Mobile Impurities and Orthogonality Catastrophe in two-dimensional Vortex Lattices

We investigate the properties of a neutral impurity atom coupled with the Tkachenko modes of a two-dimensional vortex lattice Bose-Einstein condensate. In contrast with polarons in homogeneous condensates, the marginal impurity-boson interaction in the vortex lattice leads to infrared singularities in perturbation theory and to the breakdown of the quasiparticle picture in the low energy limit. These infrared singularities are interpreted in terms of a renormalization of the coupling constant, quasiparticle weight and effective impurity mass. The divergence of the effective mass in the low energy limit gives rise to an orthogonality catastrophe which is manifested as a power law singularity in the impurity spectral function.