Email this article Entanglement of two qubits interacting with one-mode quantum field
- Authors: Bashkirov E.K1, Mastyugin M.S1
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Affiliations:
- Samara State University
- Issue: Vol 19, No 2 (2015)
- Pages: 205-220
- Section: Articles
- URL: https://bakhtiniada.ru/1991-8615/article/view/20442
- DOI: https://doi.org/10.14498/vsgtu1377
- ID: 20442
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Abstract
In the present paper we investigate the dynamics of the system of two twolevel natural or artificial atoms, in which only one atom couples to a thermal one-mode field in finite-Q cavity, since one of them can move around the cavity. For the description of the dynamics of the system we find the eigenvalues and eigenfunctions of a Hamiltonian of the system. With their help we derive the exact expression for a density matrix of the system in case of a pure initial state of atoms and a thermal state of a field. The reduced atomic density matrix is found. The one-qubit transposing of an atomic density matrix is carried out. With its help the Peres-Horodecki criterium is calculated. Numerical calculations of entanglement parameter is done for different initial pure states of atoms and mean photon numbers in a thermal mode. It is found that the thermal field can induce a high degree of qubits entanglement in considered model. Thus we have derived that one can use the strength of dipole-dipole interaction and cavity temperature for entanglement control in the considered system. It is shown also that the maximum degree of entanglement is reached for one-atom excited state.
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##article.viewOnOriginalSite##About the authors
Eugene K Bashkirov
Samara State University
Email: bash@samsu.ru
(Dr. Phys. & Math. Sci.; bash@samsu.ru; Corresponding Author), Professor, Dept. of General and Theoretical Physics 1, Academician Pavlov st., Samara, 443011, Russian Federation
Michail S Mastyugin
Samara State University
Email: mastyugin.mikhail@mail.ru
Postgraduate Student, Dept. of General and Theoretical Physics 1, Academician Pavlov st., Samara, 443011, Russian Federation
References
- Башкиров Е. К., Мастюгин М. С. Перепутывание двух кубитов, взаимодействующих с одномодовым квантованным полем / Четвертая международная конференция «Математическая физика и ее приложения»: материалы конф.; ред. чл.-корр. РАН И. В. Волович; д.ф.-м.н., проф. В. П. Радченко. Самара: СамГТУ, 2014. С. 79-80.
- Nielsen M. A., Chuang I. L. Quantum Computation and Quantum Information. Cambrige: Cambridge University Press, 2010. xxxii+676 pp.. doi: 10.1017/cbo9780511976667
- Schumacker D., Westmoreland M. D. Quantum Processes, Systems, and Information. Cambrige: Cambridge University Press, 2010. xii+469 pp.. doi: 10.1017/cbo9780511814006.
- Blatt R., Wineland D. Entangled states of trapped atomic ions // Nature, 2008. vol. 453, no. 7198. pp. 1008-1013. doi: 10.1038/nature07125.
- You J. Q., Nori F. Atomic physics and quantum optics using superconducting circuits //Nature, 2011. vol. 474, no. 7353. pp. 589-597, arXiv: 1202.1923 [quant-ph]. doi: 10.1038/nature10122.
- Saffman M., Walker T. G., Mølmer K. Quantum information with Rydberg atoms // Rev. Mod. Phys., 2010. vol. 82, no. 3. pp. 2313-2363, arXiv: 0909.4777 [quant-ph]. doi: 10.1103/revmodphys.82.2313.
- Buluta I., Ashhab F., Nori F. Natural and artificial atoms for quantum computation // Rep. Prog. Phys., 2011. vol. 74, no. 10, 104401, arXiv: 1002.1871 [quant-ph]. doi: 10.1088/0034-4885/74/10/104401.
- Gühne O., Tóth G. Entanglement detection // Physics Reports, 2014. vol. 474, no. 1-6. pp. 1-75, arXiv: 0811.2803 [quant-ph]. doi: 10.1016/j.physrep.2009.02.004.
- Plenio M. B., Huelda S. F., Beige A. , Knight P. L. Cavity-loss-induced generation of entangled atoms // Phys. Rev. A, 1999. vol. 59, no. 3. pp. 2468-2475. doi: 10.1103/physreva.59.2468.
- Башкиров Е. К., Ступацкая М. П. Перепутывание двух атомов, взаимодействующих с тепловым электромагнитным полем // Компьютерная оптика, 2011. Т. 35, № 2. С. 243-249.
- Башкиров Е. К., Мастюгин М. С. Перепутывание двух сверхпроводящих кубитов, взаимодействующих с двухмодовым тепловым полем // Компьютерная оптика, 2013. Т. 37, № 3. С. 278-285.
- Башкиров Е. К., Мастюгин М. С. Влияние диполь-дипольного взаимодействия и атомной когерентности на перепутывание двух атомов с вырожденными двухфотонными переходами // Оптика и спектроскопия, 2014. Т. 116, № 4. С. 678-683. doi: 10.7868/S0030403414040060.
- Bashkirov E. K., Mastyugin M. S. The dynamics of entanglement in two-atom Tavis-Cummings model with non-degenerate two-photon transitions for four-qubits initial atomfield entangled states // Optics Communications, 2014. vol. 313. pp. 170-174. doi: 10.1016/j.optcom.2013.10.007.
- Bose S., Fruentes-Guridi I., Knight P. L., Vedral V. Subsystem purity as an enforcer of entanglement // Phys. Rev. Lett., 2001. vol. 87, no. 5, 050401. doi: 10.1103/physrevlett.87.050401.
