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). First the quasiparticle residue of a static impurity in an ideal BEC is shown to vanish with increasing particle number as a stretched exponential, leading to a bosonic orthogonality catastrophe. Then we introduce a variational ansatz, which recovers this exact result and describes the macroscopic dressing of the impurity including its back-action onto the BEC as well as boson-boson repulsion beyond the Bogoliubov approximation. This ansatz predicts that the orthogonality catastrophe also occurs for mobile impurities, whenever the BEC becomes ideal. Finally, we show that our ansatz agrees well with experimental results.N.G. is supported by a “la Caixa-Severo Ochoa” PhD fellowship. N.G. acknowledges the Span- ish Ministry MINECO (National Plan 15 Grant: FISI- CATEAMO FIS2016-79508-P, SEVERO OCHOA SEV- 2015-0522, FPI), European Social Fund, Fundaci ́o Cellex, Fundaci ́o Mir-Puig, Generalitat de Catalunya (AGAUR Grant 2017 SGR 1341 and CERCA/Program), ERC AdG NOQIA, EU FEDER, MINECO-EU QUANTERA MAQS, and the National Science Centre Poland (Symfo- nia Grant 2016/20/W/ST4/00314). R.S. is supported by the Deutsche Forschungsgemeinschaft (DFG, Ger- man Research Foundation) under Germany’s Excellence Strategy – EXC-2111 – 390814868. G.M.B. acknowledges financial support from the Independent Research Fund Denmark - Natural Sciences via Grant No. DFF - 8021- 00233B. This work was supported by the Simons Collab- oration on Ultra-Quantum Matter, which is a grant from the Simons Foundation (651440, VG). P.M. acknowl- edges the “Ram ́on y Cajal” program, Spanish MINECO (FIS2017-84114-C2-1-P), and EU FEDER Quantumcat.Peer ReviewedPostprint (author's final draft