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Furman, Gregory B.; Meerovich, Victor M.; Sokolovsky, Vladimir L.

Entanglement in dipolar coupling spin system in equilibrium state. (English) Zbl 1263.81027

Quantum Inf. Process. 11, No. 6, 1603-1617 (2012).
Summary: We study the appearance of the entangled states in a one-dimensional finite chain of dipolar-coupling nuclear spins of 1/2 in the conditions of thermodynamic equilibrium. It is shown that entanglement is achieved by the application of a low external magnetic field in which the Zeeman interaction energy is the order of or even less than the dipolar interaction one. When these energies are equal, the critical temperature, i. e. the temperature of the entanglement appearance, coincides with the temperature at which the heat capacity of the spin chain achieves its maximum. The obtained relationship between the critical temperature and the magnetic field can be considered as an entanglement witness. The dependences of the heat capacity on temperature and magnetic field have different character for entangled and separable states and can be served for experimental detection of entangled states.

Cited in 14 Documents

MSC:

81P40 Quantum coherence, entanglement, quantum correlations
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
82B30 Statistical thermodynamics

Keywords:

entanglement; spin dynamics; dipolar coupling; heat capacity
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References:

[1] Nielsen M.A., Chuang I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000) · Zbl 1049.81015
[2] Benenti G., Casati G., Strini G.: Principles of Quantum Computation and Information, vols. I and II. World Scientific, Singapore (2007) · Zbl 1119.81002 · doi:10.1142/5838
[3] Amico L., Fazio R., Osterloh A., Vedral V.: Entanglement in many-body systems. Rev. Mod. Phys. 80, 517 (2008) · Zbl 1205.81009 · doi:10.1103/RevModPhys.80.517
[4] Horodecki R., Horodecki P., Horodecki M., Horodecki K.: Quantum entanglement. Rev. Mod. Phys. 81, 885 (2009) · Zbl 1205.81012 · doi:10.1103/RevModPhys.81.865
[5] Bennett C.H., DiVincenzo D.P.: Quantum information and computation. Nature 404, 247 (2000) · Zbl 1369.81023 · doi:10.1038/35005001
[6] Bennett C.H., Brassard G., Crépeau C., Jozsa R., Peres A., Wootters W.K.: Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett. 70, 1895 (1993) · Zbl 1051.81505 · doi:10.1103/PhysRevLett.70.1895
[7] Roos C.F., Kim K., Riebe M., Blatt R.: ‘Designer atoms’ for quantum metrology. Nature 443, 316 (2006) · doi:10.1038/nature05101
[8] Cappellaro P., Emerson J., Boulant N., Ramanathan C., Lloyd S., Cory D.G.: Entanglement assisted metrology. Phys. Rev. Lett. 94, 020502 (2005) · doi:10.1103/PhysRevLett.94.020502
[9] Bennett C.H., Bernstein H.J., Popescu S., Schumacher B.: Concentrating partial entanglement by local operations. Phys. Rev. A 53, 2046 (1996) · doi:10.1103/PhysRevA.53.2046
[10] Popescu S., Rohrlich D.: Thermodynamics and the measure of entanglement. Phys. Rev. A 56, R3319 (1997) · doi:10.1103/PhysRevA.56.R3319
[11] Wootters W.K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245 (1998) · Zbl 1368.81047 · doi:10.1103/PhysRevLett.80.2245
[12] Mintert F., Carvalho A.R.R., Kus M., Buchleitner A.: Measures and dynamics of entangled states. Phys. Rep. 415, 207 (2005) · doi:10.1016/j.physrep.2005.04.006
[13] Landau L.D., Lifshits E.M.: Statistical Physics. Butterworth-Heinemann, Oxford (1999) · Zbl 0659.76001
[14] Brout R.: Phase Transition. University of Brussels, New York (1968)
[15] Abragam A., Goldman M.: Nuclear Magnetism: Order and Disorder. Clarendon Press, Oxford (1982)
[16] Furman G.B., Meerovich V.M., Sokolovsky V.L.: Entanglement and multiple quantum coherence dynamics in spin clusters. Quantum Inf. Process. 8, 379-386 (2009) · Zbl 1175.81024 · doi:10.1007/s11128-009-0114-0
[17] Tóth G., Gühne O.: Entanglement detection in the stabilizer formalism. Phys. Rev. A 72, 022340 (2005) · doi:10.1103/PhysRevA.72.022340
[18] Vedral V., Kashefi E.: Uniqueness of entanglement measure and thermodynamics. Phys. Rev. Lett. 89, 037903 (2002) · doi:10.1103/PhysRevLett.89.037903
[19] Brandao F.G.S.L., Plenio M.B.: Entanglement theory and the second law. Nat. Phys. 4, 873 (2008) · doi:10.1038/nphys1100
[20] Barankov R., Polkovnikov A.: Microscopic diagonal entropy and its connection to basic thermodynamic relations. Ann. Phys. 326, 486 (2011) · Zbl 1211.82023 · doi:10.1016/j.aop.2010.08.004
[21] Ghosh S., Rosenbaum T.F., Aeppli G., Coppersmith S.: Entangled quantum state of magnetic dipoles. Nature 425, 48 (2003) · doi:10.1038/nature01888
