Scientific Research

An Academic Publisher

Effect of the Variable B-Field on the Dynamic of a Central Electron Spin Coupled to an Anti-Ferromagnetic Qubit Bath

**Author(s)**Leave a comment

De- partment of Physics, Faculty of Sciences and Technics, University of Abomey-Calavi, Cotonou, Benin.

Department of Mechanical Engineering, Laboratory of Integrated Production Technologies, University of Québec, Québec, Canada.

Department of Physics, Laboratory of Mesoscopic and Multilayer Structures, University of Dschang, Dschang, Cameroon.

Department of Physics, Laboratory of Mesoscopic and Multilayer Structures, University of Dschang, Dschang, Cameroon; Department of Thermal Engineering and Energetics, Douala University Institute of Technology, Douala, Cameroun.

Department of Mechanical Engineering, Laboratory of Integrated Production Technologies, University of Québec, Québec, Canada.

Department of Physics, Laboratory of Mesoscopic and Multilayer Structures, University of Dschang, Dschang, Cameroon.

Department of Physics, Laboratory of Mesoscopic and Multilayer Structures, University of Dschang, Dschang, Cameroon; Department of Thermal Engineering and Energetics, Douala University Institute of Technology, Douala, Cameroun.

This present issue is an extension of the work of Y. Xiao-Zhong

*et al*. who investigated the influence of constant external magnetic field on the decoherence of a central electron spin of atom coupled to an anti-ferromagnetic environment. We have shown in this work that the character variability of the field induces oscillations amongst the eigen modes of the environment. This observation is made via the derivation of the transition probability density of state, a manner by which critical parameters (parameters where transition occur) of the system could be obtained as it shows resonance peak. We equally observed that the two different magnons modes resulting from the frequency splitting via the application of the time-varying external B-Field, exhibit each a resonant peak of similar amplitude at different temperature ranges. This additional information shows that the probability for the central spin system to remain in its initially prepared diabatic state is enhanced for some temperature ranges for the corresponding two magnon modes. Hence, these temperature ranges where the probability density is maximum could save as decoherence free environment; an important requirement for the implementation of quantum computation and information processing in solid state circuitry. The theoretical and numerical results presented for the decoherence time and the probability density are that of a decohered central electron spin coupled to an anti-ferromagnetic spin bath. The theory is based on a spin wave approximation and on the density matrix using both transformations of Bloch, Primakov and Bogoliobuv in the adiabatic limit.Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

M. Tchoffo, G. Fouokeng, S. Massou, N. Afuoti, I. Nsangou, L. Fai, A. Tchouadeu and J. Kenné, "Effect of the Variable B-Field on the Dynamic of a Central Electron Spin Coupled to an Anti-Ferromagnetic Qubit Bath,"

*World Journal of Condensed Matter Physics*, Vol. 2 No. 4, 2012, pp. 246-256. doi: 10.4236/wjcmp.2012.24042.

[1] | D. Guilini, E. Joos, C. Kiefer, J. Kupsch, I. O. Stamatescu and H. D. Zeh, “World in Quantum Theory,” Springer-Verlag, Berlin Heidelberg, 1996. |

[2] | R. R. Chance, A. Prock and R. Silbey, “Molecular Fluorescence and Energy Transfer near Metal Interfaces,” Advances in Chemical Physics, Vol. 37, 1978, pp. 1-65. doi:10.1002/9780470142561.ch1 |

[3] | E. M. Purcell, “Spontaneous Emission Probabilities at Radio Frequencies,” Physical Review, Vol. 69, 1946, p. 681. |

[4] | Th. F?rster, “Zwischenmolekulare Energiewanderung und. Fluoreszenz,” Annalen der Physik, Vol. 437, No. 1-2, 1948, pp. 55-75. doi:10.1002/andp.19484370105 |

[5] | G. W. Ford, J. T. Lewis and R. F. O’Connell, “Quantum Measurement and Decoherence,” Physical Review A, Vol. 64, No. 3, 2001, Article ID: 032101. doi:10.1103/PhysRevA.64.032101 |

[6] | A. Venugopalan, “Pointer States via Decoherence in a Quantum Measurement,” Physical Review A, Vol. 61, No. 1, 1999, pp. 012102-012109. doi:10.1103/PhysRevA.61.012102 |

