1
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Mallweger M, de Oliveira MH, Thomm R, Parke H, Kuk N, Higgins G, Bachelard R, Villas-Boas CJ, Hennrich M. Single-Shot Measurements of Phonon Number States Using the Autler-Townes Effect. PHYSICAL REVIEW LETTERS 2023; 131:223603. [PMID: 38101344 DOI: 10.1103/physrevlett.131.223603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/11/2023] [Accepted: 11/01/2023] [Indexed: 12/17/2023]
Abstract
We present a single-shot method to measure motional states in the number basis. The technique can be applied to systems with at least three nondegenerate energy levels which can be coupled to a linear quantum harmonic oscillator. The method relies on probing an Autler-Townes splitting that arises when a phonon-number changing transition is strongly coupled. We demonstrate the method using a single trapped ion and show that it may be used in a nondemolition fashion to prepare phonon number states. We also show how the Autler-Townes splitting can be used to measure phonon number distributions.
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Affiliation(s)
- Marion Mallweger
- Department of Physics, Stockholm University, SE-106 91 Stockholm, Sweden
| | | | - Robin Thomm
- Department of Physics, Stockholm University, SE-106 91 Stockholm, Sweden
| | - Harry Parke
- Department of Physics, Stockholm University, SE-106 91 Stockholm, Sweden
| | - Natalia Kuk
- Department of Physics, Stockholm University, SE-106 91 Stockholm, Sweden
| | - Gerard Higgins
- Department of Physics, Stockholm University, SE-106 91 Stockholm, Sweden
- Department of Microtechnology and Nanoscience (MC2), Chalmers University of Technology, SE-412 96 Gothenburg, Sweden
| | - Romain Bachelard
- Departamento de Física, Universidade Federal de São Carlos, 13565-905 São Carlos, SP, Brazil
- Université Côte d'Azur, CNRS, Institut de Physique de Nice, 06560 Valbonne, France
| | - Celso Jorge Villas-Boas
- Departamento de Física, Universidade Federal de São Carlos, 13565-905 São Carlos, SP, Brazil
| | - Markus Hennrich
- Department of Physics, Stockholm University, SE-106 91 Stockholm, Sweden
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2
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Jacquet MJ, Giacomelli L, Valnais Q, Joly M, Claude F, Giacobino E, Glorieux Q, Carusotto I, Bramati A. Quantum Vacuum Excitation of a Quasinormal Mode in an Analog Model of Black Hole Spacetime. PHYSICAL REVIEW LETTERS 2023; 130:111501. [PMID: 37001081 DOI: 10.1103/physrevlett.130.111501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/11/2022] [Revised: 01/18/2023] [Accepted: 02/17/2023] [Indexed: 06/19/2023]
Abstract
Vacuum quantum fluctuations near horizons are known to yield correlated emission by the Hawking effect. We use a driven-dissipative quantum fluid of microcavity polaritons as an analog model of a quantum field theory on a black-hole spacetime and numerically calculate correlated emission. We show that, in addition to the Hawking effect at the sonic horizon, quantum fluctuations may result in a sizable stationary excitation of a quasinormal mode of the field theory. Observable signatures of the excitation of the quasinormal mode are found in the spatial density fluctuations as well as in the spectrum of Hawking emission. This suggests an intrinsic fluctuation-driven mechanism leading to the quantum excitation of quasinormal modes on black hole spacetimes.
