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Two-body effective potential between impurities in ideal BEC

G. Panochko, V. Pastukhov

Published Sep 3, 2019• 0 citations
OpenAlex

Abstract

We exactly calculate the full temperature dependence of the Casimir-like forces appearing between two static impurities loaded in the ideal Bose gas below the Bose-Einstein condensation transition point. Assuming the short-ranged character of the boson-impurity interaction we show how to calculate properties of Bose system with arbitrary number of impurities immersed.

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We exactly calculate the full temperature dependence of the Casimir-like forces appearing between two static impurities loaded in the ideal Bose gas below the Bose-Einstein condensation transition point. Assuming the short-ranged character of the boson-impurity interaction we show how to calculate properties of Bose system with arbitrary number of impurities immersed.
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.
We consider two heavy particles immersed in a Bose-Einstein condensate in three dimensions and compute their mutual interaction induced by excitations of the medium. For an ideal Bose gas, the induced interaction is Newtonian up to a shift in distance, which depends on the coupling strength between impurities and Bosons. For a real BEC, we find that, on short distances, the induced potential is dominated by three-body physics of a single Boson bound to the impurities, leading to an Efimov potential. At large distances of the order of the healing length, a Yukawa potential emerges instead. In particular, we find that both regimes are realized for all impurity-boson couplings and determine the corresponding crossover scales. The transition from the real to the ideal condensate at low gas parameters is investigated.