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Linear Entropy of a Driven Central Spin Interacting with an Antiferromagnetic Environment

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DOI: 10.4236/ns.2014.67052    2,522 Downloads   3,261 Views   Citations

ABSTRACT

We exploit a scheme to obtain a long-lived entanglement using a driven central spin interacting with an antiferromagnetic spin bath. Our numerical results show the effects of different parameters on the population inversion and the entanglement dynamics in terms of the linear entropy. It is shown that the long-lived entanglement is an intriguing result corresponding to the collapse region of the atomic inversion. As illustration, we examine the long-time interaction of the entanglement under the resonance and off-resonance regimes.


Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Abdel-Aty, M. (2014) Linear Entropy of a Driven Central Spin Interacting with an Antiferromagnetic Environment. Natural Science, 6, 532-539. doi: 10.4236/ns.2014.67052.

References

[1] Clark, C.R., Chou, C., Ellis, A.R., Hunker, J., Kemme, S.A., Maunz, P., Tabakov, B., Tigges, C. and Stick, D.L. (2013) Characterization of Fluorescence Collection Optics Integrated with a Micro-Fabricated Surface Electrode Ion Trap.
arXiv:1305.4706
[2] Buchleitner, A., Viviescas, C. and Tiersch, M. (2009) Entanglement and Decoherence. Foundations and Modern Trends, Lecture Notes in Physics. Springer, Berlin.
http://dx.doi.org/10.1007/978-3-540-88169-8
[3] Tanaka, A., Totsuka, K. and Hu, X. (2009) Geometric Phases and the Magnetization Process in Quantum Antiferromagnets. Physical Review B, 79, Article ID: 064412.
http://dx.doi.org/10.1103/PhysRevB.79.064412
[4] Welp, U., Berger, A., Miller, D.J., Vlasko-Vlasov, V.K., Gray, K.E. and Mitchell, J.F. (1999) Direct Imaging of the First-Order Spin-Flop Transition in the Layered Manganite La1.4Sr1.6Mn2O7. Physical Review Letters, 83, 4180.
http://dx.doi.org/10.1103/PhysRevLett.83.4180
[5] Ladd, T.D., Press, D., De Greve, K., McMahon, P.L., Friess, B., Schneider, C., Kamp, M., Hofling, S., Forchel, A. and Yamamoto, Y. (2010) Pulsed Nuclear Pumping and Spin Diffusion in a Single Charged Quantum Dot. Physical Review Letters, 105, Article ID: 107401.
http://dx.doi.org/10.1103/PhysRevLett.105.107401
[6] Tsyplyatyev, O. and Loss, D. (2011) Spectrum of an Electron Spin Coupled to an Unpolarized Bath of Nuclear Spins. Physical Review Letters, 106, Article ID: 106803.
http://dx.doi.org/10.1103/PhysRevLett.106.106803
[7] Takahashi, S., Hanson, R., van Tol, J., Sherwin, M.S. and Awschalom, D.D. (2008) Quenching Spin Decoherence in Diamond through Spin Bath Polarization. Physical Review Letters, 101, Article ID: 047601.
http://dx.doi.org/10.1103/PhysRevLett.101.047601
[8] Takahashi, S., Tupitsyn, I.S., van Tol, J., Beedle, C.C., Hendrickson, D.N. and Stamp, P.C.E. (2011) Decoherence in Crystals of Quantum Molecular Magnets. Nature, 476, 76-79.
http://dx.doi.org/10.1038/nature10314
[9] Hanson, R., Dobrovitski, V.V., Feiguin, A.E., Gywat, O. and Awschalom, D.D. (2008) Quantum Control over Single Spins in Diamond. Science, 320, 352-355.
http://dx.doi.org/10.1126/science.1155400
[10] Zhang, J.-S. and Chen, A.-X. (2012) Review on Quantum Discord of Bipartite and Multipartite Systems. Quantum Physics Letters, 1, 69-77.
[11] Bergli, J., Galperin, Y.M. and Altshuler, B.L. (2009) Decoherence in Qubits Due to Low-Frequency Noise. New Journal of Physics, 11, Article ID: 025002.
http://dx.doi.org/10.1088/1367-2630/11/2/025002
