有限大小量子Dicke-Stark模型的动力学性质

阎占元; 李欣阳; 邱方程; 常习者; 刘洋

doi:10.3969/j.issn.1000-1565.2024.01.005

河北大学学报(自然科学版) >

2024 , Vol. 44 >Issue 1: 34 - 41

DOI: https://doi.org/10.3969/j.issn.1000-1565.2024.01.005

有限大小量子Dicke-Stark模型的动力学性质

阎占元 ,
李欣阳 ,
邱方程 ,
常习者 ,
刘洋

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阎占元(1973— ),男,华北电力大学教授,主要从事量子光学和THz检测技术研究.
E-mail:yanzhanyuan@ncepu.edu.cn

收稿日期: 2023-09-06

网络出版日期: 2024-03-15

基金资助

河北省自然科学基金资助项目(A2013502247);南方电网科技项目(YNKJXM20220050)

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Dynamics of finite size quantum Dicke-Stark model

YAN Zhanyuan ,
LI Xinyang ,
QIU Fangcheng ,
CHANG Xizhe ,
LIU Yang

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1. Department of Mathematics and Physics, North China Electric Power University, Baoding 071003, China; 2. Electric Power Research Institute of Yunnan Power Grid Co., Ltd., Kunming 650011, China; 3.Hebei Key Laboratory of Physics and Energy Technology, North China Electric Power University, Baoding 071003, China

Received date: 2023-09-06

Online published: 2024-03-15

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摘要

利用相干态的超完备性,可以有效解决光子数空间的截断问题,在有限的相干态空间中即可得到精确的计算结果.本文在相干态空间中计算了Dicke-Stark模型的数值精确解,继而讨论了该模型的量子相变和时间演化动力学.通过计算Dicke-Stark模型基态的平均光子数和平均角动量,发现了量子相变现象,量子相变临界点会随非线性Stark作用发生移动.计算得到Dicke-Stark模型平均光子数和平均角动量随耦合强度和时间演化的相图,有助于了解有限大小Dicke-Stark模型的动力学性质.

关键词： Dicke-Stark模型; 相干态表象; 平均光子数

本文引用格式

阎占元 , 李欣阳 , 邱方程 , 常习者 , 刘洋 . 有限大小量子Dicke-Stark模型的动力学性质[J]. 河北大学学报(自然科学版), 2024 , 44(1) : 34 -41 . DOI: 10.3969/j.issn.1000-1565.2024.01.005

Abstract

Using the hyper completeness of the coherent states space, the truncation problem of the infinite dimensional photon number can be effectively avoided, and the rigorous solutions can be obtained in the finite coherent state space. In this paper, the exact solution of the Dicke-Stark model in the coherent state space are achieved, and then the quantum phase transition and time evolution dynamics of the model are discussed. By calculating the average number of photons and average angular momentum of the ground state of the Dicke-Stark model, the phenomenon of quantum phase transition was reproduced, and the critical point of quantum phase transition would shift with the nonlinear Stark interaction. By calculating the phase diagrams of the average photon number and average angular momentum of the Dicke-Stark model with respect to coupling strength and time evolution, the time evolution dynamics of the Dicke-Stark model were presented, the results are helpful to investigate the dynamics of the finite size quantum Dicke-Stark model.

Key words： Dicke-Stark model; coherent states representation; average photon number

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