X方向KSEA相互作用对几何量子失协的影响

doi:10.19596/j.cnki.1001-246x.8798

摘要/Abstract

摘要：

基于非马尔科夫量子态扩散(NMQSD)方法研究含有X方向Kaplan-Shekhtman-Entin-Wohlman-Aharony(KSEA)相互作用的系统中混合非马尔科夫/马尔科夫环境、单一非马尔科夫/马尔科夫环境下几何量子失协的动力学演化。结果表明: 含有X方向KSEA相互作用的系统中混合非马尔科夫环境下几何量子失协的提高比单一非马尔科夫环境更高; 处在同一纠缠态和不同强度的X方向KSEA相互作用时, 系统的几何量子失协在混合非马尔科夫环境中获得更好的恢复; 马尔科夫环境下单一库的情况比混合的情况要好。

关键词: 混合非马尔科夫库, Kaplan-Shekhtman-Entin-Wohlman-Aharony相互作用, 几何量子失协, 量子态扩散方法

Abstract:

Based on NMQSD (non-Markovian quantum state diffusion) method, this paper studies containing dynamical evolution of geometric quantum discord in a system with X direction Kaplan-Shekhtman-Entin-Wohlman-Aharony (KSEA) interaction in a hybrid non-Markovian/Markovian environment and a single non-Markovian/Markovian environment. The results show that the geometric quantum discord in the hybrid non-Markovian environment is higher than that in the single non-Markovian environment. When interaction with X direction KSEA in the same initial state and different directions of intensity, the geometric quantum discord of the system achieves better recovery in a hybrid non-Markov environment. And we find that the single bath in the Markovian environment is better than the hybrid bath.

Key words: hybrid non-Markovian bath, Kaplan-Shekhtman-Entin-Wohlman-Aharony interaction, geometric quantum discord, quantum state diffusion method

中图分类号:

O431.2

阿依古丽·巴吐尔, 张金峰, 艾克拜尔·阿木提江, 艾合买提·阿不力孜. X方向KSEA相互作用对几何量子失协的影响[J]. 计算物理, 2024, 41(5): 663-669.

Batur AYGUL, Jinfeng ZHANG, Hamutjan AKBAR, Abliz AHMAD. Effects of X Direction KSEA Interaction on Geometric Quantum Discord[J]. Chinese Journal of Computational Physics, 2024, 41(5): 663-669.

图/表 4

图1 混合、单一非马尔科夫环境下含有X方向KSEA相互作用的系统中几何量子失协的动力学演化，初始态为(a)$|\psi\rangle=(|00\rangle-|11\rangle) / \sqrt{2}$和(b)|φ〉= 10〉，kA=kB=1，Jx=0.2，Jy=0.4，Jz=0.9，γ=0.7，Dx=0.4, Γx=0.8

Fig.1 Dynamical evolution of geometric quantum discord in a non-Markov hybrid bath and non-Markov single bath with X-direction KSEA interaction (a) the initial states $|\psi\rangle=(|00\rangle-|11\rangle) / \sqrt{2}$ and (b) |φ〉= 10〉, kA=kB=1, Jx=0.2, Jy=0.4, Jz=0.9, γ=0.7, Dx=0.4, Γx=0.8

图2 (a) 混合非马尔科夫和(b)单一非马尔科夫环境下不同的KSEA相互作用对几何量子失协的影响，初始态为$|\psi\rangle=(|00\rangle-|11\rangle) / \sqrt{2}$。kA=kB=1，Jx=0.2，Jy=0.4，Jz=0.9，γ=0.7，Dx=0.4

Fig.2 Effects of KSEA interactions on dynamics of geometric quantum discord in (a) hybird non-Markov and (b) single non-Markov environments，the initial state $|\psi\rangle=(|00\rangle-|11\rangle) / \sqrt{2}$，kA=kB=1，Jx=0.2，Jy=0.4，Jz=0.9，γ=0.7，Dx=0.4

图3 混合库中几何量子失协随KSEA相互作用和时间变化的(a)三维图和(b)三维投影图，初始态为$|\psi\rangle=(|00\rangle-|11\rangle) / \sqrt{2}$；(c) 混合库中KSEA相互作用在ωt=5时对几何量子失协的影响，初始态为|φ〉 =|10〉，Jx=0.2，Jy=0.4，Jz=0.9，γ=0.7，Dx=0.4

Fig.3 (a) 3-D projection diagram and (b) 3-D diagram of geometric quantum discord with time and KSEA interaction in hybird non-Markov environment, the initial state $|\psi\rangle=(|00\rangle-|11\rangle) / \sqrt{2}$; (c) effect of KSEA interactions on geometric quantum discord in hybird non-Markov environments at ωt=5, the initial state |φ〉= 10〉, Jx=0.2, Jy=0.4, Jz=0.9, γ=0.7, Dx=0.4

