Journal of Interfaces, Thin Films, and Low dimensional systems

Entanglement dynamics of the two-spin system with time-dependent Heisenberg and Dzyaloshinskii-Moriya interactions

Document Type : Original Article

Authors

1 Department of Physics, Yadegar-e-Imam Khomeini (RAH) Shahre-rey Branch, Islamic Azad University, Tehran, Iran

2 Department of physics, Guilan University, Rasht, Iran

Abstract

In the present paper, we study the entanglement dynamics of a two-spin system with Heisenberg interaction and Dzyaloshinskii-Moriya (DM) interaction. We assume that both interior interactions of the system are time-dependent. We consider two different scenarios: In the first case, both Heisenberg and DM interactions are sinusoidal functions (sin (ωt)). The findings show that if the time-dependency of both interior interactions is the same, the quantum entanglement of the system presents more robustness and its temporal fluctuations reduce significantly over time. In the second case, DM interaction is considered as D ∝ cos (ωt). The findings imply that this kind of time-dependency causes strong fluctuations of the entanglement so that sometimes the correlation reaches zero. Therefore, in order to achieve a more stable entanglement over time, it is better that the time dependency of the Heisenberg interaction and DM interaction would be the same.

Keywords

Main Subjects

Article Title [Persian]

دینامیک درهمتنیدگی سیستم دواسپینی با اندرکنش‌های‌ ژیالوشینسکی-موریا وهایزنبرگ وابسته به زمان

Authors [Persian]

  • محمد رضا سلطانی 1
  • مریم محمودی 2

1 گروه فیزیک، دانشگاه آزاد اسلامی واحد یادگار امام خمینی، شهر ری، تهران، ایران

2 گروه فیزیک، دانشگاه گیلان، رشت، ایران

Abstract [Persian]

در مقاله حاضر، دینامیک درهم تنیدگی یک سیستم دو اسپین را با اندرکنش هایزنبرگ و اندرکنش ژیالوشینسکی-موریا (DM) را مورد بررسی قرار داده ایم.. فرض می کنیم که هر دو ضرایب J و D سیستم وابسته به زمان هستند. دو سناریو مختلف را در نظر می گیریم: در مورد اول، هر دو ضریب هایزنبرگ و DM تابع سینوسی هستند. یافته ها نشان می دهد که اگر وابستگی زمانی هر دو برهمکنش یکسان باشد، درهم تنیدگی کوانتومی سیستم استحکام بیشتری را نشان می دهد و نوسانات زمانی آن به طور قابل توجهی در طول زمان کاهش می یابد. در حالت دوم، ضریب هایزنبرگ و برهمکنش DM دارای اختلاف فاز در نظر میگیریم یافته ها حاکی از آن است که این نوع وابستگی به زمان باعث نوسانات شدید درهم تنیدگی می شود، به طوری که گاهی اوقات همبستگی به صفر می رسد. بنابراین، برای دستیابی به درهم تنیدگی پایدارتر در طول زمان، بهتر است وابستگی زمانی اندرکنش هایزنبرگ و اندرکنش DM یکسان باشد.

Keywords [Persian]