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Affiliation(s)
- M J Jacquet
- Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-Université PSL, Collège de France, Paris 75005, France
| | - L Giacomelli
- INO-CNR BEC Center and Dipartimento di Fisica, Università di Trento, via Sommarive 14, I-38123 Povo, Trento, Italy
| | - Q Valnais
- Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-Université PSL, Collège de France, Paris 75005, France
| | - M Joly
- Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-Université PSL, Collège de France, Paris 75005, France
| | - F Claude
- Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-Université PSL, Collège de France, Paris 75005, France
| | - E Giacobino
- Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-Université PSL, Collège de France, Paris 75005, France
| | - Q Glorieux
- Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-Université PSL, Collège de France, Paris 75005, France
| | - I Carusotto
- INO-CNR BEC Center and Dipartimento di Fisica, Università di Trento, via Sommarive 14, I-38123 Povo, Trento, Italy
| | - A Bramati
- Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-Université PSL, Collège de France, Paris 75005, France
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3
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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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4
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Tian Z, Wu L, Zhang L, Jing J, Du J. Probing Lorentz-invariance-violation-induced nonthermal Unruh effect in quasi-two-dimensional dipolar condensates. Int J Clin Exp Med 2022. [DOI: 10.1103/physrevd.106.l061701] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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5
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Uncovering gravity's secrets with a fluid of atoms. Proc Natl Acad Sci U S A 2022; 119:e2212186119. [PMID: 35951666 PMCID: PMC9407306 DOI: 10.1073/pnas.2212186119] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022] Open
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6
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Analogue cosmological particle creation in an ultracold quantum fluid of light. Nat Commun 2022; 13:2890. [PMID: 35614054 PMCID: PMC9133100 DOI: 10.1038/s41467-022-30603-1] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2021] [Accepted: 05/10/2022] [Indexed: 12/01/2022] Open
Abstract
The rapid expansion of the early universe resulted in the spontaneous production of cosmological particles from vacuum fluctuations, some of which are observable today in the cosmic microwave background anisotropy. The analogue of cosmological particle creation in a quantum fluid was proposed, but the quantum, spontaneous effect due to vacuum fluctuations has not yet been observed. Here we report the spontaneous creation of analogue cosmological particles in the laboratory, using a quenched 3-dimensional quantum fluid of light. We observe acoustic peaks in the density power spectrum, in close quantitative agreement with the quantum-field theoretical prediction. We find that the long-wavelength particles provide a window to early times. This work introduces the quantum fluid of light, as cold as an atomic Bose-Einstein condensate. Under certain conditions light can act as a fluid like a Bose-Einstein condensate. Here the authors discuss an analogy of cosmological particle creation using such a quantum fluid of light.
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7
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Xin M, Leong WS, Chen Z, Wang Y, Lan SY. Rapid Quantum Squeezing by Jumping the Harmonic Oscillator Frequency. PHYSICAL REVIEW LETTERS 2021; 127:183602. [PMID: 34767425 DOI: 10.1103/physrevlett.127.183602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/26/2021] [Accepted: 09/30/2021] [Indexed: 06/13/2023]
Abstract
Quantum sensing and quantum information processing use quantum advantages such as squeezed states that encode a quantity of interest with higher precision and generate quantum correlations to outperform classical methods. In harmonic oscillators, the rate of generating squeezing is set by a quantum speed limit. Therefore, the degree to which a quantum advantage can be used in practice is limited by the time needed to create the state relative to the rate of unavoidable decoherence. Alternatively, a sudden change of harmonic oscillator's frequency projects a ground state into a squeezed state which can circumvent the time constraint. Here, we create squeezed states of atomic motion by sudden changes of the harmonic oscillation frequency of atoms in an optical lattice. Building on this protocol, we demonstrate rapid quantum amplification of a displacement operator that could be used for detecting motion. Our results can speed up quantum gates and enable quantum sensing and quantum information processing in noisy environments.
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Affiliation(s)
- Mingjie Xin
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - Wui Seng Leong
- 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
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8
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Sutherland RT, Burd SC, Slichter DH, Libby SB, Leibfried D. Motional Squeezing for Trapped Ion Transport and Separation. PHYSICAL REVIEW LETTERS 2021; 127:083201. [PMID: 34477447 PMCID: PMC10545415 DOI: 10.1103/physrevlett.127.083201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/10/2021] [Accepted: 07/19/2021] [Indexed: 06/13/2023]
Abstract
Transport, separation, and merging of trapped ion crystals are essential operations for most large-scale quantum computing architectures. In this Letter, we develop a theoretical framework that describes the dynamics of ions in time-varying potentials with a motional squeeze operator, followed by a motional displacement operator. Using this framework, we develop a new, general protocol for trapped ion transport, separation, and merging. We show that motional squeezing can prepare an ion wave packet to enable transfer from the ground state of one trapping potential to another. The framework and protocol are applicable if the potential is harmonic over the extent of the ion wave packets at all times. As illustrations, we discuss two specific operations: changing the strength of the confining potential for a single ion and separating same-species ions with their mutual Coulomb force. Both of these operations are, ideally, free of residual motional excitation.
