260-264. [PMID: 36352135 DOI: 10.1038/s41586-022-05313-9] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2022] [Accepted: 08/02/2022] [Indexed: 11/11/2022]
Abstract
In most cosmological models, rapid expansion of space marks the first moments of the Universe and leads to the amplification of quantum fluctuations1. The description of subsequent dynamics and related questions in cosmology requires an understanding of the quantum fields of the standard model and dark matter in curved spacetime. Even the reduced problem of a scalar quantum field in an explicitly time-dependent spacetime metric is a theoretical challenge2-5, and thus a quantum field simulator can lead to insights. Here we demonstrate such a quantum field simulator in a two-dimensional Bose-Einstein condensate with a configurable trap6,7 and adjustable interaction strength to implement this model system. We explicitly show the realization of spacetimes with positive and negative spatial curvature by wave-packet propagation and observe particle-pair production in controlled power-law expansion of space, using Sakharov oscillations to extract amplitude and phase information of the produced state. We find quantitative agreement with analytical predictions for different curvatures in time and space. This benchmarks and thereby establishes a quantum field simulator of a new class. In the future, straightforward upgrades offer the possibility to enter unexplored regimes that give further insight into relativistic quantum field dynamics.
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Affiliation(s)
- Celia Viermann
- Kirchhoff-Institut für Physik, Universität Heidelberg, Heidelberg, Germany.
| | - Marius Sparn
- Kirchhoff-Institut für Physik, Universität Heidelberg, Heidelberg, Germany
| | - Nikolas Liebster
- Kirchhoff-Institut für Physik, Universität Heidelberg, Heidelberg, Germany
| | - Maurus Hans
- Kirchhoff-Institut für Physik, Universität Heidelberg, Heidelberg, Germany
| | - Elinor Kath
- Kirchhoff-Institut für Physik, Universität Heidelberg, Heidelberg, Germany
| | - Álvaro Parra-López
- Institut für Theoretische Physik, Universität Heidelberg, Heidelberg, Germany.,Departamento de Física Teórica and IPARCOS, Facultad de Ciencias Físicas, Universidad Complutense de Madrid, Ciudad Universitaria, Madrid, Spain
| | - Mireia Tolosa-Simeón
- Institut für Theoretische Physik, Universität Heidelberg, Heidelberg, Germany.,Institut für Theoretische Physik III, Ruhr-Universität Bochum, Bochum, Germany
| | | | - Tobias Haas
- Institut für Theoretische Physik, Universität Heidelberg, Heidelberg, Germany.,Centre for Quantum Information and Communication, École polytechnique de Bruxelles, CP 165/59, Université libre de Bruxelles, Brussels, Belgium
| | - Helmut Strobel
- Kirchhoff-Institut für Physik, Universität Heidelberg, Heidelberg, Germany
| | - Stefan Floerchinger
- Institut für Theoretische Physik, Universität Heidelberg, Heidelberg, Germany.,Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universität Jena, Jena, Germany
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Dutta S, Buyskikh A, Daley AJ, Mueller EJ. Density Matrix Renormalization Group for Continuous Quantum Systems. PHYSICAL REVIEW LETTERS 2022; 128:230401. [PMID: 35749177 DOI: 10.1103/physrevlett.128.230401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/20/2021] [Revised: 03/22/2022] [Accepted: 05/06/2022] [Indexed: 06/15/2023]
Abstract
We introduce a versatile and practical framework for applying matrix product state techniques to continuous quantum systems. We divide space into multiple segments and generate continuous basis functions for the many-body state in each segment. By combining this mapping with existing numerical density matrix renormalization group routines, we show how one can accurately obtain the ground-state wave function, spatial correlations, and spatial entanglement entropy directly in the continuum. For a prototypical mesoscopic system of strongly interacting bosons we demonstrate faster convergence than standard grid-based discretization. We illustrate the power of our approach by studying a superfluid-insulator transition in an external potential. We outline how one can directly apply or generalize this technique to a wide variety of experimentally relevant problems across condensed matter physics and quantum field theory.
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Affiliation(s)
- Shovan Dutta
- T.C.M. Group, Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom
- Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853, USA
- Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany
| | - Anton Buyskikh
- Department of Physics and SUPA, University of Strathclyde, Glasgow G4 0NG, United Kingdom
| | - Andrew J Daley
- Department of Physics and SUPA, University of Strathclyde, Glasgow G4 0NG, United Kingdom
| | - Erich J Mueller
- Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853, USA
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