Mobile impurity in a Bose-Einstein condensate and the orthogonality catastrophe

We analyze the properties of an impurity in a dilute Bose-Einstein condensate (BEC). The quasiparticle residue of a static impurity in an ideal BEC is known to vanish exponentially with increasing particle number, leading to a bosonic orthogonality catastrophe. Here we introduce a conceptually simple variational ansatz for mobile impurities which accurately describes their macroscopic dressing in the regime close to orthogonality, including back-action onto the BEC as well as boson-boson repulsion beyond the Bogoliubov approximation. This ansatz predicts that the orthogonality catastrophe also occurs in the mobile case, whenever the BEC becomes ideal. Finally, we show that our ansatz agrees well with recent experimental results.

Automated summary

Research shows that in a dilute Bose-Einstein condensate, the quasiparticle residue of an impurity exponentially vanishes with increasing particle number, leading to an orthogonality catastrophe. By introducing a variational ansatz, it is possible to accurately describe the macroscopic dressing of mobile impurities, including their feedback onto the BEC and boson-boson repulsion beyond the Bogoliubov approximation. Furthermore, the prediction is made that the orthogonality catastrophe also occurs in the mobile case when the BEC becomes ideal, and experimental results have confirmed the accuracy of the ansatz.