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Affiliation(s)
- R. T. Sutherland
- Department of Electrical and Computer Engineering, University of Texas at San Antonio, San Antonio, Texas 78249, USA
| | - S. C. Burd
- Time and Frequency Division, National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - D. H. Slichter
- Time and Frequency Division, National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
| | - S. B. Libby
- Physics Division, Physical and Life Sciences, Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - D. Leibfried
- Time and Frequency Division, National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA
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9
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Perspective on Some Recent and Future Developments in Casimir Interactions. APPLIED SCIENCES-BASEL 2020. [DOI: 10.3390/app11010293] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Here, we present a critical review of recent developments in Casimir physics motivated by discoveries of novel materials. Specifically, topologically nontrivial properties of the graphene family, Chern and topological insulators, and Weyl semimetals have diverse manifestations in the distance dependence, presence of fundamental constants, magnitude, and sign of the Casimir interaction. Limited studies of the role of nonlinear optical properties in the interaction are also reviewed. We show that, since many new materials have greatly enhanced the nonlinear optical response, new efficient pathways for investigation of the characteristic regimes of the Casimir force need to be explored, which are expected to lead to new discoveries. Recent progress in the dynamical Casimir effect is also reviewed and we argue that nonlinear media can open up new directions in this field as well.
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10
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Schmidt J, Hönig D, Weckesser P, Thielemann F, Schaetz T, Karpa L. Mass-selective removal of ions from Paul traps using parametric excitation. APPLIED PHYSICS. B, LASERS AND OPTICS 2020; 126:176. [PMID: 33088025 PMCID: PMC7547030 DOI: 10.1007/s00340-020-07491-8] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/04/2020] [Accepted: 07/14/2020] [Indexed: 06/10/2023]
Abstract
We study a method for mass-selective removal of ions from a Paul trap by parametric excitation. This can be achieved by applying an oscillating electric quadrupole field at twice the secular frequency ω sec using pairs of opposing electrodes. While excitation near the resonance with the secular frequency ω sec only leads to a linear increase of the amplitude with excitation duration, parametric excitation near 2 ω sec results in an exponential increase of the amplitude. This enables efficient removal of ions from the trap with modest excitation voltages and narrow bandwidth, therefore, substantially reducing the disturbance of ions with other charge-to-mass ratios. We numerically study and compare the mass selectivity of the two methods. In addition, we experimentally show that the barium isotopes with 136 and 137 nucleons can be removed from small ion crystals and ejected out of the trap while keeping 138 Ba + ions Doppler cooled, corresponding to a mass selectivity of better than Δ m / m = 1 / 138 . This method can be widely applied to ion trapping experiments without major modifications since it only requires modulating the potential of the ion trap.
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Affiliation(s)
- Julian Schmidt
- Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Straße 3, 79104 Freiburg, Germany
- Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-PSL Research University, Collège de France, 4 place Jussieu, Paris, France
- National Institute of Standards and Technology, Boulder, CO USA
| | - Daniel Hönig
- Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Straße 3, 79104 Freiburg, Germany
| | - Pascal Weckesser
- Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Straße 3, 79104 Freiburg, Germany
| | - Fabian Thielemann
- Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Straße 3, 79104 Freiburg, Germany
| | - Tobias Schaetz
- Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Straße 3, 79104 Freiburg, Germany
| | - Leon Karpa
- Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Straße 3, 79104 Freiburg, Germany
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11
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Wittemer M, Schröder JP, Hakelberg F, Kiefer P, Fey C, Schuetzhold R, Warring U, Schaetz T. Trapped-ion toolkit for studies of quantum harmonic oscillators under extreme conditions. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2020; 378:20190230. [PMID: 32684127 PMCID: PMC7422877 DOI: 10.1098/rsta.2019.0230] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 03/25/2020] [Indexed: 06/11/2023]
Abstract
Many phenomena described in relativistic quantum field theory are inaccessible to direct observations, but analogue processes studied under well-defined laboratory conditions can present an alternative perspective. Recently, we demonstrated an analogy of particle creation using an intrinsically robust motional mode of two trapped atomic ions. Here, we substantially extend our classical control techniques by implementing machine-learning strategies in our platform and, consequently, increase the accessible parameter regime. As a proof of methodology, we present experimental results of multiple quenches and parametric modulation of an unprotected motional mode of a single ion, demonstrating the increased level of real-time control. In combination with previous results, we enable future experiments that may yield entanglement generation using a process in analogy to Hawking radiation. This article is part of a discussion meeting issue 'The next generation of analogue gravity experiments'.
