[1]张云波,王丽敏,王利.两全同粒子在一维光晶格中的量子行走[J].深圳大学学报理工版,2015,32(1):1-7.[doi:10.3724/SP.J.1249.2015.01001]
　Zhang Yunbo,Wang Limin,and Wang Li.Quantum walks of two identical particles in one-dimensional lattices[J].Journal of Shenzhen University Science and Engineering,2015,32(1):1-7.[doi:10.3724/SP.J.1249.2015.01001]
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两全同粒子在一维光晶格中的量子行走()
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《深圳大学学报理工版》[ISSN:1000-2618/CN:44-1401/N]

卷:
第32卷
期数:
2015年第1期
页码:
1-7
栏目:
物理
出版日期:
2015-01-20

文章信息/Info

Title:
Quantum walks of two identical particles in one-dimensional lattices
文章编号:
201501001
作者:
张云波; 王丽敏; 王利
山西大学理论物理研究所，太原 030006
Author(s):
Zhang Yunbo;  Wang Limin;  and Wang Li
Institute of Theoretical Physics, Shanxi University, Taiyuan 030006, P.R.China
关键词:
凝聚态物理; 光晶格模型; 量子行走; 量子统计; 动力学演化; 两粒子关联; 关联涨落
Keywords:
condensed matter physics;  lattice model;  quantum walk;  quantum statistics;  dynamic evolution;  two particle correlation;  correlation fluctuation
分类号:
O 469
DOI:
10.3724/SP.J.1249.2015.01001
文献标志码:
A
摘要:
基于满足周期性边界条件的一维光晶格模型，分别研究遵从玻色-爱因斯坦统计的玻色系统、遵从费米-狄拉克统计的费米系统以及硬核玻色系统下的两粒子关联、关联涨落、平均粒子数分布以及动力学演化等问题，计算量子统计性质和相互作用强度（排斥）对两粒子量子行走（独立行走和绑定行走）的影响．结果表明，在坐标空间中，随着时间的增大，粒子向晶格边缘移动，尤其当相互作用为零时，玻色系统的两粒子关联虽呈现聚束现象，却展示出一种与众不同的对称——输入输出对称，而费米（硬核玻色）系统的两粒子关联呈现类似环类的空间分布. 随着排斥相互作用的增大，3系统都会出现两粒子绑定行走行为，在强相互作用下，研究的物理量（粒子关联、关联涨落和平均粒子数分布）在3系统中几乎相同；在动量空间中，玻色系统呈典型的聚束现象，费米系统呈反聚束现象，硬核玻色系统呈聚束现象. 计算结果为实验上研究不同系统（玻色、费米和硬核玻色）的物理性质提供了依据，并佐证了实验上排斥相互作用下束缚态产生的实验结果．
Abstract:
Based on one-dimensional lattices with periodic boundary conditions, we investigate the two-particle correlations, the correlation fluctuations, and the density distributions as well as the dynamic evolutions of the bosonic system governed by Bose-Einstein statistics, the fermionic system governed by Fermi-Dirac statistics, and the hard-core bosonic system, respectively. The dependences of independent walking and co-walking for two interacting particles on both quantum statistics and interaction strength are calculated. The results show that the particles move to the edge of the lattice with the increase of time in position space. Specifically, for zero interaction, bosonic correlations exhibit bunching but with a specific “in-out” correlation symmetry, while the fermionic correlations(hard-core bosonic correlations)are transformed into a ring-like pattern. However, two particles in the bosonic system and fermionic system (hard-core bosonic system) start to occupy adjacent lattice sites separated by one site and stick together when they are co-walking with increasing interaction. The correlations in the three systems are nearly the same under strong interactions and are the same with correlation fluctuations and density distributions. In momentum space, the quantum statistical natures for two bosonic (hard-core bosonic) walkers and two fermionic walkers result in the emergence of bunching and anti-bunching in two-particle quantum walks (QWs), respectively. In short, the results pave the way for exploring quantum statistics and can be used as evidences for the repulsively bound state observed experimentally.

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备注/Memo

备注/Memo:
Received：2014-10-29；Accepted：2014-12-13
Foundation：National Natural Science Foundation of China (11474189)
Corresponding author：Professor Zhang Yunbo．E-mail：ybzhang@sxu.edu.cn
Citation：Zhang Yunbo，Wang Limin，Wang Li．Quantum walks of two identical particles in one-dimensional lattices［J］. Journal of Shenzhen University Science and Engineering, 2015, 32(1): 1-7.（in Chinese）
基金项目：国家自然科学基金资助项目(11474189)
作者简介：张云波(1969—)，男(汉族)，山西省黎城县人，山西大学教授．E-mail：ybzhang@sxu.edu.cn
引文：张云波，王丽敏，王利. 两全同粒子在一维光晶格中的量子行走［J］. 深圳大学学报理工版，2015，32（1）：1-7.
更新日期/Last Update: 2015-01-05