Charged Bose polarons at finite momentum

Charged impurities in quantum fluids have unveiled new classes of strongly correlated many-body states across condensed matter, ultracold gases, and hybrid atom-ion platforms. While previous studies have primarily focused on their ground-state and static properties, much less is known about their finite-momentum behavior, which governs transport, dissipation, and quasiparticle stability. Here, we investigate the momentum-dependent properties of a charged Bose polaron using a diagrammatic approach within second-order perturbation theory, explicitly accounting for the finite-range nature of the ion-atom interaction. We show that the interaction range introduces a characteristic momentum scale at which many-body dressing and dissipation are maximized, leading to a non-monotonic behavior of the damping rate and quasiparticle energy. In the high-momentum regime, we uncover a scaling law $\Gamma_p \sim 1/p$, signaling the suppression of many-body dressing and the recovery of quasi-free impurity dynamics, in stark contrast to the divergent behavior predicted by contact-interaction perturbative treatments.