Abstract
We explore the time evolution of two impurities in a trapped one-dimensional Bose gas that follows a change of the boson-impurity interaction. We study the induced impurity-impurity interactions and their effect on the quench dynamics. In particular, we report on the size of the impurity cloud, the impurity-impurity entanglement, and the impurity-impurity correlation function. The presented numerical simulations are based upon the variational multilayer multiconfiguration time-dependent Hartree method for bosons. To analyze and quantify induced impurity-impurity correlations, we employ an effective two-body Hamiltonian with a contact interaction. We show that the effective model consistent with the mean-field attraction of two heavy impurities explains qualitatively our results for weak interactions. Our findings suggest that the quench dynamics in cold-atom systems can be a tool for studying impurity-impurity correlations.
Highlights
Nature provides us with a multitude of highly imbalanced two-component systems in which the first component contains many more particles than the second one
We explore the time evolution of a Bose gas with two impurities initiated by a sudden change of the boson-impurity interaction strength
Our focus is on the dynamics of the impurities, which we analyze using the many-body correlated ML-MCTDHB method [38,39] and an effective model presented in Eq (10)
Summary
Nature provides us with a multitude of highly imbalanced two-component systems in which the first component contains many more particles than the second one. We investigate the possibility of detecting impurityimpurity interactions in weakly interacting one-dimensional Bose gases To this end, we study the quench dynamics that follows a rapid change of the boson-impurity interaction strength. Our work is in line with the previous studies on induced interactions in harmonically trapped static systems It extends them by investigating a corresponding dynamical problem. Note that the induced interaction in a harmonic trap is not Galilean invariant [29], which complicates the use of a Galilean invariant effective potential characteristic for a homogeneous environment As we show, this complication can be avoided by considering weakly interacting systems. Appendix B discusses the accuracy of the numerical data, and Appendix C elaborates on the effective two-body Hamiltonian
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