Abstract
We numerically simulate quantum coherence in a system of two qubits interacting with a reservoir for non-Markovian channels. The explicit form of the master equation is taken in terms of density-operator elements and is solved according to the initial conditions. In particular, we consider the effect of an Ohmic reservoir (OR) with Lorentz–Drude regularization (LDR) on the extent of coherence during dynamics. We describe the dynamical behavior of the coherence for low, intermediate, and high-temperature reservoirs. We explain the effect of the ratio of the cutoff frequency (CF) to the quantum system frequency and the effect of temperature on the quantum coherence. We show that a decreasing ratio enhances coherence, while an increasing temperature decreases it.
Similar content being viewed by others
References
W. H. Zurek, Rev. Mod. Phys., 75, 715 (2003).
W.-L. You, Y. Wang, T.-C. Yi, et al., Phys. Rev. B, 97, 224420 (2018).
A. Streltsov, G. Adesso, and M. B. Plenio, Rev. Mod. Phys., 89, 041003 (2017).
H. Ollivier and W. H. Zurek, Phys. Rev. Lett., 88, 017901 (2001).
M. N. Bera, A. Acin, M. Kus, et al., Rep. Prog. Phys., 80, 124001 (2017).
L. K. Castelano, F. F. Fanchini, and K. Berrada, Phys. Rev. B, 94, 235433 (2016).
R. Dermez and S. Abdel-Khalek, J. Russ. Laser Res., 32, 287 (2011).
A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev., 47, 777 (1935).
E. Schrödinger, Proc. Cambridge Philos. Soc., 31, 555 (1935).
J. S. Bell, Physics (Long Island City, N.Y.), 1, 195 (1964).
V. Giovannetti, S. Lloyd, and L. Maccone, Science, 306, 1330 (2004).
K. Berrada, Phys. Rev. A, 88, 013817 (2013).
K. Berrada, J. Opt. Soc. Am. B, 34, 1912 (2017).
K. Berrada, S. Abdel-Khalek, and C. H. R. Ooi, Phys. Rev. A, 86, 033823 (2012).
M. Algarni, K. Berrada, S. Abdel-Khalek, and H. Eleuch, Symmetry, 13, 2327 (2021).
M. Lostaglio, D. Jennings, and T. Rudolph, Nat. Commun., 6, 6383 (2015).
O. Karlström, H. Linke, G. Karlström, and A. Wacker, Phys. Rev. B, 84, 113415 (2011).
M. B. Plenio and S. F. Huelga, New J. Phys., 10, 113019 (2008).
S. Lloyd, J. Phys. Conf. Ser., 302, 012037 (2011).
C.-M. Li, N. Lambert, Y.-N. Chen, et al., Sci. Rep., 2, 885 (2012).
T. Baumgratz, M. Cramer, and M. B. Plenio, Phys. Rev. Lett., 113, 140401 (2014).
A. Streltsov, U. Singh, H. S. Dhar, et al., Phys. Rev. Lett., 115, 020403 (2015).
X. Yuan, H. Zhou, Z. Cao, and X. Ma, Phys. Rev. A, 92, 022124 (2015).
A. Winter and D. Yang, Phys. Rev. Lett., 116, 120404 (2016).
M. O. Scully and M. Suhail Zubairy, Quantum Optics, Cambridge Uni. Press, New York (1997).
M. Tsang, Phys. Rev. A, 88, 021801(R) (2013).
T. Yu and J. H. Eberly, Phys. Rev. Lett., 97, 140403 (2006).
M. D. Shulman, O. E. Dial, S. P. Harvey, et al., Science, 336, 202 (2012).
M. J. A. Schuetz, E. M. Kessler, L. M. K. Vandersypen, et al., Phys. Rev. B, 89, 195310 (2014).
A. Borras and M. Blaauboer, Phy. Rev. B, 84, 033301 (2011).
T. Hiltunen and A. Harju, Phys. Rev. B, 89, 115322 (2014).
D. Culcer, L. Cywiński, Q. Li, et al., Phys. Rev. B, 80, 205302 (2009).
D. M. Kennes, V. Meden, and R. Vasseur, Phys. Rev. B, 90, 115101 (2014).
R. Vasseur, K. Trinh, S. Haas, and H. Saleur, Phys. Rev. Lett., 110, 240601 (2013).
S. R. White, Phys. Rev. Lett., 69, 2863 (1992).
G. Vidal, Phys. Rev. Lett., 93, 040502 (2004).
U. Schollwock, Ann. Phys., 326, 96 (2011).
D. Porras and J. I. Cirac, Phys. Rev. Lett., 92, 207901 (2004).
D. Leibfried, B. DeMarco, V. Meyer, et al., Nature (London), 422, 412 (2003).
F. Schmidt-Kaler, H. Häffner, M. Riebe, et al., Nature (London), 422, 408 (2003).
Y.-N. Guo, Q.-L. Tian, K. Zeng, and Z.-D. Li, Quantum Inf. Process., 16, 310 (2017).
M.-L. Hu and H. Fan, Sci. China-Phys. Mech. Astron., 63, 230322 (2020).
W. Cui, Z. R. Xi, and Y. Pan, Phys. Rev. A, 77, 032117 (2008).
S. Maniscalco, S. Olivares, and M. G. A. Paris, Phys Rev. A, 75, 062119 (2007).
S. Maniscalco, J. Piilo, F. Intravaia, et al., Phys. Rev. A, 70, 032113 (2004).
J. Zhang, R. B. Wu, C. W. Li, et al., Phys. Rev. A, 75, 022324 (2007).
U. Weiss, Quantum Dissipative System, World Scientific Publishing, Singapore (1993).
A. J. Leggett, S. Chakravarty, A. T. Dorsey, et al., Rev. Mod. Phys., 59, 1 (1987).
W. Cui, Z. Xi, and Y. Pan, J. Phys. A: Math. Theor., 42, 155303 (2009).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Algarni, M., Berrada, K. & Abdel-Khalek, S. Quantum Coherence in Non-Markovian Quantum Channels. J Russ Laser Res 43, 397–405 (2022). https://doi.org/10.1007/s10946-022-10064-z
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10946-022-10064-z