درهم‌تنیدگی و فشردگی در حالت پایه در یک شبکة مربعی اسپینی در حضور میدان مغناطیسی

نوع مقاله : مقاله پژوهشی کامل

نویسندگان

1 گروه شیمی، واحد امیدیه، دانشگاه آزاد اسلامی، امیدیه، ایران

2 گروه فیزیک، واحد امیدیه، دانشگاه آزاد اسلامی، امیدیه ، ایران

3 گروه فیزیک، واحد امیدیه، دانشگاه آزاد اسلامی، امیدیه، ایران

چکیده

در این پژوهش فشردگی اسپینی برای دو سیستم مربعی رایج، با پارامتر کیتاگاوا و برحسب متغیرهای سیستم، محاسبه شده و با درهم‌تنیدگی این سیستم‌ها برحسب دو سنجه میر-والاش و LE ، مقایسه شد. محاسبات نشان داد که در این سیستم‌ها رابطة مشخصی بین پارامتر کیتاگاوا و سنجه میر-والاش وجود دارد و در مواردی که فشردگی به‌میزان برهم‌کنش بین سایت‌ها وابسته است در همبستگی بین فشردگی و سنجة میر-والاش تغییری ایجاد نمی‌شود. همچنین هیچگونه همبستگی مابین میزان درهم‌تنیدگی برحسب سنجة LE و فشردگی در سیستم‌های مورد بررسی به‌دست نیامد. با این حال، در یکی از سیستم‌ها همبستگی ضعیفی بین آنها مشاهده شد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Entanglement and squeezing of two-dimensional spin square lattice in ground state in a magnetic field

نویسندگان [English]

  • Noushin Zalaki Ghorbanpour 1
  • Abbaas Sabour 2
  • Fereydoon Khazali 1
  • Soghra GHanavati 3
1 Department of Chemistry, Omidiyeh Branch, Islamic Azad University, Omidiyeh, Iran.
2 Department of Physics, Omidiyeh Branch, Islamic Azad University, Omidiyeh, Iran.
3 Department of Physic, Omidiyeh Branch, Islamic Azad University, Omidiyeh, Iran.
چکیده [English]

In this study, spin squeezing was calculated for two common square systems in terms of the system variables using the Kitagawa parameter, and entanglement of these systems was compared based on the Meyer–Wallach and LE measures. Calculations showed a certain relationship between the Kitagawa parameter and the Meyer–Wallach measure in the two square systems. The correlation between squeezing and the Meyer–Wallach measure remains unchanged in cases where squeezing is dependent on the interaction between the sites. No correlation was found between entanglement in terms of the LE measure and squeezing in the studied systems. However, in one of the systems, a weak correlation between them was observed.

کلیدواژه‌ها [English]

  • Spin squeezing
  • Kitagawa parameter
  • Entanglement
  • LE measure
  • Square system

[1] J. Ren, W.L. You, X. Wang, Entanglement and correlations in a one-dimensional quantum spin-12 chain with anisotropic power-law long-range interactions, Physical Review B 101 (2020) 094410. https://doi.org/10.1103/PhysRevB.101.094410

[2] G. Li, W. Nie, X. Li, A. Chen, Dynamics of ground-state cooling and quantum entanglement in a modulated optomechanical system, Physical Review A 100 (2019) 063805. https://doi.org/10.1103/PhysRevA.100.063805

[3] A. Deger, T-C. Wei, Geometric entanglement and quantum phase transition in
generalized cluster-XY models, Quantum Information Processing 18 (2019) 326. https://doi.org/10.1007/s11128-019-2439-7

[4] A. Anshu, I. Arad, D. Gosse, An Area Law for 2D Frustration-Free Spin systems,  Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing (2022).

[5] O. Guehne, G. Toth, Entanglement detection, Phys. Report. 474 (2009) 1. https://doi.org/10.1016/j.physrep.2009.02.004

[6] K.S. Akhilesh, B.G. Divyamani, A.R. Usha Devi, Spin squeezing in symmetric multi qubit states with two non-orthogonal Majorana spinors, Quantum Information 18 (2019) 144. https://doi.org/10.1007/s11128-019-2244-3

[7] L.G. Huang, F. Chen, X. Li, Y. Li, R. Lü, Y. C. Liu, Dynamic synthesis of Heisenberg-limited spin squeezing, npj quantum information 7 (2021) 168. https://doi.org/10.1038/s41534-021-00505-z

