Non-Markovianity of an atom in a semi-infinite rectangular waveguide

doi:10.1088/1674-1056/acac18

中国物理B ›› 2023, Vol. 32 ›› Issue (3): 30305-030305.doi: 10.1088/1674-1056/acac18

Non-Markovianity of an atom in a semi-infinite rectangular waveguide

Jing Zeng(曾静)¹, Yaju Song(宋亚菊)², Jing Lu(卢竞)¹, and Lan Zhou(周兰)^1,†

1 Key Laboratory of Low-Dimensional Quantum Structures and and Quantum Control of the Ministry of Education, Department of Physics and Synergetic Innovation Center of Quantum Effects and Applications, Key Laboratory for Matter Microstructure and Function of Hunan Province, Hunan Normal University, Changsha 410081, China;
2 College of Physics and Electronic Engineering, Hengyang Normal University, Hengyang 421002, China

收稿日期:2022-11-01 修回日期:2022-12-11 接受日期:2022-12-16 出版日期:2023-02-14 发布日期:2023-02-21
通讯作者: Lan Zhou E-mail:zhoulan@hunnu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11935006, 12075082, 12205088, and 11975095), the Science and Technology Innovation Program of Hunan Province, China (Grant No. 2020RC4047), the Scientific Research Fund of the Hunan Provincial Education Department (Grant No. 21B0639), and Hunan Normal University Open Foundation of Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of the Ministry of Education (Grant No. QSQC2009).

Non-Markovianity of an atom in a semi-infinite rectangular waveguide

Jing Zeng(曾静)¹, Yaju Song(宋亚菊)², Jing Lu(卢竞)¹, and Lan Zhou(周兰)^1,†

1 Key Laboratory of Low-Dimensional Quantum Structures and and Quantum Control of the Ministry of Education, Department of Physics and Synergetic Innovation Center of Quantum Effects and Applications, Key Laboratory for Matter Microstructure and Function of Hunan Province, Hunan Normal University, Changsha 410081, China;
2 College of Physics and Electronic Engineering, Hengyang Normal University, Hengyang 421002, China

Received:2022-11-01 Revised:2022-12-11 Accepted:2022-12-16 Online:2023-02-14 Published:2023-02-21
Contact: Lan Zhou E-mail:zhoulan@hunnu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11935006, 12075082, 12205088, and 11975095), the Science and Technology Innovation Program of Hunan Province, China (Grant No. 2020RC4047), the Scientific Research Fund of the Hunan Provincial Education Department (Grant No. 21B0639), and Hunan Normal University Open Foundation of Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of the Ministry of Education (Grant No. QSQC2009).

摘要/Abstract

摘要： We investigate the non-Markovianity (NM) of a waveguide QED with a two-level atom as the system and a semi-infinite rectangular waveguide as the environment, where the transverse magnetic (TM$_{mn}$) modes define the quantum channels of guided photons. The perfect mirror imposed by the finite end exerts a retarded feedback mechanism to allow for information backflow, which leads to NM dynamics. For the energy separation of the atom far away from the cutoff frequencies of transverse modes, the delay differential equations are obtained with single-excitation initial in the atom. Our attention is focused on the effects of multiple quantum channels involved in guiding photons on the degree of non-Markovian behavior. An asymptotic value of the non-Markovianity $\mathcal{N}_{1}$ can be found as the atom-mirror distance is large enough, however, the asymptotic value of $\mathcal{N}_{2}$ of the atom interacting with the effective double-modes is lower than that of the atom interacting with the effective single-mode. We also show that $\mathcal{N}_{1}$ is a constant, and the analytical expression for $\mathcal{N}_{2}$ is related to the parameters associated with the modes, which is related to the interference of the two modes.

关键词: open system, non-Markovianity, waveguide QED, quantum information

Abstract: We investigate the non-Markovianity (NM) of a waveguide QED with a two-level atom as the system and a semi-infinite rectangular waveguide as the environment, where the transverse magnetic (TM$_{mn}$) modes define the quantum channels of guided photons. The perfect mirror imposed by the finite end exerts a retarded feedback mechanism to allow for information backflow, which leads to NM dynamics. For the energy separation of the atom far away from the cutoff frequencies of transverse modes, the delay differential equations are obtained with single-excitation initial in the atom. Our attention is focused on the effects of multiple quantum channels involved in guiding photons on the degree of non-Markovian behavior. An asymptotic value of the non-Markovianity $\mathcal{N}_{1}$ can be found as the atom-mirror distance is large enough, however, the asymptotic value of $\mathcal{N}_{2}$ of the atom interacting with the effective double-modes is lower than that of the atom interacting with the effective single-mode. We also show that $\mathcal{N}_{1}$ is a constant, and the analytical expression for $\mathcal{N}_{2}$ is related to the parameters associated with the modes, which is related to the interference of the two modes.

Key words: open system, non-Markovianity, waveguide QED, quantum information

中图分类号: (Decoherence; open systems; quantum statistical methods)

03.65.Yz

32.80.Qk (Coherent control of atomic interactions with photons) 42.50.-p (Quantum optics) 03.67.-a (Quantum information)

Jing Zeng(曾静), Yaju Song(宋亚菊), Jing Lu(卢竞), and Lan Zhou(周兰). Non-Markovianity of an atom in a semi-infinite rectangular waveguide[J]. 中国物理B, 2023, 32(3): 30305-030305.

Jing Zeng(曾静), Yaju Song(宋亚菊), Jing Lu(卢竞), and Lan Zhou(周兰). Non-Markovianity of an atom in a semi-infinite rectangular waveguide[J]. Chin. Phys. B, 2023, 32(3): 30305-030305.

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Non-Markovianity of an atom in a semi-infinite rectangular waveguide

Non-Markovianity of an atom in a semi-infinite rectangular waveguide

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