图4 不同的KSEA相互作用在(a)混合马尔科夫和(b)单一马尔科夫环境下对几何量子失协的影响，初始态为$|\psi\rangle=(|00\rangle-|11\rangle) / \sqrt{2}$, kA=kB=1，Jx=0.2，Jy=0.4，Jz=0.9，γ=3，Dx=0.4

Fig.4 Dynamics of geometric quantum discord under (a) Markov hybrid bath and (b) Markov single bath with KSEA interaction, the initial state $|\psi\rangle=(|00\rangle-|11\rangle) / \sqrt{2}$, kA=kB=1, Jx=0.2, Jy=0.4, Jz=0.9, γ=3, Dx=0.4

参考文献 41

1	BENNETT C H , DIVINCENZO D P . Quantum information and computation[J]. Nature, 2000, 404 (6775): 247- 255. DOI
2	BENNETT C H , BRASSARD G , CRÉPEAU C , et al. Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels[J]. Physical Review Letters, 1993, 70 (13): 1895- 1899. DOI
3	HORODECKI R , HORODECKI P , HORODECKI M , et al. Quantum entanglement[J]. Reviews of Modern Physics, 2009, 81 (2): 865- 942. DOI
4	OLLIVIER H , ZUREK W H . Quantum discord: A measure of the quantumness of correlations[J]. Physical Review Letters, 2002, 88 (1): 017901.
5	DACIK B , VEDRAL V , BRUKNER C . Necessary and sufficient condition for nonzero quantum discord[J]. Physical Review Letters, 2010, 105 (19): 190502. DOI
6	DACIK B , LIPP Y O , MA Xiaosong , et al. Quantum discord as resource for remote state preparation[J]. Nature Physics, 2012, 8 (9): 666- 670. DOI
7	HU Mingliang , HU Xueyuan , WANG Jieci , et al. Quantum coherence and geometric quantum discord[J]. Physics Reports, 2018, 762/764, 1- 100. DOI
8	DAOUD M , KAYDI W , EI HADFI H . Distribution of geometric quantum discord in photon-added coherent states[J]. Modern Physics Letters B, 2015, 29 (35/36): 1550239.
9	SERI A , LENHARD A , RIELÄNDER D , et al. Quantum correlations between single telecom photons and a multimode on-demand solid-state quantum memory[J]. Physical Review X, 2017, 7 (2): 021028. DOI
10	BURKARD G , LOSS D , DIVINCENZO D P . Coupled quantum dots as quantum gates[J]. Physical Review B, 1999, 59 (3): 2070- 2078. DOI
11	黄睿, 吴绍全, 闫从华. 旁耦合于介观环与铁磁电极量子点系统中的自旋极化输运[J]. 计算物理, 2011, 28 (1): 131- 137.
12	郑文礼, 李志文, 孙艳秀, 等. 双电子平面量子点基态能量的计算[J]. 计算物理, 2008, 25 (5): 617- 622. DOI
13	VRIJEN R , YABLONOVITCH E , WANG Kang , et al. Electron-spin-resonance transistors for quantum computing in silicon-germanium heterostructures[J]. Physical Review A, 2000, 62 (1): 012306. DOI
14	KANE B E . A silicon-based nuclear spin quantum computer[J]. Nature, 1998, 393 (6681): 133- 137. DOI
15	MORIYA T . New Mechanism of anisotropic superexchange interaction[J]. Physical Review Letters, 1960, 4 (5): 228- 230. DOI
16	KAPLAN T A . Single-band Hubbard model with spin-orbit coupling[J]. Zeitschrift für Physik B Condensed Matter, 1983, 49 (4): 313- 317. DOI
17	SHEKHTMAN L , AHARONY A , ENTIN-WOHLMAN O . Bond-dependent symmetric and antisymmetric superexchange interactions in La2CuO4[J]. Physical Review B, Condensed Matter, 1993, 47 (1): 174- 182. DOI
18	TSUKADA I , TAKEYA J , MASUDA T , et al. Weak ferromagnetism of quasi-one-dimensional S=1/2 antiferromagnet BaCu₂Ge₂O₇[J]. Physical Review B, 2000, 62 (10): R6061- R6064. DOI
19	ZHELUDEV A , MASLOV S , SHIRANE G , et al. Magnetic anisotropy and low-energy spin waves in the Dzyaloshinskii-Moriya spiral magnet Ba₂CuGe₂O₇[J]. Physical Review B, 1999, 59 (17): 11432- 11444. DOI
20	ZHELUDEV A , MASLOV S , TSUKADA I , et al. Experimental evidence for kaplan-shekhtman-entin-wohlman-aharony interactions in Ba₂CuGe₂O₇[J]. Physical Review Letters, 1998, 81 (24): 5410- 5413. DOI