[8] MS. Rudner, LMK Vandersypen, V. Vuletić, LS. Levitov, Generating Entanglement and Squeezed States of Nuclear Spins in Quantum Dots, Physical Review Letters 107 (2011) 206806. https://doi.org/10.1103/PhysRevLett.107.206806

[9] A. Sorensen, L. Duan, J. Cirac, P. Zoller, Many-particle entanglement with Bose-Einstein condensates, Nature 409 (2001) 63. https://doi.org/10.1038/35051038

[10] N. Bigelow, Quantum engineering - Squeezing entanglement, Nature 409 (2001) 27. https://doi.org/10.1038/35051193

[11] E.S. Polzik, Quantum physics - The squeeze goes on, Nature 453 (2008) 45. https://doi.org/10.1038/453045a

[12] A.D. Cronin, J. Schmiedmayer, D.E. Pritchard, Optics and interferometry with atoms and molecules, Reviews of Modern Physics 81 (2009) 1051. https://doi.org/10.1103/RevModPhys.81.1051

 [13] I. Buluta, F. Nori, Quantum simulators, Science 326 (2009) 108. https://doi.org/10.1126/science.1177838

[14] M. Kitagawa, M. Ueda, Squeezed spin states, Physical Review A 47 (1993) 5138-5143 https://doi.org/10.1103/PhysRevA.47.5138

[15] D. Ulam-Orgikh, M. Kitagawa, Spin squeezing and decoherence limit in Ramsey spectroscopy, Physical Review A 64 (2001) 052106. https://doi.org/10.1103/PhysRevA.64.052106

[16] W.K. Wootters, Entanglement of formation of an arbitrary state of two qubits, Physical Review Letters 80 (1998) 2245. https://doi.org/10.1103/PhysRevLett.80.2245

[17] D.A. Meyer, N.R. Wallach, Global entanglement in multiparticle systems, Journal of Mathematical Physics 43 (2002) 4273. https://doi.org/10.1063/1.1497700

[18] A.J. Scott, Multipartite entanglement quantum-error-correcting codes and entangling power of quantum evolutions, Physical Review A 69 (2004) 052330. https://doi.org/10.1103/PhysRevA.69.052330

[19] F. Verstraete, J. Dehaene, B.D. Moor, Normal forms and entanglement measures for multipartite quantum states, Physical Review A 68 (2003) 012103. https://doi.org/10.1103/PhysRevA.68.012103

[20] T.C. Wei, P.M. Goldbart, Geometric measure of entanglement and applications to bipartite and multipartite quantum states, Physical Review A 68 (2003) 042307. https://doi.org/10.1103/PhysRevA.68.042307

[21] L. Amico, R. Fazio, A. Osterloh, V. Vedral, Entanglement in many-body systems, Reviews of modern physics 80 (2008) 517. https://doi.org/10.1103/RevModPhys.80.517

[22] P.A.M. Dirac, Note on exchange phenomena in the Thomas atom, In Mathematical proceedings of the Cambridge philosophical society, Cambridge University Press Cambridge, (1930).

[23] M. Popp, F. Verstraete, M.A.M. Delgado, J.I. Cirac, Localizable entanglement, Physical Review A 71 (2005) 042306. https://doi.org/10.1103/PhysRevA.71.042306

[24] A. Sabour, M. Jafarpour, A probability measure for entanglement of pure two-qubit systems and a useful interpretation for concurrence, Chinese Physics Letters 28 (2011) 070301. https://doi.org/10.1088/0256-307X/28/7/070301

[25] A.C. Rencher, W.F. Christensen, Methods of Multivariate Analysis, John Wiley, New York (2012).

[26] J. MaX. WangC.P. SunF. Nori, Quantum spin squeezing, Physics Reports 509 (2011) 89-165. https://doi.org/10.1016/j.physrep.2011.08.003

