Entanglement of two qubits interacting with one-mode quantum field

E. K. Bashkirov ; M. S. Mastyugin

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 19 (2015) no. 2, pp. 205-220.

Résumé

In the present paper we investigate the dynamics of the system of two two-level 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.

Détail

Mots-clés : entanglement, thermal noise, dipole-dipole interaction
Keywords: qubit, Peres–Horodecki criterium.

Bibliographie

[1] Bashkirov E. K., Mastyugin M. S., “Entanglement of two qubits interacting with one-mode quantum field”, The 4nd International Conference “Mathematical Physics and its Applications”, Book of Abstracts and Conference Materials, eds. I. V. Volovich; V. P. Radchenko, Samara State Technical Univ., Samara, 2014, 79–80 (In Russian)

[2] Nielsen M. A., Chuang I. L., Quantum Computation and Quantum Information, Cambridge University Press, Cambrige, 2010, xxxii+676 pp. | DOI | MR | Zbl

[3] Schumacker D., Westmoreland M. D., Quantum Processes, Systems, and Information, Cambridge University Press, Cambrige, 2010, xii+469 pp. | DOI | MR

[4] Blatt R., Wineland D., “Entangled states of trapped atomic ions”, Nature, 453:7198 (2008), 1008–1013 | DOI

[5] You J. Q., Nori F., “Atomic physics and quantum optics using superconducting circuits”, Nature, 474:7353 (2011), 589–597, arXiv: [quant-ph] 1202.1923 | DOI

[6] Saffman M., Walker T. G., Mølmer K., “Quantum information with Rydberg atoms”, Rev. Mod. Phys., 82:3 (2010), 2313–2363, arXiv: [quant-ph] 0909.4777 | DOI

[7] Buluta I., Ashhab F., Nori F., “Natural and artificial atoms for quantum computation”, Rep. Prog. Phys., 74:10 (2011), 104401, arXiv: [quant-ph] 1002.1871 | DOI

[8] Gühne O., Tóth G., “Entanglement detection”, Physics Reports, 474:1–6 (2014), 1–75, arXiv: [quant-ph] 0811.2803 | DOI | MR

[9] Plenio M. B., Huelda S. F., Beige A. , Knight P. L., “Cavity-loss-induced generation of entangled atoms”, Phys. Rev. A, 59:3 (1999), 2468–2475 | DOI

[10] Bashkirov E. K., Stupatskaya M. P., “Entanglement of two atoms interacting with a thermal electromagnetic field”, Computer Optics, 35:2 (2011), 243–249 (In Russian)

[11] Bashkirov E. K., Mastyugin M. S., “Entanglement of two superconducting qubits interacting with two-mode thermal field”, Computer Optics, 37:3 (2013), 278–285 (In Russian)

[12] Bashkirov E. K., Mastyugin M. S., “The influence of the dipole-dipole interaction and atomic coherence on the entanglement of two atoms with degenerate two-photon transitions”, Optics and Spectroscopy, 116:4 (2014), 630–634 | DOI | DOI

[13] 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 atom-field entangled states”, Optics Communications, 313 (2014), 170–174 | DOI

[14] Bose S., Fruentes-Guridi I., Knight P. L., Vedral V., “Subsystem purity as an enforcer of entanglement”, Phys. Rev. Lett., 87:5 (2001), 050401 | DOI | MR

[15] Kim M. S., Lee J., Ahn D., Knight P. L., “Entanglement induced by a single-mode heat environment”, Phys. Rev. A, 65:4 (2002), 040101, arXiv: quant-ph/0109052 | DOI

[16] 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., 6:9 (2004), 378–382, arXiv: quant-ph/0308086 | DOI | MR

[17] Bashkirov E. K., “Entanglement in the system of two nonidentical atoms interacting with thermal noise”, Vestnik SamGU. Estestvenno-Nauchnaya Ser., 2006, no. 3/3(43), 21–29 (In Russian)

[18] 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., 4:6 (2002), 425–429 | DOI

[19] Bashkirov E. K., “Entanglement induced by the two-mode thermal noise”, Laser Phys. Lett., 3:3 (2006), 145–150 | DOI

[20] Ghosh B., Majumdar A. S., Nayak N., “Effects of cavity-field statistics on atomic entanglement in the Jaynes–Cummings model”, Int. J. Quantum Inform., 05:01n02 (2007), 169–177, arXiv: quant-ph/0603039 | DOI

[21] Yan X.-Q., “Entanglement sudden death of two atoms successive passing a cavity”, Chaos, Solitons Fractals, 41:4 (2009), 1645–1650 | DOI

[22] Liao Q., Fang G., Ahmad M. A., Liu S., “Sudden birth of entanglement between two atoms successively passing a thermal cavity”, Optics Communications, 284:1 (2011), 301–305 | DOI

[23] 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., 7:12 (2005), S769–S771 | DOI

[24] Bashkirov E. K., Stupatskaya M. P., “Entanglement of Two Dipole-Coupled Atoms”, Fizika volnovykh protsessov i radiotekhnicheskie sistemy, 12:2 (2009), 85–89 (In Russian)

[25] 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, 17:6 (2008), 2137–2142 | DOI

[26] Bashkirov E. K., Stupatskaya M. P., “The entanglement of two dipole-dipole coupled atoms induced by nondegenerate two-mode thermal noise”, Laser Phys., 19:3 (2009), 525–530 | DOI

[27] Marr C., Beige A., Rempe G., “Entangled-state preparation via dissipation-assisted adiabatic passages”, Phys. Rev. A, 68:3 (2003), 033817, arXiv: quant-ph/0305116 | DOI

[28] Mancini S, Bose S., “Engineering an interaction and entanglement between distant atoms”, Phys. Rev. A, 70:2 (2004), 022307, arXiv: quant-ph/0111055 | DOI

[29] Chimczak G., “Efficient generation of distant atom entanglement via cavity decay”, Phys. Rev. A, 71:5 (2005), 052305 | DOI

[30] 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, 89:1 (2014), 012326, arXiv: [quant-ph] 1310.5323 | DOI

[31] 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

[32] Peres A., “Separability Criterion for Density Matrices”, Phys. Rev. Lett., 77:8 (1996), 1413–1415, arXiv: quant-ph/9604005 | DOI | MR | Zbl

[33] Horodecki M., Horodecki P., Horodecki R., “Separability of mixed states: necessary and sufficient conditions”, Phys. Lett. A, 223:1–2 (1996), 1–8, arXiv: quant-ph/9605038 | DOI | MR | Zbl

[34] Hu Y.-H., Fang M.-F., Wu Q., “Atomic coherence control on the entanglement of two atoms in two-photon processes”, Chinese Phys., 16:8 (2007), 2407–2414 | DOI

[35] Hu Y.-H., Fang M.-F., “Coherence-Enhanced Entanglement Induced by a Two-Mode Thermal Field”, Commun. Theor. Phys., 54:3 (2010), 421–426 | DOI | Zbl