Abstract
Many-spin entanglement is investigated in one-dimensional zigzag chains, consisting of up to 12 spins 1/2, with nearest neighbor and next nearest neighbor interactions at high and low temperatures. We consider multiple quantum (MQ) nuclear magnetic resonance (NMR) dynamics. The second moment of the distribution of MQ coherences, which provides a lower bound on the quantum Fisher information, is calculated for different temperatures and evolution times. The dependence of the number of the entangled spins on the temperature and the chain length is obtained.
Similar content being viewed by others
References
M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000)
A.M. Kaufman, M.E. Tai, A. Lukin, M. Rispoli, R. Schittko, P.M. Preiss, M. Greiner, Science 353, 794 (2016)
C. Neill, P. Roushan, M. Fang, Y. Chen, M. Kolodrubetz, Z. Chen, A. Megrant, R. Barends, B. Campbell, B. Chiaro, A. Dunsworth, E. Jeffrey, J. Kelly, J. Mutus, P.J.J. O’Malley, C. Quintana, D. Sank, A. Vainsencher, J. Wenner, T.C. White, A. Polkovnikov, J.M. Martinis, Nat. Phys. 12, 1037 (2016)
M. Gärtner, P. Hauke, A.M. Rey, Phys. Rev. Lett. 120, 040402 (2018)
S.I. Doronin, E.B. Fel’dman, I.D. Lazarev, Phys. Rev. A 100, 022330 (2019)
J. Baum, M. Munowitz, A.N. Garroway, A. Pines, J. Chem. Phys. 83, 2015 (1985)
G.B. Furman, V.M. Meerovich, V.L. Sokolovsky, Phys. Rev. A 78, 042301 (2008)
E.B. Fel’dman, A.N. Pyrkov, A.I. Zenchuk, Philos. Trans. R. Soc. A 370, 4690 (2012)
G. Tóth, I. Appelaniz, J. Phys. A 47, 424006 (2014)
L. Pezzé, A. Smerzi, M.K. Oberthaler, R. Schmited, P. Treutlein, Rev. Mod. Phys. 90, 035005 (2018)
J. Baugh, A. Kleinhammes, D. Han, Q. Wang, Y. Wu, Science 294, 1505 (2001)
E.B. Fel’dman, M.G. Rudavets, J. Exp. Theor. Phys. 98, 207 (2004)
E.B. Fel’dman, M.G. Rudavets, JETP Lett. 81, 47 (2005)
E.I. Kuznetsova, E.B. Fel’dman, J. Exp. Theor. Phys. 102, 882 (2006)
W.H. Zachariasen, Kristallogr. Mineral. Petrogr. 76, 289–302 (1931)
G. Cho, J.P. Yesinowski, J. Phys. Chem. 100, 157716 (1996)
G.D. Gatta, G.J. McIntyre, G. Bromiley, A. Guastoni, F. Nestola, Am. Mineral. 97, 1891–1897 (2012)
S.I. Doronin, I.I. Maksimov, E.B. Fel’dman, J. Exp. Theor. Phys. 91, 597 (2000)
A. Abragam, The Principles of Nuclear Magnetism (Clarendon Press, Oxford, 1961)
M. Goldman, Spin Temperature and Nuclear Magnetic Resonance in Solids (Clarendon Press, Oxford, 1970)
A.K. Khitrin, Chem. Phys. Lett. 274, 217 (1997)
J. Liu, H.-N. Xiong, F. Song, X. Wang, Phys. A 410, 167–173 (2014)
J. Liu, H. Yuan, X.-M. Lu, X. Wang, J. Phys. A Math. Theor. 53, 023001 (2020)
P. Hyllus, W. Laskowski, R. Krischek, C. Schwemmer, W. Wieczorek, H. Weinfurter, L. Pezzé, A. Smerzi, Phys. Rev. A 85, 022321 (2012)
J. Liu, H. Yuan, Phys. Rev. A 96, 042114 (2017)
J. Liu, H. Yuan, Phys. Rev. A 96, 012117 (2017)
Funding
This work was performed as a part of a state task, State Registration no. 0089-2019-0002. This work was supported by the Russian Foundation for Basic Research, Grant no. 20-03-00147. I.L. acknowledges support from the Foundation for the Advancement of Theoretical Physics and Mathematics BASIS no. 19-1-5-130-1.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Bochkin, G.A., Vasil’ev, S.G., Doronin, S.I. et al. Many-Spin Entanglement in Zigzag Spin Chain in Multiple Quantum NMR. Appl Magn Reson 51, 667–678 (2020). https://doi.org/10.1007/s00723-020-01206-0
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00723-020-01206-0