Charges in a Bose-Einstein condensate

In recent years, rapid progress has been made in ultracold hybrid systems in which ions are embedded in neutral atom samples [1]. Originally investigated as a way to efficiently sympathetically cool ions by elastic collisions with ultracold atoms [2] due to the very long-range atom-ion polarization potential, it was realized that the charge exchange could play an important role in the case of identical ions and parent atoms.

Extension of this work to denser samples, like an ion immersed in an atomic Bose-Einstein condensate, predicted the formation of mesoscopic molecular ions [3]. Recent experiments used the Rydberg blockade mechanism [4] to obtain a single ion in a BEC [5].

Here, we describe how the induced polarization on atoms in a Bose-Einstein condensate create a dipolar polaron that effectively screen the impact of the ion. We show that the van der Waals atom-atom interaction is modified by a dipole-dipole interaction. We derive expression for the BEC wave function and show that the result is similar to the Clausius-Mossotti equation for polarizable medium. We give two interpretations of the result: a modified atom-atom scattering length or a modified atom polarizability. We discuss implications on the properties of ions in BECs and detection schemes.

[1] M. Tomza et al., RMP 91, 035001 (2019).

[2] R. Côté and A. Dalgarno, PRA 62, 012709 (2000).

[3] R. Côté, V. Kharchenko, and M.D. Lukin, PRL 89, 093001 (2002).

[4] M.D. Lukin et al., PRL 87, 037901 (2001).

[5] K.S. Kleinbach et. Al, PRL 120, 193401 (2018).