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Entanglement Dynamics of Two Atoms in the Squeezed Vacuum and the Coherent Fields

Abstract

We investigate the entanglement dynamics of two atoms in a double damping Jaynes-Cummings model. The two atoms are initially in the Bell states and each is in a squeezed vacuum cavity field or coherent cavity field. Compared with the case in coherent field, the atomic entanglement in the squeezed vacuum field is stronger under the same conditions. The results show that we can adopt appropriate parameters such as mean photon number, detuning, the atomic spontaneous decay and the cavity decay, to realize better control of atomic entanglement in quantum information processing. What’s worth mentioning is that proper choosing of the last two parameters enables us to decrease disentanglement period and postpone the moment when the entanglement disappears. Finally, the atomic entanglement in double damping and non-identical Jaynes-Cummings model is obtained

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Acknowledgements

The work was supported by the National Natural Science Foundation of China (Grant No: 11504218), the Program of State Key Laboratory of Quantum Optics and Quantum Optics Devices (No: KF201704) and the program of graduate innovation in Shanxi province (No: 2019BY108).

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Correspondence to Zhi-jian Li.

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Appendix The Elements of the Reduced Density Matrix \( {\rho}_{AB}^{\psi }(t) \)

Appendix The Elements of the Reduced Density Matrix \( {\rho}_{AB}^{\psi }(t) \)

The reduced density matrix \( {\rho}_{AB}^{\psi }(t) \) in the basis of {∣ee〉, ∣eg〉, ∣ge〉, ∣gg〉} can be written as the form of Eq. (8). And the elements of the matrix are the following:

$$ {\displaystyle \begin{array}{c}\begin{array}{c}a(t)={\cos}^2\alpha \sum \limits_a{c}_a{x}_1(t)\sum \limits_a{c}_a^{\ast }{x}_1^{\ast }(t)\sum \limits_b{c}_b{y}_2(t)\sum \limits_b{c}_b^{\ast }{y}_2^{\ast }(t)\\ {}+{\sin}^2\alpha \sum \limits_a{c}_a{y}_2(t)\sum \limits_a{c}_a^{\ast }{y}_2^{\ast }(t)\sum \limits_b{c}_b{x}_1(t)\sum \limits_b{c}_b^{\ast }{x}_1^{\ast }(t)\kern0.3em ,\end{array}\\ {}\begin{array}{c}b(t)={\cos}^2\alpha \sum \limits_a{c}_a{x}_1(t)\sum \limits_a{c}_a^{\ast }{x}_1^{\ast }(t)\sum \limits_b{c}_b{y}_1(t)\sum \limits_b{c}_b^{\ast }{y}_1^{\ast }(t)\\ {}+{\sin}^2\alpha \sum \limits_a{c}_a{y}_2(t)\sum \limits_a{c}_a^{\ast }{y}_2^{\ast }(t)\sum \limits_b{c}_b{x}_2(t)\sum \limits_b{c}_b^{\ast }{x}_2^{\ast }(t)\kern0.3em ,\end{array}\\ {}\begin{array}{c}c(t)={\cos}^2\alpha \sum \limits_a{c}_a{x}_2(t)\sum \limits_a{c}_a^{\ast }{x}_2^{\ast }(t)\sum \limits_b{c}_b{y}_2(t)\sum \limits_b{c}_b^{\ast }{y}_2^{\ast }(t)\\ {}+{\sin}^2\alpha \sum \limits_a{c}_a{y}_1(t)\sum \limits_a{c}_a^{\ast }{y}_1^{\ast }(t)\sum \limits_b{c}_b{x}_1(t)\sum \limits_b{c}_b^{\ast }{x}_1^{\ast }(t)\kern0.3em ,\end{array}\\ {}\begin{array}{c}d(t)={\cos}^2\alpha \sum \limits_a{c}_a{x}_2(t)\sum \limits_a{c}_a^{\ast }{x}_2^{\ast }(t)\sum \limits_b{c}_b{y}_1(t)\sum \limits_b{c}_b^{\ast }{y}_1^{\ast }(t)\\ {}+{\sin}^2\alpha \sum \limits_a{c}_a{y}_1(t)\sum \limits_a{c}_a^{\ast }{y}_1^{\ast }(t)\sum \limits_b{c}_b{x}_2(t)\sum \limits_b{c}_b^{\ast }{x}_2^{\ast }(t)\kern0.3em ,\end{array}\\ {}\begin{array}{c}z(t)=\cos \alpha \sin \alpha \sum \limits_a{c}_a{x}_1(t)\sum \limits_a{c}_a^{\ast }{y}_1^{\ast }(t)\sum \limits_b{c}_b{y}_1(t)\sum \limits_b{c}_b^{\ast }{x}_1^{\ast }(t)\\ {}+\cos \alpha \sin \alpha \sum \limits_a{c}_a{y}_{2,n+2}(t)\sum \limits_a{c}_a^{\ast }{x}_2^{\ast }(t)\sum \limits_b{c}_b{x}_2(t)\sum \limits_b{c}_b^{\ast }{y}_{2,n+2}^{\ast }(t)\kern0.3em ,\end{array}\\ {}\begin{array}{c}w(t)=\cos \alpha \sin \alpha \sum \limits_a{c}_a{x}_1(t)\sum \limits_a{c}_a^{\ast }{y}_1^{\ast }(t)\sum \limits_b{c}_b{y}_{2,n+2}(t)\sum \limits_b{c}_b^{\ast }{x}_2^{\ast }(t)\\ {}+\cos \alpha \sin \alpha \sum \limits_a{c}_a{y}_{2,n+2}(t)\sum \limits_a{c}_a^{\ast }{x}_2^{\ast }(t)\sum \limits_b{c}_b{x}_1(t)\sum \limits_b{c}_b^{\ast }{y}_1^{\ast }(t)\kern0.3em .\end{array}\end{array}} $$

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Li, Z., Zhang, J., Hu, P. et al. Entanglement Dynamics of Two Atoms in the Squeezed Vacuum and the Coherent Fields. Int J Theor Phys (2020). https://doi.org/10.1007/s10773-019-04359-2

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Keywords

  • Entanglement
  • Concurrence
  • Squeezed vacuum field
  • Detuning
  • Decay

PACS

  • 0365Ud
  • 4250Dv
  • 4250Ct