Entanglement of two three-level atoms in a cavity in the presence of detuning and Dissipation

Document Type : Research

Authors

1 Graduate University of Advanced Technolohy

2 Vali-e-Asr University of Rafsanjan

Abstract
In this paper, the interaction between two Lambda-type three-level atoms and a single-mode field is investigated in the presence of detuning parameters and dissipation. Assuming that the two atoms are initially prepared in their excited states and the field is in a coherent state, the state vector of the total system is obtained analytically under resonance conditions in the absence of dissipation, and numerically under off-resonant conditions in the presence of dissipation. The entanglement between the atoms and the field is quantified using the linear entropy, while the entanglement between the two atoms is evaluated by means of the negativity measure. The numerical results show that the behavior of the entanglement measures strongly depends on the system parameters, and that both the maximum value and the persistence of entanglement can be controlled by adjusting the resonance conditions and the strength of dissipation.

Keywords


[1] C. H. Bennett and D. P. DiVincenzo, "Quantum information and computation," Nature, vol. 404, no. 6775, pp. 247-255, 2000. [DOI:10.1038/35005001] [PMID]
[2] R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, "Quantum entanglement," Reviews of Modern Physics, vol. 81, no. 2, pp. 865-942, 2009. [DOI:10.1103/RevModPhys.81.865]
[3] M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, Cambridge, Cambridge University Press, 2010.
[4] E. T. Jaynes and F. W. Cummings, "Comparison of quantum and semiclassical radiation theories with application to the beam maser," Proceedings of the IEEE, vol. 51, no. 1, pp. 89-109, 1963. [DOI:10.1109/PROC.1963.1664]
[5] F. W. Cummings, "Stimulated emission of radiation in a single mode," Physical Review, vol. 140, no. 4A, pp. A1051-A1056, 1965. [DOI:10.1103/PhysRev.140.A1051]
[6] S. J. Anwar, M. Usman, M. Ramzan, and M. K. Khan, "Decoherence effects on quantum Fisher information for moving two four-level atoms in the presence of Stark effect and Kerr-like medium," European Physical Journal D, vol. 75, no. 9, Art. no. 235, 2021. [DOI:10.1140/epjd/s10053-021-00252-y]
[7] H. R. Baghshahi, M. K. Tavassoly, and M. J. Faghihi, "Entanglement analysis of a two-atom nonlinear Jaynes-Cummings model with nondegenerate two-photon transition, Kerr nonlinearity, and two-mode Stark shift," Laser Physics, vol. 24, no. 12, Art. no. 125203, 2014. [DOI:10.1088/1054-660X/24/12/125203]
[8] M. J. Faghihi and M. K. Tavassoly, "Dynamics of entropy and nonclassical properties of the state of a Λ-type three-level atom interacting with a single-mode cavity field with intensity-dependent coupling in a Kerr medium," Journal of Physics B: Atomic, Molecular and Optical Physics, vol. 45, no. 3, Art. no. 035502, 2012. [DOI:10.1088/0953-4075/45/3/035502]
[9] L. Thabet, T. El-Shahat, A. Abdel-Aty, and B. Rababh, "Dynamics of entanglement and non-classicality features of a single-mode nonlinear Jaynes-Cummings model," Chaos, Solitons and Fractals, vol. 126, pp. 106-115, 2019. [DOI:10.1016/j.chaos.2019.05.038]
[10] A. Garg and N. D. Mermin, "Bell inequalities with a range of violation that does not diminish as the spin becomes arbitrarily large," Physical Review Letters, vol. 49, no. 13, pp. 901-904, 1982. [DOI:10.1103/PhysRevLett.49.901]
[11] M. Fleischhauer, A. Imamoglu, and J. P. Marangos, "Electromagnetically induced transparency: Optics in coherent media," Reviews of Modern Physics, vol. 77, no. 2, pp. 633-673, 2005. [DOI:10.1103/RevModPhys.77.633]
[12] M. O. Scully and M. S. Zubairy, Quantum Optics, Cambridge, Cambridge University Press, 1997. [DOI:10.1017/CBO9780511813993]
[13] D. D. Awschalom, R. Hanson, J. Wrachtrup, and B. B. Zhou, "Quantum technologies with optically interfaced solid-state spins," Nature Photonics, vol. 12, no. 9, pp. 516-527, 2018. [DOI:10.1038/s41566-018-0232-2]
[14] X. Zhang, C.-L. Zou, L. Jiang, and H. X. Tang, "Cavity magnomechanics," Science Advances, vol. 2, no. 3, Art. no. e1501286, 2016. [DOI:10.1126/sciadv.1501286] [PMID]
