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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] [What about the content of this article? (0)] [Affiliation(s)] [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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Hans M, Schmutte F, Viermann C, Liebster N, Sparn M, Oberthaler MK, Strobel H. High signal to noise absorption imaging of alkali atoms at moderate magnetic fields. Rev Sci Instrum 2021; 92:023203. [PMID: 33648052 DOI: 10.1063/5.0040677] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/16/2020] [Accepted: 01/22/2021] [Indexed: 06/12/2023]
Abstract
We present an improved scheme for absorption imaging of alkali atoms at moderate magnetic fields, where the excited state is well in the Paschen-Back regime, but the ground state hyperfine manifold is not. It utilizes four atomic levels to obtain an approximately closed optical cycle. With the resulting absorption of the corresponding two laser frequencies, we extract the atomic column density of a 39K Bose-Einstein condensate. The scheme can be readily applied to all other alkali-like species.
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Affiliation(s)
- Maurus Hans
- Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Finn Schmutte
- Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Celia Viermann
- Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Nikolas Liebster
- Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
| | - Marius Sparn
- 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
| | - Helmut Strobel
- Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany
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Viermann C, Fabis F, Kozlikin E, Lilow R, Bartelmann M. Nonequilibrium statistical field theory for classical particles: Basic kinetic theory. Phys Rev E 2015; 91:062120. [PMID: 26172674 DOI: 10.1103/physreve.91.062120] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/11/2014] [Indexed: 11/07/2022]
Abstract
Recently Mazenko and Das and Mazenko [Phys. Rev. E 81, 061102 (2010); J. Stat. Phys. 149, 643 (2012); J. Stat. Phys. 152, 159 (2013); Phys. Rev. E 83, 041125 (2011)] introduced a nonequilibrium field-theoretical approach to describe the statistical properties of a classical particle ensemble starting from the microscopic equations of motion of each individual particle. We use this theory to investigate the transition from those microscopic degrees of freedom to the evolution equations of the macroscopic observables of the ensemble. For the free theory, we recover the continuity and Jeans equations of a collisionless gas. For a theory containing two-particle interactions in a canonical perturbation series, we find the macroscopic evolution equations to be described by the Born-Bogoliubov-Green-Kirkwood-Yvon hierarchy with a truncation criterion depending on the order in perturbation theory. This establishes a direct link between the classical and the field-theoretical approaches to kinetic theory that might serve as a starting point to investigate kinetic theory beyond the classical limits.
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Affiliation(s)
- Celia Viermann
- Heidelberg University, Zentrum für Astronomie, Institut für Theoretische Astrophysik, Philosophenweg 12, 69120 Heidelberg, Germany
| | - Felix Fabis
- Heidelberg University, Zentrum für Astronomie, Institut für Theoretische Astrophysik, Philosophenweg 12, 69120 Heidelberg, Germany
| | - Elena Kozlikin
- Heidelberg University, Zentrum für Astronomie, Institut für Theoretische Astrophysik, Philosophenweg 12, 69120 Heidelberg, Germany
| | - Robert Lilow
- Heidelberg University, Zentrum für Astronomie, Institut für Theoretische Astrophysik, Philosophenweg 12, 69120 Heidelberg, Germany
| | - Matthias Bartelmann
- Heidelberg University, Zentrum für Astronomie, Institut für Theoretische Astrophysik, Philosophenweg 12, 69120 Heidelberg, Germany
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