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Barbado LC, Báez-Camargo AL, Fuentes I. Evolution of confined quantum scalar fields in curved spacetime. Part II: Spacetimes with moving boundaries in any synchronous gauge. THE EUROPEAN PHYSICAL JOURNAL. C, PARTICLES AND FIELDS 2021; 81:953. [PMID: 34744505 PMCID: PMC8553737 DOI: 10.1140/epjc/s10052-021-09737-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/02/2021] [Revised: 09/13/2021] [Accepted: 10/10/2021] [Indexed: 06/13/2023]
Abstract
We develop a method for computing the Bogoliubov transformation experienced by a confined quantum scalar field in a globally hyperbolic spacetime, due to the changes in the geometry and/or the confining boundaries. The method constructs a basis of solutions to the Klein-Gordon equation associated to each compact Cauchy hypersurface of constant time. It then provides a differential equation for the linear transformation between bases at different times. The transformation can be interpreted physically as a Bogoliubov transformation when it connects two regions in which a time symmetry allows for a Fock quantisation. This second article on the method is dedicated to spacetimes with timelike boundaries that do not remain static in any synchronous gauge. The method proves especially useful in the regime of small perturbations, where it allows one to easily make quantitative predictions on the amplitude of the resonances of the field. Therefore, it provides a crucial tool in the growing research area of confined quantum fields in table-top experiments. We prove this utility by addressing two problems in the perturbative regime: Dynamical Casimir Effect and gravitational wave resonance. We reproduce many previous results on these phenomena and find novel results in an unified way. Possible extensions of the method are indicated. We expect that our method will become standard in quantum field theory for confined fields.
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Affiliation(s)
- Luis C. Barbado
- Quantenoptik, Quantennanophysik und Quanteninformation, Fakultät für Physik, Universität Wien, Boltzmanngasse 5, 1090 Vienna, Austria
- Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, Boltzmanngasse 3, 1090 Vienna, Austria
| | - Ana L. Báez-Camargo
- Quantenoptik, Quantennanophysik und Quanteninformation, Fakultät für Physik, Universität Wien, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Ivette Fuentes
- Quantenoptik, Quantennanophysik und Quanteninformation, Fakultät für Physik, Universität Wien, Boltzmanngasse 5, 1090 Vienna, Austria
- School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD UK
- School of Physics and Astronomy, University of Southampton, Southampton, SO17 1BJ UK
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Quantum Power Distribution of Relativistic Acceleration Radiation: Classical Electrodynamic Analogies with Perfectly Reflecting Moving Mirrors. Symmetry (Basel) 2021. [DOI: 10.3390/sym13040653] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
We find the quantum power emitted and distribution in 3 + 1-dimensions of relativistic acceleration radiation using a single perfectly reflecting mirror via Lorentz invariance, demonstrating close analogies to point charge radiation in classical electrodynamics.
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Gooding C, Biermann S, Erne S, Louko J, Unruh WG, Schmiedmayer J, Weinfurtner S. Interferometric Unruh Detectors for Bose-Einstein Condensates. PHYSICAL REVIEW LETTERS 2020; 125:213603. [PMID: 33274966 DOI: 10.1103/physrevlett.125.213603] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/24/2020] [Accepted: 10/07/2020] [Indexed: 06/12/2023]
Abstract
The Unruh effect predicts a thermal response for an accelerated detector moving through the vacuum. Here we propose an interferometric scheme to observe an analogue of the circular Unruh effect using a localized laser coupled to a Bose-Einstein condensate (BEC). Quantum fluctuations in the condensate are governed by an effective relativistic field theory, and as demonstrated, the coupled laser field acts as an effective Unruh-DeWitt detector thereof. The effective speed of light is lowered by 12 orders of magnitude to the sound velocity in the BEC. For detectors traveling close to the sound speed, observation of the Unruh effect in the analogue system becomes experimentally feasible.
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Affiliation(s)
- Cisco Gooding
- School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
| | - Steffen Biermann
- School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
| | - Sebastian Erne
- School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
- Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien, Stadionallee 2, 1020 Vienna, Austria
- Wolfgang Pauli Institut, c/o Fak. Mathematik, Universität Wien, Nordbergstrasse 15, 1090 Vienna, Austria
| | - Jorma Louko
- School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
| | - William G Unruh
- Department of Physics & Astronomy, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada
- Hagler IAS, IQSE, Texas A&M, College Station, Texas 77843-4242, USA
| | - Joerg Schmiedmayer
- Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien, Stadionallee 2, 1020 Vienna, Austria
| | - Silke Weinfurtner
- School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
- Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
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