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Recent studies have demonstrated that higher than two-body bath-impuritycorrelations are not important for quantitatively describing the ground stateof the Bose polaron. Motivated by the above, we employ the so-called GrossAnsatz (GA) approach to unravel the stationary and dynamical properties of thehomogeneous one-dimensional Bose-polaron for different impurity momenta andbath-impurity couplings. We explicate that the character of the equilibriumstate crossovers from the quasi-particle Bose polaron regime to thecollective-excitation stationary dark-bright soliton for varying impuritymomentum and interactions. Following an interspecies interaction quench thetemporal orthogonality catastrophe is identified, provided that bath-impurityinteractions are sufficiently stronger than the intraspecies bath ones, thusgeneralizing the results of the confined case. This catastrophe originates fromthe formation of dispersive shock wave structures associated with thezero-range character of the bath-impurity potential. For initially movingimpurities, a momentum transfer process from the impurity to the dispersiveshock waves via the exerted drag force is demonstrated, resulting in a finalpolaronic state with reduced velocity. Our results clearly demonstrate thecrucial role of non-linear excitations for determining the behavior of theone-dimensional Bose polaron.

Pattern formation in one-dimensional polaron systems and temporal orthogonality catastrophe