Abstract
We investigate how nontrivial topology affects the entanglement dynamics between a detector and a quantum field and between two detectors mediated by a quantum field. Nontrivial topology refers to both that of the base space and that of the bundle. Using a derivative-coupling Unruh-DeWitt-like detector model interacting with a quantum scalar field in an Einstein cylinder S 1 (space) × R 1 (time), we see the beating behaviors in the dynamics of the detector-field entanglement and the detector-detector entanglement, which distinguish from the results in the non-compact (1+1) dimensional Minkowski space. The beat patterns of entanglement dynamics in a normal and a twisted field with the same parameter values are different because of the difference in the spectrum of the field modes. In terms of the kinetic momentum of the detectors, we find that the contribution by the zero mode in a normal field to entanglement dynamics has no qualitative difference from those by the nonzero modes.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
International Society for Relativistic Quantum Information, www.isrqi.net.
S.-Y. Lin, C.-H. Chou and B.L. Hu, Disentanglement of two harmonic oscillators in relativistic motion, Phys. Rev. D 78 (2008) 125025 [arXiv:0803.3995] [INSPIRE].
S.-Y. Lin, C.-H. Chou and B.L. Hu, Quantum teleportation between moving detectors, Phys. Rev. D 91 (2015) 084063 [arXiv:1502.03539] [INSPIRE].
P. Langlois, Causal particle detectors and topology, Annals Phys. 321 (2006) 2027 [gr-qc/0510049] [INSPIRE].
P. Langlois, Imprints of spacetime topology in the Hawking-Unruh effect, Ph.D. Thesis, University of Nottingham (2005) [gr-qc/0510127] [INSPIRE].
R. Zhou, R.O. Behunin, S.-Y. Lin and B.L. Hu, Boundary effects on quantum entanglement and its dynamics in a detector-field system, JHEP 08 (2013) 040 [arXiv:1301.0073] [INSPIRE].
T.H. Boyle, Casimir forces and boundary conditions in one dimension: attraction, repulsion, Planck spectrum, and entropy, Am. J. Phys. 71 (2003) 990 [quant-ph/0211109].
T. Aoki et al., Observation of strong coupling between one atom and a monolithic microresonator, Nature 443 (2006) 671 [quant-ph/0606033].
C.J. Isham, Twisted quantum fields in a curved space-time, Proc. Roy. Soc. Lond. A 362 (1978) 383.
S.J. Avis and C.J. Isham, Vacuum solutions for a twisted scalar field, Proc. Roy. Soc. Lond. A 363 (1978) 581.
J.S. Dowker and R. Banach, Quantum field theory on Clifford-Klein space-times. The effective Lagrangian and vacuum stress energy tensor, J. Phys. A 11 (1978) 2255 [INSPIRE].
B.S. DeWitt, C.F. Hart and C.J. Isham, Topology and quantum field theory, Physica A 96 (1979) 197 [INSPIRE].
E. Martın-Martínez, A.R.H. Smith and D.R. Terno, Spacetime structure and vacuum entanglement, Phys. Rev. D 93 (2016) 044001 [arXiv:1507.02688] [INSPIRE].
I. Bengtsson and K. Życzkowski, Geometry of quantum states: an introduction to quantum entanglement, Cambridge University Press, Cambridge U.K. (2006).
D. Zhou, G.W. Chern, J. Fei and R. Joynt, Topology of entanglement evolution of two qubits, Int. J. Mod. Phys. B 26 (2012) 1250054 [arXiv:1007.1749].
N.T.T. Nguyen and R. Joynt, Topology of quantum discord, arXiv:1310.5286.
S.-Y. Lin and B.L. Hu, Temporal and spatial dependence of quantum entanglement from a field theory perspective, Phys. Rev. D 79 (2009) 085020 [arXiv:0812.4391] [INSPIRE].
M. Kac, Some remarks on the use of probability in classical statistical mechanics, Acad. Roy. Belg. Bull. Cl. Sci. 42 (1956) 356.
J.M. Oberreuter, I. Homrighausen and S. Kehrein, Entanglement propagation and typicality of measurements in the quantum Kac ring, Annals Phys. 348 (2014) 324 [arXiv:1312.1726].
W.G. Unruh, Notes on black hole evaporation, Phys. Rev. D 14 (1976) 870 [INSPIRE].
B.S. DeWitt, Quantum gravity: the new synthesis, in General relativity: an Einstein centenary survey, S.W. Hawking and W. Israel eds., Cambridge University Press, Cambridge U.K. (1979).
W.G. Unruh and W.H. Zurek, Reduction of a wave packet in quantum Brownian motion, Phys. Rev. D 40 (1989) 1071 [INSPIRE].
D.J. Raine, D.W. Sciama and P.G. Grove, Does a uniformly accelerated quantum oscillator radiate?, Proc. Roy. Soc. Lond. A 435 (1991) 205.
A. Raval, B.L. Hu and J. Anglin, Stochastic theory of accelerated detectors in a quantum field, Phys. Rev. D 53 (1996) 7003 [gr-qc/9510002] [INSPIRE].
B.L. Hu and A. Raval, Is there emitted radiation in Unruh effect?, quant-ph/0012134 [INSPIRE].
J. Louko, Unruh-DeWitt detector response across a Rindler firewall is finite, JHEP 09 (2014) 142 [arXiv:1407.6299] [INSPIRE].
E. Martín-Martínez and J. Louko, Particle detectors and the zero mode of a quantum field, Phys. Rev. D 90 (2014) 024015 [arXiv:1404.5621] [INSPIRE].
S.-Y. Lin and B.L. Hu, Accelerated detector-quantum field correlations: from vacuum fluctuations to radiation flux, Phys. Rev. D 73 (2006) 124018 [gr-qc/0507054] [INSPIRE].
N.D. Birrell and P.C.W. Davies, Quantum fields in curved space, Cambridge University Press, Cambridge U.K. (1982) [INSPIRE].
S.-Y. Lin and B.L. Hu, Backreaction and the Unruh effect: new insights from exact solutions of uniformly accelerated detectors, Phys. Rev. D 76 (2007) 064008 [gr-qc/0611062] [INSPIRE].
G. Vidal and R.F. Werner, Computable measure of entanglement, Phys. Rev. A 65 (2002) 032314 [INSPIRE].
M.B. Plenio, Logarithmic negativity: a full entanglement monotone that is not convex, Phys. Rev. Lett. 95 (2005) 090503 [Erratum ibid. 95 (2005) 119902] [quant-ph/0505071].
A. Mari and D. Vitali, Optimal fidelity of teleportation of coherent states and entanglement, Phys. Rev. A 78 (2008) 062340 [arXiv:0808.2829].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1508.06221
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Lin, SY., Chou, CH. & Hu, B.L. Entanglement dynamics of detectors in an Einstein cylinder. J. High Energ. Phys. 2016, 47 (2016). https://doi.org/10.1007/JHEP03(2016)047
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2016)047