  • دینامیک درهمتنیدگی
  • برهمکنش هایزنبرگ
  • برهمکنش ژیالوشینسکی - موریا
  • سیستم وابسته به زمان اسپینی
[1] M. A. Nielsen, I. L. Chuang, “Quantum Computation and Quantum Information”,Cambridge University Press, Cambridge, 2000
[2] D. Bruß, G. Leuchs, “Lectures on Quantum information.” Wiley-Vch GmbH & Co. KGaA, 2007.
[3] R. L. Franco, an G. Compagno, “Indistinguishability of elementary systems as a resource for quantum information processing.” Physical review letters, 120 (2018) 240403.
[4] Jonathan Barrett, Lucien Hardy, and Adrian Kent. "No signaling and quantum key distribution." Physical review letters, 95 (2005) 010503.
[5] M. D. Barrett et al., "Deterministic quantum teleportation of atomic qubits." Nature, 429 (2004) 737.
[6] Jietai Jing et al., "Experimental demonstration of tripartite entanglement and controlled dense coding for continuous variables." Physical review letters, 90 (2003) 167903.
[7] Bruce E. Kane, "A silicon-based nuclear spin quantum computer." Nature, 393 (1998) 133.
[8] Björn Trauzettel et al., "Spin qubits in graphene quantum dots." Nature Physics, 3 (2007) 192.
[9] M. Y. Inada Nishiyama and Guo-qing Zheng. "Spin triplet superconducting state due to broken inversion symmetry in Li 2 Pt 3 B." Physical review letters, 98 (2007) 047002.
[10] Takashige Omatsu et al., "Optical Manipulation and Structured Materials Conference 2020." Optical Manipulation and Structured Materials Conference, 11522 (2020).
[11] Mohammad Reza Soltani et al., “Dynamics of the entanglement in a two-spin system with long-range interaction”, Journal of Interfaces, Thin films, and Low dimensional systems, 4 (2020) 323.
[12] Da-Chuang Li and Zhuo-Liang Cao. "Thermal entanglement in the anisotropic Heisenberg XYZ model with different inhomogeneous magnetic fields." Optics communications, 282 (2009) 1226.
[13] S. Mahdavifar et al., "Thermal Classical and Quantum Correlations in Spin-1/2 XX Chains with the Dzyaloshinskii-Moriya Interaction." Journal of Superconductivity and Novel Magnetism, 28 (2015) 1807.
[14] Fernanda Pinheiro et al., "X Y Z Quantum Heisenberg Models with p-Orbital Bosons." Physical review letters, 111 (2013) 205302.
[15] Peotta, Sebastiano, et al. "The XYZ chain with Dzyaloshinsky–Moriya interactions: from spin orbit-coupled lattice bosons to interacting Kitaev chains." Journal of Statistical Mechanics: Theory and Experiment, 2014 (2014) P09005.
[16] Moriya, Tôru. "Recent progress in the theory of itinerant electron magnetism." Journal of Magnetism and Magnetic Materials, 14 (1979) 1.
[17] M. Mahmoudi, S. Mahdavifar, M. R. Soltani, Physica A: Statistical Mechanics and its Applications, 456 (2016) 176.
[18] M. Tchoffo et al., "Dzyaloshinskii–Moriya interaction effects on the entanglement dynamics of a two qubit XXZ spin system in non-Markovian environment." Journal of Magnetism and Magnetic Materials, 407 (2016) 358.
[19] Anas Ait Chlih, Habiballah Nabil, and Mostafa Nassik. "Dynamics of quantum correlations under intrinsic decoherence in a Heisenberg spin chain model with Dzyaloshinskii–Moriya interaction." Quantum Information Processing, 20 (2021) 1. 523
[20] Ying-Yue Yang et al., "Dynamical characteristic of measurement uncertainty under Heisenberg spin models with Dzyaloshinskii–Moriya interactions." Frontiers of Physics, 14 (2019) 1.
[21] M. R. Soltani, "Dynamics of the Bipartite and Multipartite Entanglement in the Heisenberg Chain with Dzyaloshinskii-Moriya Interaction." Journal of Superconductivity and Novel Magnetism, 29 (2016) 847.
[22] M. Tchoffo, G. C. Fouokeng, E. Tendong, and L. C. Fai. "Dzyaloshinskii–Moriya interaction effects on the entanglement dynamics of a two qubit XXZ spin system in non-Markovian environment." Journal of Magnetism and Magnetic Materials, 407 (2016) 358.
[23] Maryam Mahmoudi, "The effects of Dzyaloshinskii–Moriya interaction on entanglement dynamics of a spin chain in a non- Markovian regime." Physica A: Statistical Mechanics and its Applications, 545 (2020) 123707.
[24] Vladimir E. Dmitrienko et al., "Dzyaloshinskii Moriya interaction: How to measure its sign in weak ferromagnets?" JETP letters, 92 (2010) 383.
[25] Martin, Tchoffo and Tene Alain Giresse, "Entanglement Dynamics of a Two-qubit XYZ Spin Chain Under both Dzyaloshinskii-Moriya Interaction and Time-dependent Anisotropic Magnetic Field." International Journal of Theoretical Physics, 59 (2020) 2232.
[26] Maryam Mahmoudi and Mohammad Reza Soltani. "Entanglement Dynamics in the System of Two Spin-1/2 Particles with Ising Interaction and Time-Dependent Dzyaloshinskii-Moriya Interaction." Journal of Superconductivity and Novel Magnetism, (2022) 1.
[27] Galve, Fernando, et al. "Entanglement resonance in driven spin chains." Physical Review A, 79 (2009) 032332.
[28] D. Das, T. Chakraborty, T. K. Sen, H. Singh, S. K. Mandal, and C. Mitra, “Experimental quantification of entanglement in quantum spin systems.” In AIP Conference Proceedings 1384 (2011) American Institute of Physics.
[29] C. Sackett, D. Kielpinski, B. King et al., “Experimental entanglement of four
particles.” Nature, 404 (2000) 256.
[30] Y. Pu, Y. Wu, N. Jiang, W. Chang, C. Li, S. Zhang, and L. Duan, “Experimental entanglement of 25individually accessible atomic quantum
interfaces.” Science advances, 4 (2018) 3931.
[31] Sam A. Hill and William K. Wootters,"Entanglement of a pair of quantum bits." Physical Review Letters, 78 (1997) 5022.
Journal of Interfaces, Thin Films, and Low dimensional systems
Volume 5, Issue 2
February 2022
Pages 517-523