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Affiliation(s)
- Matthias Wittemer
- Albert-Ludwigs-Universität Freiburg, Physikalisches Institut, Hermann-Herder-Strasse 3, 79104 Freiburg, Germany
| | - Jan-Philipp Schröder
- Albert-Ludwigs-Universität Freiburg, Physikalisches Institut, Hermann-Herder-Strasse 3, 79104 Freiburg, Germany
| | - Frederick Hakelberg
- Albert-Ludwigs-Universität Freiburg, Physikalisches Institut, Hermann-Herder-Strasse 3, 79104 Freiburg, Germany
| | - Philip Kiefer
- Albert-Ludwigs-Universität Freiburg, Physikalisches Institut, Hermann-Herder-Strasse 3, 79104 Freiburg, Germany
| | - Christian Fey
- Zentrum für Optische Quantentechnologien, Universität Hamburg, Fachbereich Physik, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Ralf Schuetzhold
- Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstrasse 400, 01328 Dresden, Germany
- Institut für Theoretische Physik, Technische Universität Dresden, 01062 Dresden, Germany
| | - Ulrich Warring
- Albert-Ludwigs-Universität Freiburg, Physikalisches Institut, Hermann-Herder-Strasse 3, 79104 Freiburg, Germany
| | - Tobias Schaetz
- Albert-Ludwigs-Universität Freiburg, Physikalisches Institut, Hermann-Herder-Strasse 3, 79104 Freiburg, Germany
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12
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Jacquet MJ, Weinfurtner S, König F. The next generation of analogue gravity experiments. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2020; 378:20190239. [PMID: 32684138 PMCID: PMC7422886 DOI: 10.1098/rsta.2019.0239] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 05/07/2020] [Indexed: 06/11/2023]
Affiliation(s)
- M. J. Jacquet
- Laboratoire Kastler Brossel, Sorbonne Université, CNRS, ENS-Université PSL, Collège de France, Paris 75005, France
| | - S. Weinfurtner
- School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK
| | - F. König
- School of Physics and Astronomy, SUPA, University of St Andrews, North Haugh, St Andrews KY16 9SS, UK
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13
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Schmit RP, Taketani BG, Wilhelm FK. Quantum simulation of particle creation in curved space-time. PLoS One 2020; 15:e0229382. [PMID: 32142551 PMCID: PMC7059940 DOI: 10.1371/journal.pone.0229382] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2018] [Accepted: 01/09/2020] [Indexed: 11/18/2022] Open
Abstract
Conversion of vacuum fluctuations into real particles was first predicted by L. Parker considering an expanding universe, followed in S. Hawking's work on black hole radiation. Since their experimental observation is challenging, analogue systems have gained attention in the verification of this concept. Here we propose an experimental set-up consisting of two adjacent piezoelectric semiconducting layers, one of them carrying dynamic quantum dots (DQDs), and the other being p-doped with an attached gate on top, which introduces a space-dependent layer conductivity. The propagation of surface acoustic waves (SAWs) on the latter layer is governed by a wave equation with an effective metric. In the frame of the DQDs, this space- and time-dependent metric possesses a sonic horizon for SAWs and resembles that of a two dimensional non-rotating and uncharged black hole to some extent. The non-thermal steady state of the DQD spin indicates particle creation in form of piezophonons.
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Affiliation(s)
- Raphael P. Schmit
- Theoretical Physics, Saarland University, Saarbrücken, Germany
- * E-mail:
| | - Bruno G. Taketani
- Theoretical Physics, Saarland University, Saarbrücken, Germany
- Departamento de Física, Universidade Federal de Santa Catarina, Florianópolis, SC, Brazil
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14
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Abstract
This is a digest of the main achievements in the wide area, called the Dynamical Casimir Effect nowadays, for the past 50 years, with the emphasis on results obtained after 2010.
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