21	ELGHAAYDA S , KHEDR A N , TAMMAM M , et al. Quantum entanglement versus skew information correlations in dipole-dipole system under KSEA and DM interactions[J]. Quantum Information Processing, 2023, 22 (2): 117. DOI
22	KHEDIF Y , ERREHYMY A , DAOUD M . Behavior of local quantum fisher information and local quantum uncertainty in dipolar spin system with DM and KSEA interactions[J]. Modern Physics Letters A, 2022, 37 (22): 2250147. DOI
23	FEDOROVA A V , YURISCHEV M A . Quantum entanglement in the anisotropic Heisenberg model with multicomponent DM and KSEA interactions[J]. Quantum Information Processing, 2021, 20 (5): 169. DOI
24	OUMENNANA M , DAHBI Z , MANSOUR M , et al. Geometric measures of quantum correlations in a two-qubit heisenberg XXZ model under multiple interactions effects[J]. Journal of Russian Laser Research, 2022, 43, 533- 545. DOI
25	BREUER H P , PETRUCCIONE F . The theory of open quantum systems[M]. New York: Oxford University Press, 2007: 219- 280.
26	DIÓSI L , STRUNZ W T . The non-Markovian stochastic schrödinger equation for open systems[J]. Physics Letters A, 1997, 235 (6): 569- 573. DOI
27	DIÓSI L , GISIN N , STRUNZ W T . Non-Markovian quantum state diffusion[J]. Physical Review A, 1998, 58 (3): 1699- 1712. DOI
28	JING J , ZHAO X , YOU J , et al. Many-body quantum trajectories of non-Markovian open systems[J]. Physical Review A, 2013, 88 (5): 052122. DOI
29	CHEN Yusui , YOU J Q , YU Ting . Exact non-Markovian master equations for multiple qubit systems: Quantum-trajectory approach[J]. Physical Review A, 2014, 90 (5): 052104. DOI
30	ZHAO Xinyu , JING Jun , CORN B , et al. Dynamics of interacting qubits coupled to a common bath: Non-Markovian quantum-state-diffusion approach[J]. Physical Review A, 2011, 84 (3): 032101. DOI
31	ZHAO Xinyu , SHI Wufu , WU Lianao , et al. Fermionic stochastic Schrödinger equation and master equation: An open-system model[J]. Physical Review A, 2012, 86 (3): 032116. DOI
32	唐诗生, 艾合买提·阿不力孜. 非马尔科夫环境中各向异性海森堡自旋链的量子失协[J]. 计算物理, 2022, 39 (2): 165- 172.
33	LACROIX D , SARGSYAN V V , ADAMIAN G G , et al. Non-Markovian modeling of Fermi-Bose systems coupled to one or several Fermi-Bose thermal baths[J]. Physical Review A, 2020, 102 (2): 022209. DOI
34	RITSCHEL G , SUESS D , MÖBIUS S , et al. Non-Markovian quantum state diffusion for temperature-dependent linear spectra of light harvesting aggregates[J]. The Journal of Chemical Physics, 2015, 142 (3): 034115. DOI
35	LAMBERT N , NORI F . Detecting quantum-coherent nanomechanical oscillations using the current-noise spectrum of a double quantum dot[J]. Physical Review B, 2008, 78 (21): 214302. DOI
36	AHMADI F , HASELI S , HADIPOUR M , et al. Quantum speed limit time of topological qubits influenced by the fermionic and bosonic environments[J]. Brazilian Journal of Physics, 2022, 52 (3): 85. DOI
37	BÄTGE J , KE Y , KASPAR C , et al. Nonequilibrium open quantum systems with multiple bosonic and fermionic environments: A hierarchical equations of motion approach[J]. Physical Review B, 2021, 103 (23): 235413. DOI
38	ZHAO Xinyu , SHI Wufu , YOU Jq , et al. Non-Markovian dynamics of quantum open systems embedded in a hybrid environment[J]. Annals of Physics, 2017, 381, 121- 136. DOI
39	艾克拜尔·阿木提江, 阿拉帕提·阿不力米提, 杨帆, 等. 混杂非马尔可夫库对海森伯XYZ自旋链模型的量子纠缠与量子稠密编码的影响[J]. 激光与光电子学进展, 2022, 59 (5): 320- 326.
40	杨帆, 阿拉帕提·阿不力米提, 艾合买提·阿不力孜. 非马尔可夫环境下Dzyaloshinskii-Moriya相互作用和非均匀磁场对自旋系统的纠缠影响[J]. 激光与光电子学进展, 2021, 58 (7): 372- 379.
41	张金峰, 阿拉帕提·阿不力米提, 杨帆, 等. 不同外加磁场中Kaplan-Shekhtman-Entin-Wohlman-Aharony相互作用对量子失协非马尔科夫演化的影响[J]. 物理学报, 2021, 70 (22): 40- 47.