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Pedernales JS, Beau M, Pittman SM, Egusquiza IL, Lamata L, Solano E, Del Campo A. Dirac Equation in (1+1)-Dimensional Curved Spacetime and the Multiphoton Quantum Rabi Model. PHYSICAL REVIEW LETTERS 2018; 120:160403. [PMID: 29756911 DOI: 10.1103/physrevlett.120.160403] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/29/2017] [Revised: 01/25/2018] [Indexed: 06/08/2023]
Abstract
We introduce an exact mapping between the Dirac equation in (1+1)-dimensional curved spacetime (DCS) and a multiphoton quantum Rabi model (QRM). A background of a (1+1)-dimensional black hole requires a QRM with one- and two-photon terms that can be implemented in a trapped ion for the quantum simulation of Dirac particles in curved spacetime. We illustrate our proposal with a numerical analysis of the free fall of a Dirac particle into a (1+1)-dimensional black hole, and find that the Zitterbewegung effect, measurable via the oscillatory trajectory of the Dirac particle, persists in the presence of gravity. From the duality between the squeezing term in the multiphoton QRM and the metric coupling in the DCS, we show that gravity generates squeezing of the Dirac particle wave function.
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Affiliation(s)
- J S Pedernales
- Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain
- Institute for Theoretical Physics and IQST, Albert-Einstein-Allee 11, Universität Ulm, D-89069 Ulm, Germany
| | - M Beau
- Department of Physics, University of Massachusetts, Boston, Massachusetts 02125, USA
| | - S M Pittman
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - I L Egusquiza
- Department of Theoretical Physics and History of Science, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain
| | - L Lamata
- Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain
| | - E Solano
- Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain
- IKERBASQUE, Basque Foundation for Science, Maria Diaz de Haro 3, 48013 Bilbao, Spain
- Department of Physics, Shanghai University, 200444 Shanghai, China
| | - A Del Campo
- Department of Physics, University of Massachusetts, Boston, Massachusetts 02125, USA
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