[1] J. Ren, W.L. You, X. Wang, Entanglement and correlations in a one-dimensional quantum spin-12 chain with anisotropic power-law long-range interactions, Physical Review B 101 (2020) 094410. https://doi.org/10.1103/PhysRevB.101.094410
[2] G. Li, W. Nie, X. Li, A. Chen, Dynamics of ground-state cooling and quantum entanglement in a modulated optomechanical system, Physical Review A 100 (2019) 063805. https://doi.org/10.1103/PhysRevA.100.063805
[3] A. Deger, T-C. Wei, Geometric entanglement and quantum phase transition in
generalized cluster-XY models, Quantum Information Processing 18 (2019) 326. https://doi.org/10.1007/s11128-019-2439-7
[4] A. Anshu, I. Arad, D. Gosse, An Area Law for 2D Frustration-Free Spin systems,  Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing (2022).
[5] O. Guehne, G. Toth, Entanglement detection, Phys. Report. 474 (2009) 1. https://doi.org/10.1016/j.physrep.2009.02.004
[6] K.S. Akhilesh, B.G. Divyamani, A.R. Usha Devi, Spin squeezing in symmetric multi qubit states with two non-orthogonal Majorana spinors, Quantum Information 18 (2019) 144. https://doi.org/10.1007/s11128-019-2244-3
[7] L.G. Huang, F. Chen, X. Li, Y. Li, R. Lü, Y. C. Liu, Dynamic synthesis of Heisenberg-limited spin squeezing, npj quantum information 7 (2021) 168. https://doi.org/10.1038/s41534-021-00505-z
[8] MS. Rudner, LMK Vandersypen, V. Vuletić, LS. Levitov, Generating Entanglement and Squeezed States of Nuclear Spins in Quantum Dots, Physical Review Letters 107 (2011) 206806. https://doi.org/10.1103/PhysRevLett.107.206806
[9] A. Sorensen, L. Duan, J. Cirac, P. Zoller, Many-particle entanglement with Bose-Einstein condensates, Nature 409 (2001) 63. https://doi.org/10.1038/35051038
[10] N. Bigelow, Quantum engineering - Squeezing entanglement, Nature 409 (2001) 27. https://doi.org/10.1038/35051193
[11] E.S. Polzik, Quantum physics - The squeeze goes on, Nature 453 (2008) 45. https://doi.org/10.1038/453045a
[12] A.D. Cronin, J. Schmiedmayer, D.E. Pritchard, Optics and interferometry with atoms and molecules, Reviews of Modern Physics 81 (2009) 1051. https://doi.org/10.1103/RevModPhys.81.1051
 [13] I. Buluta, F. Nori, Quantum simulators, Science 326 (2009) 108. https://doi.org/10.1126/science.1177838
[14] M. Kitagawa, M. Ueda, Squeezed spin states, Physical Review A 47 (1993) 5138-5143 https://doi.org/10.1103/PhysRevA.47.5138
[15] D. Ulam-Orgikh, M. Kitagawa, Spin squeezing and decoherence limit in Ramsey spectroscopy, Physical Review A 64 (2001) 052106. https://doi.org/10.1103/PhysRevA.64.052106
[16] W.K. Wootters, Entanglement of formation of an arbitrary state of two qubits, Physical Review Letters 80 (1998) 2245. https://doi.org/10.1103/PhysRevLett.80.2245
[17] D.A. Meyer, N.R. Wallach, Global entanglement in multiparticle systems, Journal of Mathematical Physics 43 (2002) 4273. https://doi.org/10.1063/1.1497700
[18] A.J. Scott, Multipartite entanglement quantum-error-correcting codes and entangling power of quantum evolutions, Physical Review A 69 (2004) 052330. https://doi.org/10.1103/PhysRevA.69.052330
[19] F. Verstraete, J. Dehaene, B.D. Moor, Normal forms and entanglement measures for multipartite quantum states, Physical Review A 68 (2003) 012103. https://doi.org/10.1103/PhysRevA.68.012103
[20] T.C. Wei, P.M. Goldbart, Geometric measure of entanglement and applications to bipartite and multipartite quantum states, Physical Review A 68 (2003) 042307. https://doi.org/10.1103/PhysRevA.68.042307
[21] L. Amico, R. Fazio, A. Osterloh, V. Vedral, Entanglement in many-body systems, Reviews of modern physics 80 (2008) 517. https://doi.org/10.1103/RevModPhys.80.517
[22] P.A.M. Dirac, Note on exchange phenomena in the Thomas atom, In Mathematical proceedings of the Cambridge philosophical society, Cambridge University Press Cambridge, (1930).
[23] M. Popp, F. Verstraete, M.A.M. Delgado, J.I. Cirac, Localizable entanglement, Physical Review A 71 (2005) 042306. https://doi.org/10.1103/PhysRevA.71.042306
[24] A. Sabour, M. Jafarpour, A probability measure for entanglement of pure two-qubit systems and a useful interpretation for concurrence, Chinese Physics Letters 28 (2011) 070301. https://doi.org/10.1088/0256-307X/28/7/070301
[25] A.C. Rencher, W.F. Christensen, Methods of Multivariate Analysis, John Wiley, New York (2012).
[26] J. MaX. WangC.P. SunF. Nori, Quantum spin squeezing, Physics Reports 509 (2011) 89-165. https://doi.org/10.1016/j.physrep.2011.08.003