[15] C. C. Gerry and P. L. Knight, Introductory Quantum Optics, Cambridge, Cambridge University Press, 2005. [DOI:10.1017/CBO9780511791239]
[16] T. Yu and J. H. Eberly, "Finite-time disentanglement via spontaneous emission," Physical Review Letters, vol. 93, no. 14, p. 140404, 2004. [DOI:10.1103/PhysRevLett.93.140404] [PMID]
[17] M. P. Almeida et al., "Environment-induced sudden death of entanglement," Science, vol. 316, no. 5824, pp. 579-582, 2007. [DOI:10.1126/science.1139892] [PMID]
[18] T. Yu and J. H. Eberly, "Sudden death of entanglement," Science, vol. 323, no. 5914, pp. 598-601, 2009. [DOI:10.1126/science.1167343] [PMID]
[19] H.-P. Breuer and F. Petruccione, The Theory of Open Quantum Systems, Oxford, Oxford University Press, 2002.
[20] Y. Tabuchi et al., "Coherent coupling between a ferromagnetic magnon and a superconducting qubit," Science, vol. 349, no. 6246, pp. 405-408, 2015. [DOI:10.1126/science.aaa3693] [PMID]
[21] H. R. Baghshahi and M. J. Faghihi, "f-deformed cavity mode coupled to a Λ-type atom in the presence of dissipation and Kerr nonlinearity," Journal of the Optical Society of America B, vol. 39, no. 11, pp. 2925-2933, 2022. [DOI:10.1364/JOSAB.467962]
[22] H. R. Baghshahi, M. K. Tavassoly, and A. Behjat, "Entanglement of a damped non-degenerate diamond-type atom interacting nonlinearly with a single-mode cavity," European Physical Journal Plus, vol. 131, no. 4, Art. no. 80, 2016. [DOI:10.1140/epjp/i2016-16080-0]
[23] J. Gea-Banacloche, Y.-Q. Li, S.-Z. Jin, and M. Xiao, "Electromagnetically induced transparency in ladder-type inhomogeneously broadened media: Theory and experiment," Physical Review A, vol. 51, no. 1, pp. 576-584, 1995. [DOI:10.1103/PhysRevA.51.576] [PMID]
[24] G. S. Agarwal, Quantum Optics, Cambridge, Cambridge University Press, 2012.
[25] S. M. Barnett and J. Jeffers, "The damped Jaynes-Cummings model," Journal of Modern Optics, vol. 54, no. 13-15, pp. 2033-2048, 2007. [DOI:10.1080/09500340701352813]
[26] W. Vogel and D. G. Welsch, Quantum Optics, 3rd ed. Hoboken, NJ, John Wiley & Sons, 2006. [DOI:10.1002/3527608524]
[27] A. B. A. Mohamed, "Bipartite non-classical correlations for a lossy two connected qubit-cavity systems: Trace distance discord and Bell's non-locality," Quantum Information Processing, vol. 17, pp. 1-18, 2018. [DOI:10.1007/s11128-018-1865-2]
[28] M. M. Alqahtani, "Multiphoton process in cavity QED photons for implementing a three-qubit quantum gate operation," Quantum Information Processing, vol. 19, pp. 1-15, 2020. [DOI:10.1007/s11128-019-2498-9]
[29] C. Di Fidio, W. Vogel, M. Khanbekyan, and D. G. Welsch, "Photon emission by an atom in a lossy cavity," Physical Review A, vol. 77, no. 4, p. 043822, 2008. [DOI:10.1103/PhysRevA.77.043822]
[30] H. Xie, C.-G. Liao, X. Shang, M.-Y. Ye, and X.-M. Lin, "Phonon blockade in a quadratically coupled optomechanical system," Physical Review A, vol. 96, no. 1, p. 013861, 2017. [DOI:10.1103/PhysRevA.96.013861]
[31] J.-S. Zhang, M.-C. Li, and A.-X. Chen, "Enhancing quadratic optomechanical coupling via a nonlinear medium and lasers," Physical Review A, vol. 99, no. 1, p. 013843, 2019. [DOI:10.1103/PhysRevA.99.013843]
[32] D.-Y. Wang, C.-H. Bai, S. Liu, S. Zhang, and H.-F. Wang, "Photon blockade in a double-cavity optomechanical system with nonreciprocal coupling," New Journal of Physics, vol. 22, p. 093006, 2020. [DOI:10.1088/1367-2630/abaa8a]
[33] R. M. Angelo, K. Furuya, M. C. Nemes, and G. Q. Pellegrino, "Recoherence in the entanglement dynamics and classical orbits in the N-atom Jaynes-Cummings model," Physical Review A, vol. 64, no. 4, p. 043801, 2001. [DOI:10.1103/PhysRevA.64.043801]
[34] N. A. Peters, T. C. Wei, and P. G. Kwiat, "Mixed-state sensitivity of several quantum-information benchmarks," Physical Review A, vol. 70, no. 5, p. 052309, 2004. [DOI:10.1103/PhysRevA.70.052309]
[35] S. Lee, D. P. Chi, S. D. Oh, and J. Kim, "Convex-roof extended negativity as an entanglement measure for bipartite quantum systems," Physical Review A, vol. 68, p. 062304, 2003. [DOI:10.1103/PhysRevA.68.062304]
[36] S. J. Akhtarshenas and M. Farsi, "Negativity as entanglement degree of the Jaynes-Cummings model," Physica Scripta, vol. 75, pp. 608-611, 2007. [DOI:10.1088/0031-8949/75/5/003]