Journal of Interfaces, Thin Films, and Low dimensional systems
Investigating the evolution of quantum entanglement of a qubit-qubit system with Dzyaloshinskii-Moriya interaction in the presence of magnetic fields
Document Type : Original Article
Author
Department of Physics, Faculty of Basic Sciences, Ayatollah Boroujerdi University, Boroujerd, Iran.
Abstract
This paper presents a detailed investigation into the quantum entanglement dynamics of a qubit-qubit compound system, specifically exploring its behavior within the framework of both the isotropic XXX Heisenberg model and the anisotropic XYZ model. The analysis also considers the presence of Dzyaloshinskii-Moriya interaction, particularly in the context of external magnetic fields. For the study, the initial state of the system is assumed to be a spin coherence state, which serves as a crucial starting point for understanding the entanglement properties. The dynamics of entanglement in this compound system are thoroughly analyzed using the negativity criterion, which is employed as a measure of entanglement. This approach allows for a comprehensive assessment of how the Dzyaloshinskii-Moriya interaction and varying magnetic fields influence the entanglement dynamics throughout the evolution of the system.
Keywords
Main Subjects
Article Title [Persian]
بررسی تکامل درهم تنیدگی کوانتومی یک سیستم کیوبیت-کیوبیت با اندرکنش ژیالوشینسکی- موریا در حضور میدان های مغناطیسی
Author [Persian]
- سید محسن موسوی خوانساری
گروه فیزیک، دانشکده علوم پایه، دانشگاه آیت ا... بروجردی (ره)، بروجرد، ایران.
Abstract [Persian]
در این مقاله، دینامیک درهم‌تنیدگی کوانتومی یک سیستم ترکیبی کیوبیت-کیوبیت در مدل‌های همسانگرد XXX هایزنبرگ و ناهمسانگرد XYZ با برهمکنش Dzyaloshinskii-Moriya تحت میدان‌های مغناطیسی مورد بررسی قرار می‌گیرد. حالت اولیه سیستم به عنوان یک حالت همدوس اسپینی در نظر گرفته می شود و دینامیک درهم تنیدگی این سیستم ترکیبی با استفاده از معیار منفیت به عنوان معیار درهم تنیدگی برای ارزیابی تأثیر اندرکنش دزیالوشینسکی - موریا و میدان های مغناطیسی مورد تجزیه و تحلیل قرار می گیرد.
Keywords [Persian]
- منفیت
- درهم تنیدگی کوانتومی
- حالت همدوس اسپینی
[2] C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels.” Physical Review Letters, 70 (1993) 1895.
[3] C. H. Bennett and S. J. Wiesner, “Communication via One- and Two- Particle Operators on Einstein-Podolsky-Rosen States.” Physical Review Letters, 69 (1992) 2881.
[4] C. H. Bennett, “ Quantum Cryptography Using Any Two Nonorthogonal States.” Physical Review Letters, 68 (1992) 3121.
[5] M. A. Nielsen and I. L. Chuang; Quantum Computation and Quantum Information; Cambridge University Press, Cambridge (2000).
[6] S. Van Enk, O. Hirota, “Entangled coherent states: Teleportation and decoherence.” Physical Review A, 64 (2001) 022313.
[8] S. Sivakumar, “Entanglement in bipartite generalized coherent states.” International Journal of. Theoretical Phyics, 48 (2009) 894.
[9] M. Ashrafpour, M. Jafarpour, A. Sabour; Entangled Three Qutrit Coherent States and Localizable Entanglement ; Communications in Theoretical Physics, 61 (2014) 177.
[10] M. Jafarpour, M. Ashrafpour; “Entanglement dynamics of a two- qutrit system under DM interaction and the relevance of the initial state.” Quantum Information Processing, 12 (2013) 761.
[11] P. J. Van Koningsbruggen, O. Kahn, K. Nakatani, et al., “Magnetism of ACu(II) Bimetallic Chain Compounds (A = Fe, Co, Ni): One- and Three-Dimensional Behaviors.” Inorganic Chemistry Journal, 29 ( 1990) 3325.
[12] I. Dzyaloshinsky, “A thermodynamic theory of weak ferromagnetism of antiferromagnetics.”Journal of Physics and Chemistry of Solids, 4(1958) 241.
[13] T. Moriya, “New Mechanism of Anisotropic Superexchange Interaction.” Physical Review Letters, 4 (1960) 228.
[14] G. Karpat, Z. Gedik, “Correlation dynamics of qubit-qutrit systems in a classical dephasing environment.” Physics Letters A, 375 (2011) 4166.
[15] A. Peres, “Separability Criterion for Density Matrices.” Physical Review Letters, 77 (1996) 1413.
[16] M. Horodecki, P. Horodecki, and R. Horodecki, “Separability of mixed states: necessary and sufficient conditions.” Physics Letters A, 223 (1996) 1.
[17] G. Vidal, R. F. Werner, “A computable measure of entanglement.” Physical Review A, 65 (2002) 032314.
[18] M. A. Chamgordani, N, Naderi, H. Koppelaar, M.Bordbar, “The entanglement dynamics of superposition of fermionic coherent states in Heisenberg spin chains.” International Journal of Modern Physics B, 33 (17) 1950180.
[19] Guo-Feng Zhang, Yu-Chen Hou, Ai-Ling Ji, “Measurement-induced disturbance and thermal negativity of qutrit–qubit mixed spin chain.” Solid State Communications, 151, (2011) 790.
)