Thermodynamic Properties and Decoherence of a Central Electron Spin of Atom Coupled to an Anti-Ferromagnetic Spin Bath


The decoherence of a central electron spin of an atom coupled to an anti-ferromagnetic spin bath in the presence of a time varying B-Field (VBF) is investigated applying the Holstein-Primak off and Bloch transformations approaches. The Boltzmann entropy and the specific heat capacity at a given temperature are obtained and show the correlation of the coupling of the spin bath and the electron spin of the central atom. At low frequencies the coherence of the coupled system is dominated by the magnetic field intensity. At low VBF intensity, there is decrease in entropy and heat capacity at increase external magnetic field that show the decoherence suppression of the central electron spin atom. The crossing observed in the specific heat capacity corresponds to the critical field point Bc of the system which represents the point of transition from the anti-ferromagnetic system to the ferromagnetic one.

Share and Cite:

M. Tchoffo, G. Fouokeng, L. Fai and M. Ateuafack, "Thermodynamic Properties and Decoherence of a Central Electron Spin of Atom Coupled to an Anti-Ferromagnetic Spin Bath," Journal of Quantum Information Science, Vol. 3 No. 1, 2013, pp. 10-15. doi: 10.4236/jqis.2013.31003.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] R. S. Whitney, “Thermodynamic and Quantum Bounds on Nonlinear dc Thermoelectric Transport,” Physical Review B, Vol. 87, No. 11, 2013, pp. 115404-1-115404-8.
[2] D. Gatteschi and R. Sessoli, “Quantum Tunneling of Magnetization and Related Phenomena in Molecular Materials,” Angewandte Chemie International Edition, Vol. 42, No. 3, 2003, pp. 268-297.
[3] S. A. Kumar, H. Prakash, N. Chandra and R. Prakash, “Teleportation of Superposition of Coherent States Using 4-Partite States and Effect of Decoherence on Fidelity,” Journal of Quantum Information Science, Vol. 2, No. 4, 2012, pp. 123-138. doi:10.4236/jqis.2012.24019
[4] A. A. Oladunjoye, N. I. Akpan, et al., “Thermodynamic Properties of the Harmonic Oscillator and a Four Level System,” Applied Physics Research, Vol. 3, No. 1, 2011, pp. 47-59.
[5] F. Benatti, “Quantum Dynamical Entropies and Gács Algorithmic Entropy,” Entropy, Vol. 14, No. 7, 2012, pp. 1259-1273. doi:10.3390/e14071259
[6] R. Alicki and M. Fannes, “Defining Quantum Dynamical Entropy,” Letters in Mathematical Physics, Vol. 32, No. 1, 1994, pp. 75-82. doi:10.1007/BF00761125
[7] P. Crompton, “The Decoherence of the Electron Spin and Meta-Stability of 13C Nuclear Spins in Diamond,” Entropy, Vol. 13, No. 5, 2011, pp. 949-965. doi:10.3390/e13050949
[8] L. Accardi, M. Ohya and N. Watanabe, “Dynamical Entropy through Quantum Markov Chains,” Open Systems & Information Dynamics, Vol. 4, No. 1, 1997, pp. 71-87. doi:10.1023/A:1009609602126
[9] H. N. Wu, G. Z. Wei, P. Zhang, G. Y. Yi and W. J. Gong, “Thermodynamic Properties of the Mixed Spin-1/2 and Spin-1 Ising Chain with both Longitudinal and Transverse Single-Ion Anisotropies,” Journal of Magnetism and Magnetic Materials, Vol. 322, No. 21, 2010, pp. 3502-3507. doi:10.1016/j.jmmm.2010.06.053
[10] A. W. Rost, S. A. Grigera, J. A. N. Bruin, R. S. Perry, D. Tian, S. Raghu, S. A. Kivelson and A. P. Mackenzie, “Thermodynamics of Phase Formation in the Quantum Critical Metal Sr3Ru2O7,” Proceedings of the National Academy of Sciences of the United States of America, Vol. 108, No. 40, 2011, pp. 16549-16553.
[11] B. Frescha and G. J. Morob, “Emergence of Equilibrium Thermodynamic Properties in Quantum Pure States. II. Analysis of a Spin Model System,” Journal of Chemical Physics, Vol. 133, No. 3, 2010, Article ID: 034510. doi:10.1063/1.3456000
[12] G. Ingold, P. Hanggi and P. Talkner, “Specific Heat Anomalies of Open Quantum Systems,” Physical Review E, Vol. 79, No. 6, 2009, Article ID: 061105. doi:10.1103/PhysRevE.79.061105
[13] L. Childress, M. V. G. Dutt, J. M. Taylor, A. S. Zibrov, F. Jelezko, J. Wrachtrup, P. R. Hemmer and M. D. Lukin, “Coherent Dynamics of Coupled Electron and Nuclear Spin Qubits in Diamond,” Science, Vol. 314, No. 5797, 2006, pp. 281-285. doi:10.1126/science.1131871
[14] S. Takahashi, R. Hanson, J. Van Tol, M. S. Sherwin and D. D. Awschalom, “Quenching Spin Decoherence in Diamond through Spin Bath Polarization,” Physical Review Letters, Vol. 101, No. 4, 2008, Article ID: 047601. doi:10.1103/PhysRevLett.101.047601
