An impurity immersed in a Bose condensate can form a quasiparticle known as a Bose polaron. When the impurity-boson interaction is short ranged and three-body Efimov correlations are neglected, the quasiparticle properties can be characterized in terms of the impurity-boson scattering length $a_{\mathrm{IB}}$ and the condensate coherence length $\xi$. This description remains valid irrespective of the bath density $n_0$. Long-ranged interactions—such as provided by Rydberg or ionic impurities—introduce an effective interaction range $r_{\mathrm{eff}}$ as the third length scale. The interplay among these competing length scales raises the question of whether a robust description across different bath densities can still be maintained. In this study, we discuss the quasiparticle nature of long-range impurities and its dependence on the length scales $n_0^{-1/3}, r_{\mathrm{eff}}$, and $\xi$. We employ two complementary theories—the coherent-state ansatz and the perturbative Gross-Pitaevskii theory—which incorporate beyond-Fröhlich interactions. We derive an analytical expression for the beyond-Fröhlich effective mass for a contact interaction and numerically compute the effective mass for long-range impurities. We argue that the coupling parameter $|a_{\mathrm{IB}}|n_0^{1/3}$ remains the principal parameter governing the properties of the polaron. For weak ($|a_{\mathrm{IB}}|n_0^{1/3}\ll 1$) and intermediate ($|a_{\mathrm{IB}}|n_0^{1/3}\simeq 1$) values of the coupling parameter, long-range impurities in a Bose condensate are well described as quasiparticles with a finite quasiparticle weight and a well-defined effective mass. However, the quasiparticle weight becomes significantly suppressed as the effective impurity volume is occupied by an increasing number of bath particles ($r_{\mathrm{eff}}{n}_0^{1/3}\gg 1$).

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• Bose gases
• Bose-Bose mixtures
• Polarons
• Bose-Einstein condensates
• Ions
• Rydberg atoms & molecules