Abstract
Within the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of the continuous variable entanglement for a system consisting of two uncoupled modes interacting with a thermal environment. Using the Peres–Simon necessary and sufficient criterion for separability of two-mode Gaussian states, we describe the generation and evolution of entanglement in terms of the covariance matrix for a Gaussian input state. For some values of the temperature of environment, the state keeps for all times its initial type — separable or entangled. In other cases, entanglement generation, entanglement sudden death, or a periodic collapse and revival of entanglement take place. We analyze also the time evolution of the logarithmic negativity, which characterizes the degree of entanglement of the quantum state.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
S. L. Braunstein and P. van Loock, Rev. Mod. Phys., 77, 513 (2005).
R. Simon, Phys. Rev. Lett., 84, 2726 (2000).
L. M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, Phys. Rev. Lett., 84, 2722 (2000).
G. Vidal and R. F. Werner, Phys. Rev. A, 65, 032314 (2002).
G. Giedke, M. M. Wolf, O. Kruger, et al., Phys. Rev. Lett., 91, 107901 (2003).
S. Olivares, M. G. A. Paris, and A. R. Rossi, Phys. Lett. A, 319, 32 (2003).
J. S. Prauzner-Bechcicki, J. Phys. A: Math. Gen., 37, L173 (2004).
G. Adesso, A. Serafini, and F. Illuminati, Phys. Rev. A, 73, 032345 (2006).
F. Benatti and R. Floreanini, J. Phys. A: Math. Gen., 39, 2689 (2006).
A. V. Dodonov, V. V. Dodonov, and S. S. Mizrahi, J. Phys. A: Math. Gen., 38, 683 (2005).
S. Maniscalco, S. Olivares, and M. G. A. Paris, Phys. Rev. A, 75, 062119 (2007).
A. Isar and W. Scheid, Physica A, 373, 298 (2007).
A. Isar, Eur. J. Phys. Special Topics, 160, 225 (2008).
V. V. Dodonov, O. V. Man’ko, and V. I. Man’ko, J. Russ. Laser Res., 16, 1 (1995).
F. Benatti and R. Floreanini, Int. J. Mod. Phys. B, 19, 3063 (2005).
A. Peres, Phys. Rev. Lett., 77, 1413 (1996).
G. Lindblad, Commun. Math. Phys., 48, 119 (1976).
A. Isar, A. Sandulescu, H. Scutaru, et al., Int. J. Mod. Phys. E, 3, 635 (1994).
A. Sandulescu, H. Scutaru, and W. Scheid, J. Phys. A: Math. Gen., 20, 2121 (1987).
A. Isar, J. Russ. Laser Res., 28, 439 (2007).
O. V. Man’ko, V. I. Man’ko, G. Marmo, et al., Phys. Lett. A, 339, 194 (2005).
A. Isar, Phys. Scr., Topical Issue, 135, 014033 (2009).
A. Isar, Open Sys. Inform. Dynam., 16, 205 (2009).
A. Isar, Int. J. Quant. Inform., 6, 689 (2008).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Isar, A. Entanglement dynamics of two-mode Gaussian states in a thermal environment. J Russ Laser Res 30, 458–465 (2009). https://doi.org/10.1007/s10946-009-9097-7
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10946-009-9097-7