[12] Brox, H., Bergli, J. and Galperin, Y.M. (2012) The Importance of Level Statistics for the Decoherence of a Central Spin Due to a Spin Environment. Physical Review A, 85, Article ID: 052117.
http://dx.doi.org/10.1103/PhysRevA.85.052117
[13] Yuan, X.-Z., Goan, H.-S. and Zhu, K.-D. (2010) Geometric Phase of a Central Spin Coupled to an Antiferromagnetic Environment. Physical Review A, 81, Article ID: 034102.
http://dx.doi.org/10.1103/PhysRevA.81.034102
[14] Yuan, X.-Z., Goan, H.-S. and Zhu, K.-D. (2011) Dynamics of a Driven Spin Coupled to an Antiferromagnetic Spin Bath. New Journal of Physics, 13, Article ID: 023018.
http://dx.doi.org/10.1088/1367-2630/13/2/023018
[15] Leggett, A.J., Chakravarty, S., Dorsey, A.T., Fisher, M.P.A., Garg, A. and Zwerger, W. (1987) Dynamics of the Dissipative Two-Level System. Reviews of Modern Physics, 59, 1.
http://dx.doi.org/10.1103/RevModPhys.59.1
[16] Irish, E.K., Gea-Banacloche, J., Martin, I. and Schwab, K.C. (2005) Dynamics of a Two-Level System Strongly Coupled to a High-Frequency Quantum Oscillator. Physical Review B, 72, Article ID: 195410.
http://dx.doi.org/10.1103/PhysRevB.72.195410
[17] Yuan, X.-Z., Goan, H.-S. and Zhu, K.-D. (2007) Influence of an External Magnetic Field on the Decoherence of a Central Spin Coupled to an Antiferromagnetic Environment. New Journal of Physics, 9, 219.
http://dx.doi.org/10.1088/1367-2630/9/7/219
[18] Pramanik, T., Chowdhury, P. and Majumdar, A.S. (2013) Fine-Grained Lower Limit of Entropic Uncertainty in the Presence of Quantum Memory. Physical Review Letters, 110, Article ID: 020402.
http://dx.doi.org/10.1103/PhysRevLett.110.020402
[19] Wilde, M.M., Hayden, P., Buscemi, F. and Hsieh, M.-H. (2012) The Information-Theoretic Costs of Simulating Quantum Measurements. Journal of Physics A: Mathematical and Theoretical, 45, Article ID: 453001.
http://dx.doi.org/10.1088/1751-8113/45/45/453001
[20] Zhang, J.S., Chen, A.X. and Abdel-Aty, M. (2010) Two Atoms in Dissipative Cavities in Dispersive Limit: Entanglement Sudden Death and Long-Lived Entanglement. Journal of Physics B: Atomic, Molecular and Optical Physics, 43, Article ID: 025501.
http://dx.doi.org/10.1088/0953-4075/43/2/025501
[21] Obada, A.S.F., Hessian, H.A. and Mohamed, A.B.A. (2008) Entropy and Entanglement in the Jaynes-Cummings Model with Effects of Cavity Damping. Journal of Physics B: Atomic, Molecular and Optical Physics, 41, Article ID: 135503.
http://dx.doi.org/10.1088/0953-4075/41/13/135503
[22] Abdel-Aty, M., Abdalla, M.S. and Obada, A.S.F. (2001) Quantum Information and Entropy Squeezing of a Two-Level Atom with a Non-Linear Medium. Journal of Physics A: Mathematical and General, 34, 9129.
http://dx.doi.org/10.1088/0305-4470/34/43/303
[23] Mohamed, A.B.A. (2013) Pairwise Quantum Correlations of a Three-Qubit XY Chain with Phase Decoherence. Quantum Information Processing, 12, 1141-1153. http://dx.doi.org/10.1007/s11128-012-0460-1
[24] Eisert, J., Cramer, M. and Plenio, M.B. (2010) Colloquium: Area Laws for the Entanglement Entropy—A Review. Reviews of Modern Physics, 82, 277.
http://dx.doi.org/10.1103/RevModPhys.82.277
[25] Abdel-Aty, M. and Yu, T. (2008) Entanglement Sudden Birth of Two Trapped Ions Interacting with a Time-Dependent Laser Field. Journal of Physics B: Atomic, Molecular and Optical Physics, 41, Article ID: 235503.
http://dx.doi.org/10.1088/0953-4075/41/23/235503
[26] Mohamed, A.B.A. (2013) Quantum Discord and Its Geometric Measure with Death Entanglement in Correlated Dephasing Two Qubits System. Quantum Information Review, 1, 1-7.
http://dx.doi.org/10.12785/qir/010101
