中国物理B ›› 2025, Vol. 34 ›› Issue (12): 126702-126702.doi: 10.1088/1674-1056/adea99

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Mediated interactions between two impurities immersed in a Bose-Einstein condensate

Dong-Chen Zheng(郑东琛)1,2, Chun-Rong Ye(叶春荣)1,2, Yan-Xue Lin(林燕雪)1,2, Lin Wen(文林)3,†, and Renyuan Liao(廖任远)1,2,‡   

  1. 1 College of Physics and Energy, Fujian Normal University, Fujian Provincial Key Laboratory of Quantum Manipulation and New Energy Materials, Fuzhou 350117, China;
    2 Fujian Provincial Engineering Technology Research Center of Solar Energy Conversion and Energy Storage, Fuzhou 350117, China;
    3 College of Physics and Electronic Engineering, Chongqing Normal University, Chongqing 401331, China
  • 收稿日期:2025-04-02 修回日期:2025-06-22 接受日期:2025-07-02 发布日期:2025-11-25
  • 通讯作者: Lin Wen, Renyuan Liao E-mail:wlqx@cqnu.edu.cn;ryliao@fjnu.edu.cn
  • 基金资助:
    R. Liao acknowledges funding from the National Natural Science Foundation of China (Grant Nos. 12174055 and 11674058) and the Natural Science Foundation of Fujian (Grant No. 2020J01195). LinWen acknowledges funding from the National Natural Science Foundation of China (Grant No. 12175027).

Mediated interactions between two impurities immersed in a Bose-Einstein condensate

Dong-Chen Zheng(郑东琛)1,2, Chun-Rong Ye(叶春荣)1,2, Yan-Xue Lin(林燕雪)1,2, Lin Wen(文林)3,†, and Renyuan Liao(廖任远)1,2,‡   

  1. 1 College of Physics and Energy, Fujian Normal University, Fujian Provincial Key Laboratory of Quantum Manipulation and New Energy Materials, Fuzhou 350117, China;
    2 Fujian Provincial Engineering Technology Research Center of Solar Energy Conversion and Energy Storage, Fuzhou 350117, China;
    3 College of Physics and Electronic Engineering, Chongqing Normal University, Chongqing 401331, China
  • Received:2025-04-02 Revised:2025-06-22 Accepted:2025-07-02 Published:2025-11-25
  • Contact: Lin Wen, Renyuan Liao E-mail:wlqx@cqnu.edu.cn;ryliao@fjnu.edu.cn
  • About author:2025-126702-250569.pdf
  • Supported by:
    R. Liao acknowledges funding from the National Natural Science Foundation of China (Grant Nos. 12174055 and 11674058) and the Natural Science Foundation of Fujian (Grant No. 2020J01195). LinWen acknowledges funding from the National Natural Science Foundation of China (Grant No. 12175027).

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摘要： We consider two pointlike static impurities without direct interaction immersed in a three-dimensional Bose-Einstein condensate (BEC) at zero temperature. By solving the Gross-Pitaevskii (GP) equation in a perturbative manner, we calculate the ground state energy in the region where the atom-impurity interaction is assumed to be weak. We obtain an analytical expression for the spatial distribution of atom number density and the effective force between these two impurities. The effective force is found to be closely related to the strength of the atom-impurity interaction and the relative distance between these two impurities. Two critical relative distances are found between the two impurities. The first one corresponds to the vanishing of the perturbed energy with impurities, although the effective force between the two impurities still exists. At the second critical value, the energy of the impurities changes linearly with the atom-impurity interaction; otherwise, it changes quadratically with the atom-impurity interaction.

关键词: quantum gases, Bose-Einstein condensate, Bose polaron, mediated interaction

Abstract: We consider two pointlike static impurities without direct interaction immersed in a three-dimensional Bose-Einstein condensate (BEC) at zero temperature. By solving the Gross-Pitaevskii (GP) equation in a perturbative manner, we calculate the ground state energy in the region where the atom-impurity interaction is assumed to be weak. We obtain an analytical expression for the spatial distribution of atom number density and the effective force between these two impurities. The effective force is found to be closely related to the strength of the atom-impurity interaction and the relative distance between these two impurities. Two critical relative distances are found between the two impurities. The first one corresponds to the vanishing of the perturbed energy with impurities, although the effective force between the two impurities still exists. At the second critical value, the energy of the impurities changes linearly with the atom-impurity interaction; otherwise, it changes quadratically with the atom-impurity interaction.

Key words: quantum gases, Bose-Einstein condensate, Bose polaron, mediated interaction

中图分类号:  (Ultracold gases, trapped gases)

  • 67.85.-d
67.85.Bc (Static properties of condensates) 71.38.Mx (Bipolarons)