- Kim M. S., Lee J., Ahn D., Knight P. L. Entanglement induced by a single-mode heat environment // Phys. Rev. A, 2002. vol. 65, no. 4, 040101, arXiv: quant-ph/0109052. doi: 10.1103/physreva.65.040101.
- Zhou L., Yi X. X., Song H.-S., Quo Y.-Q. Entanglement of two atoms through different couplings and thermal noise // J. Opt. B: Quantum Semiclass. Opt., 2004. vol. 6, no. 9. pp. 378-382, arXiv: quant-ph/0308086. doi: 10.1088/1464-4266/6/9/003.
- Башкиров Е. К. Перепутанные состояния в системе двух неидентичных атомов, взаимодействующих с тепловым полем // Вестн. СамГУ. Естественнонаучн. сер., 2006. № 3(43). С. 21-29.
- Zhou L., Song H.-S., Li C. Entanglement induced by a single-mode thermal field and criteria for entanglement // J. Opt. B: Quantum Semiclass. Opt., 2002. vol. 4, no. 6. pp. 425-429. doi: 10.1088/1464-4266/4/6/310.
- Bashkirov E. K. Entanglement induced by the two-mode thermal noise // Laser Phys. Lett., 2006. vol. 3, no. 3. pp. 145-150. doi: 10.1002/lapl.200510081.
- Ghosh B., Majumdar A. S., Nayak N. Effects of cavity-field statistics on atomic entanglement in the Jaynes-Cummings model // Int. J. Quantum Inform., 2007. vol. 05, no. 01n02. pp. 169-177, arXiv: quant-ph/0603039. doi: 10.1142/s0219749907002840.
- Yan X.-Q. Entanglement sudden death of two atoms successive passing a cavity // Chaos, Solitons & Fractals, 2009. vol. 41, no. 4. pp. 1645-1650. doi: 10.1016/j.chaos.2008.07.007.
- Liao Q., Fang G., Ahmad M. A., Liu S. Sudden birth of entanglement between two atoms successively passing a thermal cavity // Optics Communications, 2011. vol. 284, no. 1. pp. 301-305. doi: 10.1016/j.optcom.2010.09.043.
- Aguiar L. S., Munhoa P. P., Vidiella-Barranco A., Roversi J. A. The entanglement of two dipole-dipole coupled atoms in a cavity interacting with a thermal field // J. Opt. B: Quantum Semiclass. Opt., 2005. vol. 7, no. 12. pp. S769-S771. doi: 10.1088/1464-4266/7/12/049.
- Башкиров Е. К., Ступацкая М. П. Перепутывание двух дипольно связанных атомов // Физика волновых процессов и радиотехнические системы, 2009. Т. 12, № 2. С. 85-89.
- Liao Xiang-Ping, Fang Mao-Fa, Cai Jian-Wu, Zheng Xiao-Juan The entanglement of two dipole-dipole coupled atoms interacting with a thermal field via a two-photon process // Chinese Phys. B, 2008. vol. 17, no. 6. pp. 2137-2142. doi: 10.1088/1674-1056/17/6/032.
- Bashkirov E. K., Stupatskaya M. P. The entanglement of two dipole-dipole coupled atoms induced by nondegenerate two-mode thermal noise // Laser Phys., 2009. vol. 19, no. 3. pp. 525-530. doi: 10.1134/s1054660x09030281.
- Marr C., Beige A., Rempe G. Entangled-state preparation via dissipation-assisted adiabatic passages // Phys. Rev. A, 2003. vol. 68, no. 3, 033817, arXiv: quant-ph/0305116. doi: 10.1103/physreva.68.033817.
- Mancini S, Bose S. Engineering an interaction and entanglement between distant atoms // Phys. Rev. A, 2004. vol. 70, no. 2, 022307, arXiv: quant-ph/0111055. doi: 10.1103/physreva.70.022307.
- Chimczak G. Effcient generation of distant atom entanglement via cavity decay // Phys. Rev. A, 2005. vol. 71, no. 5, 052305. doi: 10.1103/physreva.71.052305.
- Lu M., Xia Y., Shen L.-T., Song J., An N. B. Shortcuts to adiabatic passage for population transfer and maximum entanglement creation between two atoms in a cavity // Phys. Rev. A, 2014. vol. 89, no. 1, 012326, arXiv: 1310.5323 [quant-ph]. doi: 10.1103/physreva.89.012326.
- Guo Y.-Q., Cao H.-J., Song H.-S. Field tuned atom-atom entanglement via dipole-dipole interaction, 2005. 7 pp., arXiv: quant-ph/0509142
- Peres A. Separability Criterion for Density Matrices // Phys. Rev. Lett., 1996. vol. 77, no. 8. pp. 1413-1415, arXiv: quant-ph/9604005. doi: 10.1103/physrevlett.77.1413.
- Horodecki M., Horodecki P., Horodecki R. Separability of mixed states: necessary and suffcient conditions // Phys. Lett. A, 1996. vol. 223, no. 1-2. pp. 1-8, arXiv: quantph/9605038. doi: 10.1016/s0375-9601(96)00706-2.
- Hu Y.-H., Fang M.-F., Wu Q. Atomic coherence control on the entanglement of two atoms in two-photon processes // Chinese Phys., 2007. vol. 16, no. 8. pp. 2407-2414. doi: 10.1088/1009-1963/16/8/042.
- Hu Y.-H., Fang M.-F. Coherence-Enhanced Entanglement Induced by a Two-Mode Thermal Field // Commun. Theor. Phys., 2010. vol. 54, no. 3. pp. 421-426. doi: 10.1088/0253-6102/54/3/08.
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