Abstract
Understanding the dynamics of open quantum systems is a highly important task for the implementation of emerging quantum technologies. To make the problem tractable theoretically, it is common to neglect initial system–environment correlations. However, this assumption is questionable in situations where the system is interacting strongly with the environment. In particular, the system state preparation can then influence the dynamics of the system via the system–environment correlations. To gain insight into the effect of these correlations, we solve an exactly solvable model of a quantum spin interacting with a spin environment both with and without initial correlations for arbitrary system–environment coupling strengths. We show that the effect of the system state preparation may or may not be significant in the strong system–environment coupling regime at low temperatures. We also study the dynamics of the entanglement between two spins interacting with a common spin environment with and without initial system–environment correlations to demonstrate that the correlations can play a significant role in the dynamics of two-qubit systems as well.
Graphical abstract
Similar content being viewed by others
References
H.-P. Breuer, F. Petruccione The Theory of Open Quantum Systems (Oxford University Press, Oxford, 2007)
U. Weiss, Quantum dissipative systems (World Scientific, Singapore, 2008)
K. Modi, Open Syst. Inf. Dyn. 18, 253 (2011)
V. Hakim, V. Ambegaokar, Phys. Rev. A 32, 423 (1985)
F. Haake, R. Reibold, Phys. Rev. A 32, 2462 (1985)
H. Grabert, P. Schramm, G.-L. Ingold, Phys. Rep. 168, 115 (1988)
C.M. Smith, A.O. Caldeira, Phys. Rev. A 41, 3103 (1990)
R. Karrlein, H. Grabert, Phys. Rev. E 55, 153 (1997)
L. Dávila Romero, J. Pablo Paz, Phys. Rev. A 55, 4070 (1997)
E. Lutz, Phys. Rev. A 67, 022109 (2003)
S. Banerjee, R. Ghosh, Phys. Rev. E 67, 056120 (2003)
N.G. van Kampen, J. Stat. Phys. 115, 1057 (2004)
M. Ban, Phys. Rev. A 80, 064103 (2009)
M. Campisi, P. Talkner, P. Hänggi, Phys. Rev. Lett. 102, 210401 (2009)
C. Uchiyama, M. Aihara, Phys. Rev. A 82, 044104 (2010)
A.G. Dijkstra, Y. Tanimura, Phys. Rev. Lett. 104, 250401 (2010)
A. Smirne, H.-P. Breuer, J. Piilo, B. Vacchini, Phys. Rev. A 82, 062114 (2010)
J. Dajka, J. Łuczka, Phys. Rev. A 82, 012341 (2010)
Y.-J. Zhang, X.-B. Zou, Y.-J. Xia, G.-C. Guo, Phys. Rev. A 82, 022108 (2010)
H.-T. Tan, W.-M. Zhang, Phys. Rev. A 83, 032102 (2011)
C.K. Lee, J. Cao, J. Gong, Phys. Rev. E 86, 021109 (2012)
V.G. Morozov, S. Mathey, G. Röpke, Phys. Rev. A 85, 022101 (2012)
V. Semin, I. Sinayskiy, F. Petruccione, Phys. Rev. A 86, 062114 (2012)
E.-M. Laine, H.-P. Breuer, J. Piilo, C.-F. Li, G.-C. Guo, Phys. Rev. Lett. 108, 210402 (2012)
A.Z. Chaudhry, J. Gong, Phys. Rev. A 87, 012129 (2013)
A.Z. Chaudhry, J. Gong, Phys. Rev. A 88, 052107 (2013)
A.Z. Chaudhry, J. Gong, Can. J. Chem. 92, 119 (2013)
J. Reina, C. Susa, F. Fanchini, Sci. Rep. 4, 7443 (2014)
F. Buscemi, Phys. Rev. Lett. 113, 140502 (2014)
Y.-J. Zhang, W. Han, Y.-J. Xia, Y.-M. Yu, H. Fan, Sci. Rep. 5, 13359 (2015)
C.-C. Chen, H.-S. Goan, Phys. Rev. A 93, 032113 (2016)
I. de Vega, D. Alonso, Rev. Mod. Phys. 89, 015001 (2017)
J.C. Halimeh, I. de Vega, Phys. Rev. A 95, 052108 (2017)
S. Kitajima, M. Ban, F. Shibata, J. Phys. A: Math. Theor. 50, 125303 (2017)
M. Buser, J. Cerrillo, G. Schaller, J. Cao, Phys. Rev. A 96, 062122 (2017)
F.M. Cucchietti, J.P. Paz, W.H. Zurek, Phys. Rev. A 72, 052113 (2005)
T. Yu, J.H. Eberly, Phys. Rev. Lett. 93, 140404 (2004)
J. Eberly, T. Yu, Science 316, 555 (2007)
T. Yu, J.H. Eberly, Science 323, 598 (2009)
C. López, G. Romero, F. Lastra, E. Solano, J. Retamal, Phys. Rev. Lett. 101, 080503 (2008)
E. Pollak, J. Shao, D.H. Zhang, Phys. Rev. E 77, 021107 (2008)
N.J. Cerf, C. Adami, Phys. Rev. Lett. 79, 5194 (1997)
W.K. Wootters, Phys. Rev. Lett. 80, 2245 (1998)
Author information
Authors and Affiliations
Corresponding author
Additional information
Contribution to the Topical Issue “Quantum Correlations”, edited by Marco Genovese, Vahid Karimipour, Sergei Kulik, and Olivier Pfister.
Rights and permissions
About this article
Cite this article
Majeed, M., Chaudhry, A.Z. Effect of initial system–environment correlations with spin environments. Eur. Phys. J. D 73, 16 (2019). https://doi.org/10.1140/epjd/e2018-90416-0
Received:
Revised:
Published:
DOI: https://doi.org/10.1140/epjd/e2018-90416-0