Abstract
The dynamic generation of spin entanglement between two distant sites in a XY model with 1/r 2 decay long-range couplings was studied. Due to the linear dispersion relation ε(k)∼|k| of magnons in such a model, a well-located spin state can be dynamically split into two moving entangled local wave packets without changing their shapes. Interestingly, when such two wave packets meet at the diametrically opposite site after the fast period τ = Nπ/J, the initial well-located state is completely recurrent. Numerical calculation was performed to confirm the analytical result even if the ring system of sizes N up to several thousands is considered. The truncation approximation for the coupling strengths was also studied. Numerical simulation shows that the above conclusions still hold even if the range of the coupling strength is truncated to a relatively short scale compared with the size of the spin system.
Similar content being viewed by others
References
Costa J A T, Bose S, Omar Y. Entanglement of two impurities through electron scattering. Phys Rev Lett, 2006, 96(23): 230501
Boness T, Bose S, Monteiro T S. Entanglement and dynamics of spin chains in periodically pulsed magnetic fields: Accelerator modes. Phys Rev Lett, 2006, 96(18): 187201
Paternostro M, Kim M S, Park E, et al. Entanglement generation in harmonic chains: Tagging by squeezing. Phys Rev A, 2005, 72(5): 052307
Yang S, Song Z, Sun C P. Quantum dynamics of magnetically controlled network for Bloch electrons. Front Phys Chin, 2007, 2(1): 1–16
Chen B, Song Z, Sun C P. Fractional revivals of quantum state in tight-binding chain. Phys Rev A, 2007, 75(1): 012113
Subrahmanyam V. Entanglement dynamics and quantum-state transport in spin chains. Phys Rev A, 2004, 69(3): 034304
Bose S. Quantum communication through an unmodulated spin chain. Phys Rev Lett, 2003, 91(20): 207901
Christandl M, Datta N, Ekert A, et al. Perfect state transfer in quantum spin networks. Phys Rev Lett, 2004, 92(18): 187902
Albanese C, Christandl M, Datta N, et al. Mirror inversion of quantum states in linear registers. Phys Rev Lett, 2004, 93(23): 230502
Shi T, Li Y, Song Z, et al. Quantum-state transfer via the ferromagnetic chain in a spatially modulated field. Phys Rev A, 2005, 71(3): 032309
Plenio M B, Semiao F L. High efficiency transfer of quantum information and multiparticle entanglement generation in translation-invariant quantum chains. New J Phys, 2005, 7: 73
Burgarth D, Bose S. Conclusive and arbitrarily perfect quantum-state transfer using parallel spin-chain channels. Phys Rev A, 2005, 71(5): 052315
Burgarth D, Giovannetti V, Bose S. Efficient and perfect state transfer in quantum chains. J Phys A, 2005, 38(30): 6793
Amico L, Osterloh A, Plastina F, et al. Dynamics of entanglement in one-dimensional spin systems. Phys Rev A, 2004, 69(2): 022304
Plenio M B, Hartley J, Eisert J. Dynamics and manipulation of entanglement in coupled harmonic systems with many degrees of freedom. New J Phys, 2004, 6: 36
Osborne T J, Linden N. Propagation of quantum information through a spin system. Phys Rev A, 2004, 69(5): 052315
Yang S, Song Z, Sun C P. Wave-packet transmission of Bloch electrons manipulated by magnetic field. Phys Rev A, 2006, 73(2): 022317
Li Y, Shi T, Chen B, et al. Quantum-state transmission via a spin ladder as a robust data bus. Phys Rev A. 2005, 71(2): 022301
Qian X F, Li Y, Li Y, et al. Quantum-state transfer characterized by mode entanglement. Phys Rev A, 2005, 72(6): 062329
Li Y, Song Z, Sun C P. Perfect transfer of many-particle quantum state via high-dimensional systems with spectrum-matched symmetry. Comm Theor Phys, 2007, 48(3): 445
Bose I, Tribedi A. Thermal entanglement properties of small spin clusters. Phys Rev A, 2005, 72(2): 022314
Kay A. Perfect state transfer: Beyond nearest-neighbor couplings. Phys Rev A, 2006, 73(3): 032306
Avellino M, Fisher A J, Bose S. Quantum communication in spin systems with long-range interactions. Phys Rev A, 2006, 74(1): 012321
Kamenev D I, Berman G P, Tsifrinovich V I. Creation of entanglement in a scalable spin quantum computer with long-range dipole-dipole interaction between qubits. Phys Rev A, 2006, 73(6): 062336
Hill S, Wootters W K. Entanglement of a pair of quantum bits. Phys Rev Lett, 1997, 78(26): 5022–5025
Wootters W K. Entanglement of formation of an arbitrary state of two qubits. Phys Rev Lett, 1998, 80(10): 2245–2248
Coffman V, Kundu J, Wootters W K. Distributed entanglement. Phys Rev A, 2000, 61(5): 052306
Wang X G, Zanardi P. Quantum entanglement and Bell inequalities in Heisenberg spin chains. Phys Lett A, 2002, 301(1–2): 1–6
Wang X G. Thermal and ground-state entanglement in Heisenberg XX qubit rings. Phys Rev A, 2002, 66(3): 034302
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by the National Natural Science Foundation of China (Grant Nos. 90203018, 10474104 and 60433050) and the National Fundamental Research Program of China (Grant Nos. 2001CB309310 and 2005CB724508)
Rights and permissions
About this article
Cite this article
Yang, S., Song, Z. & Sun, C. Dynamic generation of entangling wave packets in XY spin system with decaying long-range couplings. Sci. China Ser. G-Phys. Mech. Astron. 51, 45–55 (2008). https://doi.org/10.1007/s11433-008-0002-0
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s11433-008-0002-0