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Chinese Physics B

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

Dong-Chen Zheng, Chun-Rong 春荣 Ye 叶, Ye Lin, Lin 林 Wen 文, Renyuan Liao

Published Jul 2, 2025• 0 citations

Abstract

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.

DOI: 10.1088/1674-1056/adea99

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We study the motion of a pointlike impurity in a Bose-Einstein condensate at

T=0

. By solving the Gross-Pitaevskii (GP) equation in a perturbative manner we calculate the induced mass of the impurity and the drag force on the impurity in three-, two-, and one-dimensional (1D) cases. The relationship between the induced mass and the normal mass of fluid is found, and coincides with the result of the Bogoliubov theory. The drag force appears for the supersonic motion of the impurity. In 1D the drag force is investigated also on the basis of the exact Lieb-Liniger theory, using the dynamic form factor, which has been evaluated by the Haldane method of the calculation of correlation functions. In this theory the force appears for an arbitrarily small velocity of the impurity. The possibility of measuring the form factor in existing experiments is noted.

We investigate the influence of a Bose–Einstein condensate (BEC) on the properties of immersed impurity atoms, which are trapped in an optical lattice. Assuming a weak coupling of the impurity atoms to the BEC, we derive a quantum master equation (QME) for the lattice system. In the special case of fixed impurities with two internal states the atoms represent a quantum register and the QME reproduces the exact evolution of the qubits. We characterize the qubit dephasing which is caused by the interspecies coupling and show that the effect of sub- and super-decoherence is observable for realistic experimental parameters. Furthermore, the BEC phonons mediate an attractive interaction between the impurities, which has an important impact on their spatial distribution. If the lattice atoms are allowed to move, there occurs a sharp transition with the impurities aggregating in a macroscopic cluster at experimentally achievable temperatures. We also investigate the impact of the BEC on the transport properties of the impurity atoms and show that a crossover from coherent to diffusive behaviour occurs with increasing interaction strength.