[15] M. D. Lukin and A. Imamoglu, “Nonlinear Optics and Quantum Entanglement of Ultraslow Single Photons,” Physical Review Letters, Vol. 84, No. 7, 2000, pp. 1419-1422. doi:10.1103/PhysRevLett.84.1419
[16] D. Press, K. de Greve, P. L. McMahon, T. D. Ladd, B. Friess, C. Schneider, M. Kamp, S. H?fling, A. Forchel and Y. Ya-Mamoto, “Ultrafast Optical Spin Echo in a Single Quantum Dot,” Nature Photonics, Vol. 4, No. 6, 2010, pp. 367-370. doi:10.1038/nphoton.2010.83
[17] T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe and J. L. O’Brien, “Quantum Computers,” Nature, Vol. 464, 2010, pp. 45-53. doi:10.1038/nature08812
[18] J. Du, X. Rong, N. Zhao, Y. Wang, J. Yang and R. B. Liu, “Preserving Electron Spin Coherence in Solids by Optimal Dynamical Decoupling,” Nature, Vol. 461, No. 7268, 2009, pp. 1265-1268. doi:10.1038/nature08470
[19] C. A. Ryan, J. S. Hodges and D. G. Cory, “Robust Decoupling Techniques to Extend Quantum Coherence in Diamond,” Physical Review Letters, Vol. 105, No. 20, 2010, Article ID: 200402. doi:10.1103/PhysRevLett.105.200402
[20] N. Zhao, J. Honert, et al., “Sensing Single Remote Nuclear Spins,” Nature Nanotechnology, Vol. 7, No. 10, 2012, pp. 657-662.
[21] W. Yang and R. B. Liu, “Quantum Many-Body Theory of Qubit Decoherence in a Finite-Size Spin Bath,” Physical Review B, Vol. 78, No. 8, 2008, Article ID: 085315. doi:10.1103/PhysRevB.78.085315
[22] W. Yao, R. B. Liu and L. J. Sham, “Restoring Coherence Lost to a Slow Interacting Mesoscopic Spin Bath,” Physical Review Letters, Vol. 98, No. 5, 2007, Article ID: 077602.
[23] J. M. Taylor, C. M. Marcus and M. D. Lukin, “Long-Lived Memory for Mesoscopic Quantum Bits,” Physical Review Letters, Vol. 90, No. 20, 2003, Article ID: 206803. ddoi:10.1103/PhysRevLett.90.206803
[24] M. Bortz and J. Stolze, “Spin and Entanglement Dynamics in the Central-Spin Model with Homogeneous Couplings,” Journal of Statistical Mechanics: Theory and Experiment, Vol. 2007, 2007, Article ID: P06018. doi:10.1088/1742-5468/2007/06/P06018
[25] J. Lages, V. V. Dobrovitski, M. I. Katsnelson, H. A. De Raedt and B. N. Harmon, “Decoherence by a Chaotic Many-Spin Bath,” Physical Review E, Vol. 72, No. 2, 2005, Article ID: 026225. doi:10.1103/PhysRevE.72.026225
[26] X.-Z. Yuan, H.-S. Goan and K.-D. Zhu, “Influence 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
[27] M. Tchoffo, G. C. Fouokeng, et al., “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
[28] L. Gunther and B. Barbara, “Quantum Tunneling of Magnetization—QTM’94,” Kluwer, Dordrecht, 1995.
[29] K. Saito, S. Miyashita and H. De Raedt, “Effects of the Environment on Nonadiabatic Magnetization Process in Uniaxial Molecular Magnets at Very Low Temperatures,” Physical Review B, Vol. 60, No. 21, 1999, pp. 14553-14556. doi:10.1103/PhysRevB.60.14553
[30] M. I. Katsnelson, V. V. Dobrovitski, H. A. De Raedt and B. N. Harmon, “Destruction of the Kondo Effect by a Local Measurement,” Physical Letters A, Vol. 318, No. 4-5, 2003, pp. 445-451. doi:10.1016/j.physleta.2003.08.046
[31] C. P. Slichter, “Principles of Magnetic Resonance,” 3rd Edition, Springer Verlag, Berlin, Heidelberg, New York, 1992.
[32] L. Viola, E. Knill and S. Lloyd, “Dynamical Decoupling of Open Quantum Systems,” Physical Review Letters, Vol. 82, No. 12, 1999, pp. 2417-2421. doi:10.1103/PhysRevLett.82.2417
[33] V. V. Dobrovitski, H. A. De Raedt, M. Katsnelson and B. N. Harmon, “Numerical Simulations of Decoherence Suppression in Open Quantum Spin Systems,” HAIT Journal of Science and Engineering, Vol. 1, No. 3, 2004, pp. 586- 597.
[34] V. Privman, “Initial Decoherence of Open Quantum Systems,” Journal of Statistical Physics, Vol. 110, No. 3-6, 2003, pp. 957-970.
[35] H. Tal-Ezer and R. Kosloff, “An Accurate and Efficient Scheme for Propagating the Time Dependent Schr?dinger Equation,” Journal of Chemical Physics, Vol. 81, No. 9, 1984, p. 3967. doi:10.1063/1.448136
[36] R. Kosloff, “Propagation Methods for Quantum Molecular Dynamics,” Annual Review of Physical Chemistry, Vol. 45, 1994, pp. 145-178. doi:10.1146/annurev.pc.45.100194.001045
[37] J. Schliemann, A. V. Khaetskii, D. Loss, “Spin Decay and Quantum Parallelism,” Physical Review B, Vol. 66, No. 24, 2003, Article ID: 245303. doi:10.1103/PhysRevB.66.245303

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

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