[7] | G. Dominique, D. V. Jan and A. Vinay, “Comment on Quantum Measurement and Decoherence,” Physical Review A, Vol. 70, No. 2, 2004, pp. 1-4. doi:10.1103/PhysRevA.70.026101 |

[8] | V. Ambegaokar, “Negotiating the Tricky Border between Quantum and Classical,” Physics Today, Vol. 46, No. 4, 1993, p. 82. |

[9] | R. ADAMI and C. Negulescu, “A Numerical Study of Quantum Decoherence,” Communications in Computational Physics, Vol. 12, 2012, pp. 85-108. doi:10.4208/cicp.011010.010611a |

[10] | R. Adami and L. Erdos, “Rate of Decoherence for an Electron Weakly Coupled to a Phonon Gas,” Journal of Statistical Physics, Vol. 132, 2008, pp. 301-328. doi:10.1007/s10955-008-9561-8 |

[11] | A. Bertoni, “Simulation of Electron Decoherence Induced by Carrier-Carrier Scattering,” Journal of Computational Electronics, Vol. 2, 2003, pp. 291-295. doi:10.1023/B:JCEL.0000011440.86454.13 |

[12] | L. Novotny and B. Hecht, “Principles of Nano-Optics,” Cambridge University Press, Cambridge, 2006. doi:10.1017/CBO9780511813535 |

[13] | Y. Xiao-Zhong, G. Hsi-Sheng and Z. Ka-Di, “In?uence of an External Magnetic Field on the Decoherence of a Central Spin Coupled to an Antiferromagnetic Environment,” New Journal of Physics, Vol. 9, 2007, p. 219. doi:10.1088/1367-2630/9/7/219 |

[14] | C. L. Garrido Alzar, M. A. G. Martinez and P. Nussenzveig, “Classical Analog of Electromagnetically Induced Transparency,” American Journal of Physics, Vol. 70, No. 1, 2000, p. 37. doi:10.1119/1.1412644 |

[15] | W. Frank and P. von Brentano, “Classical Analogy to Quantum Mechanical Level Repulsion,” American Journal of Physics, Vol. 62, No. 8, 1994, pp. 706-709. doi:10.1119/1.17500 |

[16] | H. J. Maris and Q. Xiong, “Adiabatic and Nondiabatic Processes in Classical and Quantum Mechanics,” American Journal of Physics, Vol. 56, No. 12, 1988, pp. 1114-1117. doi:10.1119/1.15734 |

[17] | B. W. Shore, M. V. Gromovyy, L. P. Yatsenko and V. I. Romanenko, “Simple Mechanical Analogs of Rapid Adiabatic Passage in Atomic Physics,” American Journal of Physics, Vol. 77, No. 12, 2009, pp. 1183-1194. |

[18] | C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres and W. K. Wootters, “Teleporting an Unknown Quantum State via Dual Classical and Einstein-Podolsky-Rosen Channels,” Physical Review Letters, Vol. 70, 1993, pp. 1895-1899. doi:10.1103/PhysRevLett.70.1895 |

[19] | D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter and A. Zeilinger, “Experimental Quantum Teleportation,” Nature, Vol. 390, 1997, pp. 575-579. doi:10.1038/37539 |

[20] | C. H. Bennett, G. Brassard and A. K. Ekert, “Quantum Cryptography,” Scientific American, Vol. 267, No. 4, 1992, pp. 50-57. doi:10.1038/scientificamerican1092-50 |

[21] | C. H. Bennett and S. J. Wiesner, “Communication via One- and Two-Particle Operators on Rosen states,” Physical Review Letters, Vol. 69, 1992, pp. 2881-2884. doi:10.1103/PhysRevLett.69.2881 |

[22] | M. Murao, D. Jonathan, M. B. Plenio and V. Vedral, “Quantum Telecloning and Multiparticle Entanglement,” Physical Review A, Vol. 59, No. 1, 1999, pp. 156-161. doi:10.1103/PhysRevA.59.156 |

[23] | H. Le Gall, “Dynamique de Spin et Interactions Spin-Pho-Ton,” Revue de Physique Appliquée, Vol. 9, No. 5, 1974, pp. 793-818. doi:10.1051/rphysap:0197400905079300 |