[22] Dowling M.R., Doherty A.C., Bartlett S.D.: Energy as an entanglement witness for quantum many-body systems. Phys. Rev. A 70, 062113 (2004) · doi:10.1103/PhysRevA.70.062113
[23] Toth G.: Entanglement witnesses in spin models. Phys. Rev. A 71, 010301(R) (2005) · Zbl 1227.81133 · doi:10.1103/PhysRevA.71.010301
[24] Gong S.-S., Su G.: Thermal entanglement in one-dimensional Heisenberg quantum spin chains under magnetic fields. Phys. Rev. A 80, 012323 (2009) · doi:10.1103/PhysRevA.80.012323
[25] Anders J., Kaszlikowski D., Lunkes C., Ohshima T., Vedral V.: Detecting entanglement with a thermometer. New J. Phys. 8, 140 (2006) · doi:10.1088/1367-2630/8/8/140
[26] Brukner, C., Vedral, V.: Macroscopic thermodynamical witnesses of quantum entanglement. http://arxiv.org/abs/quant-ph/0406040v1 · Zbl 1073.81540
[27] Furman G.B., Meerovich V.M., Sokolovsky V.L.: Nuclear polarization and entanglement in spin systems. Quantum Inf. Process. 8, 283 (2009) · Zbl 1181.81023 · doi:10.1007/s11128-009-0103-3
[28] Wiesniak M., Vedral V., Brukner C.: Magnetic susceptibility as a macroscopic entanglement witness. New J. Phys. 7, 258 (2005) · doi:10.1088/1367-2630/7/1/258
[29] Brukner C., Vedral V., Zeilinger A.: Crucial role of quantum entanglement in bulk properties of solids. Phys. Rev. A 73, 012110 (2006) · doi:10.1103/PhysRevA.73.012110
[30] Wiesniak M., Vedral V., Brukner C.: Heat capacity as an indicator of entanglement. Phys. Rev. B 78, 064108 (2008) · doi:10.1103/PhysRevB.78.064108
[31] Doronin S.I.: Multiple quantum spin dynamics of entanglement. Phys. Rev. A 68, 052306 (2003) · doi:10.1103/PhysRevA.68.052306
[32] Fel’dman E.B., Pyrkov A.N.: Evolution of spin entanglement and an entanglement witness in multiple-quantum NMR experiments. Pis’ma Zh. Eksp. Teor. Fiz. 88, 454 (2008)
[33] Furman G.B., Meerovich V.M., Sokolovsky V.L.: Dynamics of entanglement in a one-dimensional Ising chain. Phys.Rev. A 78, 042301 (2008) · doi:10.1103/PhysRevA.78.042301
[34] Brukner, C., Vedral, V.: Macroscopic thermodynamical witnesses of quantum entanglement. arXiv: 0406040 (quant-ph) (2004)
[35] Wang X.: Effects of anisotropy on thermal entanglement. Phys. Lett. A 281, 101 (2001) · Zbl 0974.82013 · doi:10.1016/S0375-9601(01)00123-2
[36] Wang X.: Thermal and ground-state entanglement in Heisenberg XX qubit rings. Phys. Rev. A 66, 034302 (2002) · doi:10.1103/PhysRevA.66.034302
[37] Asoudeh M., Karimipour V.: Thermal entanglement of spins in an inhomogeneous magnetic field. Phys. Rev. A 71, 022308 (2005) · doi:10.1103/PhysRevA.71.022308
[38] Zhang G.-F., Li S.-S.: Thermal entanglement in a two-qubit Heisenberg XXZ spin chain under an inhomogeneous magnetic field. Phys. Rev. A 72, 034302 (2005) · doi:10.1103/PhysRevA.72.034302
[39] Asoudeh M., Karimipour V.: Thermal entanglement of spins in mean-field clusters. Phys. Rev. A 73, 062109 (2006) · doi:10.1103/PhysRevA.73.062109
[40] Rossignoli R., Schmiegelow C.T.: Entanglement generation resonances in XY chains. Phys. Rev. A 75, 012320 (2007) · doi:10.1103/PhysRevA.75.012320
[41] Abdalla M.S., Lashin E., Sadiek G.: Entropy and variance squeezing for time-dependent two-coupled atoms in an external magnetic field. J. Phys. B 41, 015502 (2008) · doi:10.1088/0953-4075/41/1/015502
[42] Sadiek G., Lashin E., Abdalla M.S.: Entanglement of a two-qubit system with anisotropic XYZ exchange coupling in a nonuniform time-dependent external magnetic field. Physica B 404, 1719 (2009) · doi:10.1016/j.physb.2009.02.011
[43] Wichterich H., Bose S.: Exploiting quench dynamics in spin chains for distant entanglement and quantum communication. Phys. Rev. A 79, 060302(R) (2009) · doi:10.1103/PhysRevA.79.060302
[44] Sadiek G., Alkurtass B., Aldossary O.: Entanglement in a time-dependent coupled XY spin chain in an external magnetic field. Phys. Rev. A 82, 052337 (2010) · doi:10.1103/PhysRevA.82.052337
[45] Doronin S.I., Pyrkov A.N., Fel’dman E.B.: Entanglement in alternating open chains of nuclear spins s = 1/2 with the XY Hamiltonian. JETP Lett. 85, 519 (2007) · doi:10.1134/S0021364007100104
[46] Doronin S.I., Fel’dman E.B., Kucherov M.M., Pyrkov A.N.: Entanglement of systems of dipolar coupled nuclear spins at the adiabatic demagnetization. J. Phys. Condens. Matter 21, 025601 (2009) · doi:10.1088/0953-8984/21/2/025601
[47] Furman G.B., Meerovich V.M., Sokolovsky V.L.: Entanglement of dipolar coupling spins. Quantum Inf. Process. 10, 307 (2011) · Zbl 1216.81028 · doi:10.1007/s11128-010-0198-6
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