Pattern Formation in One-Dimensional Polaron Systems and Temporal Orthogonality Catastrophe

Recent studies have demonstrated that higher than two-body bath-impurity correlations are not important for quantitatively describing the ground state of the Bose polaron. Motivated by the above, we employ the so-called Gross Ansatz (GA) approach to unravel the stationary and dynamical properties of the homogeneous one-dimensional Bose-polaron for different impurity momenta and bath-impurity couplings. We explicate that the character of the equilibrium state crossovers from the quasi-particle Bose polaron regime to the collective-excitation stationary dark-bright soliton for varying impurity momentum and interactions. Following an interspecies interaction quench the temporal orthogonality catastrophe is identified, provided that bath-impurity interactions are sufficiently stronger than the intraspecies bath ones, thus generalizing the results of the confined case. This catastrophe originates from the formation of dispersive shock wave structures associated with the zero-range character of the bath-impurity potential. For initially moving impurities, a momentum transfer process from the impurity to the dispersive shock waves via the exerted drag force is demonstrated, resulting in a final polaronic state with reduced velocity. Our results clearly demonstrate the crucial role of non-linear excitations for determining the behavior of the one-dimensional Bose polaron.

Automated summary

Recent studies have shown that higher than two-body bath-impurity correlations are not crucial for quantitatively describing the ground state of the Bose polaron. In this study, the Gross Ansatz approach is used to investigate the stationary and dynamical properties of the one-dimensional Bose-polarn with different impurity momenta and bath-impurity couplings. The results demonstrate the transition of the equilibrium state from the quasi-particle Bose polaron regime to the collective-excitation stationary dark-bright soliton with varying impurity momentum and interactions. The temporal orthogonality catastrophe is observed after an interspecies interaction quench, provided that bath-impurity interactions are stronger than intraspecies bath ones. This catastrophe is caused by the formation of dispersive shock wave structures associated with the zero-range character of the bath-impurity potential. Additionally, a momentum transfer process from the impurity to the dispersive shock waves via the exerted drag force is demonstrated for initially moving impurities, resulting in a final polaronic state with reduced velocity.