[27] Abdel-Aty, M. (2003) Quantum Field Entropy and Entanglement of a Three-Level Atom Two-Mode System with an Arbitrary Nonlinear Medium. Journal of Modern Optics, 50, 161.
http://dx.doi.org/10.1080/09500340308235167
[28] Ficek, Z. (2009) Quantum Entanglement Processing with Atoms. Applied Mathematics & Information Sciences, 3, 375.
[29] Sun, L.H., Li, G.X. and Ficek, Z. (2010) Continuous Variables Approach to Entanglement Creation and Processing. Applied Mathematics & Information Sciences, 4, 315.
[30] Al-Showaikh, F.N.M. (2008) Entropy of a Two-Level Atom Driven by a Detuned Monochromatic Laser Field and Damped by a Squeezed Vacuum. Applied Mathematics & Information Sciences, 2, 21.
[31] Abdel-Aty, M. (2007) Quantum Information Entropy and Multi-Qubit Entanglement. Progress in Quantum Electronics, 31, 1.
http://dx.doi.org/10.1016/j.pquantelec.2007.03.002
[32] Yuan, X.Z., Goan, H.S. and Zhu, K.D. (2007) Non-Markovian Reduced Dynamics and Entanglement Evolution of Two Coupled Spins in a Quantum Spin Environment. Physical Review B, 75, Article ID: 045331.
http://dx.doi.org/10.1103/PhysRevB.75.045331
[33] Eleuch, H. and Rachid, N. (2010) Autocorrelation Function of Microcavity-Emitting Field in the Non-Linear Regime. European Physical Journal D, 57, 259.
http://dx.doi.org/10.1140/epjd/e2010-00031-x
[34] Eleuch, H. (2010) Entanglement and Autocorrelation Function in Semiconductor Microcavities. International Journal of Modern Physics B, 24, 5653.
http://dx.doi.org/10.1142/S0217979210057511
[35] Buzek, V. and Jex, I. (1991) Emission Spectra of a Two-Level Atom in a Kerr-Like Medium. Journal of Modern Optics, 38, 987-996.
http://dx.doi.org/10.1080/09500349114550961
[36] Jabri, H., Eleuch, H. and Djerad, T. (2005) Lifetimes of Atomic Rydberg States by Autocorrelation Function. Laser Physics Letters, 2, 253.
http://dx.doi.org/10.1002/lapl.200410184
[37] Eleuch, H., Ben Nessib, N. and Bennaceur, R. (2004) Quantum Model of Emission in Weakly Non Ideal Plasma. European Physical Journal D, 29, 391-395.
http://dx.doi.org/10.1140/epjd/e2004-00061-y
[38] Tsallis, C. (1988) Possible Generalization of Boltzmann-Gibbs Statistics. Journal of Statistical Physics, 52, 479-487.
http://dx.doi.org/10.1007/BF01016429
[39] Rajagopal, A.K. and Rendell, R.W. (2005) Nonextensive Statistical Mechanics: Implications to Quantum Information. Europhysics News, 36, 221-224.
http://dx.doi.org/10.1051/epn:2005613
[40] Buscemi, F., Bordone, P. and Bertoni, A. (2007) Linear Entropy as an Entanglement Measure in Two-Fermion Systems. Physical Review A, 75, Article ID: 032301.
http://dx.doi.org/10.1103/PhysRevA.75.032301
[41] Manfredi, G. and Feix, M.R. (2000) Entropy and Wigner Functions. Physical Review E, 62, 4665.
http://dx.doi.org/10.1103/PhysRevE.62.4665
[42] Leibfried, D., Meekhof, D.M., King, B.E., Monroe, C., Itano, W.M. and Wineland, D.J. (1996) Experimental Determination of the Motional Quantum State of a Trapped Atom. Physical Review Letters, 77, 4281-8285.
http://dx.doi.org/10.1103/PhysRevLett.77.4281
[43] Abdel-Aty, M., Abdel-Khalek, S. and Obada, A.S.F. (2001) Entropy Evolution of the Bimodal Field Interacting with an Effective Two-Level Atom via the Raman Transition in Kerr Medium. Chaos, Solitons & Fractals, 12, 2015-2022.
http://dx.doi.org/10.1016/S0960-0779(00)00116-8
[44] Obada, A.S.F., Abdel-Khalek, S. and Plastino, A. (2011) Information Quantifiers’s Description of Weak Field vs. Strong Field Dynamics for a Trapped Ion in a Laser Field. Physica A, 390, 525-533.
http://dx.doi.org/10.1016/j.physa.2010.09.003

  
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