[24] | G. Jona-Lasinio, C. Presilla and C. Toninelli, “A Mean Field Model and Comparison with Experiments,” Physical Review Letters, Vol. 88, 2002, Article ID: 123001. doi:10.1103/PhysRevLett.88.123001 |

[25] | R. Silbey and R. A. Harris, “Variational Calculation of the Dynamics of a Two Level System Interacting with a Bath,” Journal of Chemical Physics, Vol. 80, No. 6, 1984, p. 2615. doi:10.1063/1.447055 |

[26] | P. G. de Gennes “Nuclear Magnetic Resonance Modes in Magnetic Material. I. Theory,” Physical Review, Vol. 129, No. 3, 1963, pp. 1105-1115. doi:10.1103/PhysRev.129.1105 |

[27] | U. Upadhyaya and K. Sinha, “Phonon-Magnon Interaction in Magnetic Crystals. II. Antiferromagnetic Systems,” Physical Review, Vol. 130, No. 3, 1963, pp. 939-944. doi:10.1103/PhysRev.130.939 |

[28] | K. Yosida, “Theory of Magnetism,” Springer Series in Solid-State Sciences, Vol. 122, 2010, 320 p. |

[29] | C. Cohen-Tannoudji, J. Dupont-Roc and G. Grynberg, “Atom-Photon Interactions,” Wiley-VCH Verlag, Weinheim, 2004. |

[30] | L. Novotny and Strong Coupling, “Energy Splitting, and Level Crossings: A Classical Perspective,” University of Rochester, Rochester, 2010. |

[31] | S. Yunoki, “Numerical Study of the Spin-Flop Transition in Anisotropic Spin-1/2 Antiferromagnets,” Physical Review B, Vol. 65, No. 9, 2002, Article ID: 092402. doi:10.1103/PhysRevB.65.092402 |

[32] | A. L. Dantas, S. R. Vieira, N. S. Almeida and A. S. Carrico, “Soft Mode of Antiferromagnetic Multilayers near the Surface Spin-Flop Transition,” Physical Review B, Vol. 71, No. 1, 2005, Article ID: 014409. doi:10.1103/PhysRevB.71.014409 |

[33] | D. Joonghoe, C. W. Leung, Z. H. Barber and M. G. Blamire, “Competing Functionality in Multiferroic YMnO3,” Physical Review B, Vol. 71, No. 18, 2005, Article ID: 180402. |

[34] | Y. Xiao-Zhong, G. Hsi-Sheng and Z. Ka-Di, “Dynamics of a Driven Spin Coupled to an Antiferromagnetic Spin Bath,” New Journal of Physics, Vol. 13, 2011, Article ID: 023018. doi:10.1088/1367-2630/13/2/023018 |

[35] | H. Hwang and P. J. Rossky, “An Analysis of Electronic Dephasing in the Spin-Boson Mode,” Journal of Chemical Physics, Vol. 120, No. 24, 2004, Article ID: 11380. doi:10.1063/1.1742979 |

[36] | S. Paganelli, F. De Pasquale and S. M. Giampaolo, “Decoherence Slowing down in a Symmetry-Broken Environment,” Physical Review A, Vol. 66, No. 5, 2002, Article ID: 052317. |

[37] | H. T. Quan, Z. Song, X. F. Liu, P. Zanardi and C. P. Sun, “Decay of Loschmidt Echo Enhanced by Quantum Criticality,” Physical Review Letters, Vol. 96, 2006, Article ID: 140604. doi:10.1103/PhysRevLett.96.140604 |

[38] | F. M. Cucchietti, S. Fernandez-Vidal and J. P. Paz, “Universal decoherence induced by an environmental quantum phase transition”, Physical Review A, Vol. 75, No. 3, 2007, Article ID: 032337. doi:10.1103/PhysRevA.75.032337 |

[39] | P. Zanardi, H. T. Quan, X. G. Wang and C. P. Sun, “Mixed-State Fidelity and Quantum Criticality at Finite Temperature,” Physical Review A, Vol. 75, No. 2007, pp. 1-7. |

Copyright © 2019 by authors and Scientific Research Publishing Inc.

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.