We consider the real time dynamics of an initially localized distinguishable impurity injected into the ground state of the Lieb-Liniger model. Focusing on the case where integrability is preserved, we numerically compute the time evolution of the impurity density operator in regimes far from analytically tractable limits. We find that the injected impurity undergoes a stuttering motion as it moves and expands. For an initially stationary impurity, the interaction-driven formation of a quasibound state with a hole in the background gas leads to arrested expansion -a period of quasistationary behavior. When the impurity is injected with a finite center of mass momentum, the impurity moves through the background gas in a snaking manner, arising from a quantum Newton's cradle-like scenario where momentum is exchanged back-and-forth between the impurity and the background gas.Introduction.-With recent experimental advances in the field of cold atomic gases, the physics of the onedimensional Bose gas is receiving an increasing amount of attention.1-15 These systems, in which one has unprecedented isolation from the environment and fine control of interparticle interactions, are excellent tools for examining novel phenomena arising from strong correlations.One such phenomenon which has piqued both theoretical 8,14,[16][17][18][19][20][21] and experimental 19,22 curiosity is the expansion dynamics of a gas of cold atoms. A number of surprising and interesting effects have been observed, of which arrested expansion (or self trapping)16-18 is of particular relevance to this work. A gas (bosons 19 or fermions 23,24 ) is released from a confining potential and allowed to expand on the lattice. Under this time evolution 'bimodal' expansion is observed: the sparse outer regions of the cloud rapidly expand whilst the dense central region spreads only very slowly. This can be partially understood by considering the limit of strong interactions: doubly occupied sites are high energy configurations which, thanks to the lattice imposing a finite bandwidth and energy conservation, cannot release their energy to the rest of the system and decay.
18With these recent experimental advances 25 has also come the ability to examine systems in which there is a large imbalance between two species; 6,7,9,26-29 a natural starting point for the study of impurity physics. This gives insight in to a diverse range of problems, 29 from the physics of polarons 27,30 to the x-ray edge singularity 31,32 and the orthogonality catastrophe. 33 The physics of impurities also plays an important role in the calculation of edge exponents in dynamical correlation functions 34 and in understanding the nonequilibrium dynamics following a local quantum quench.
13,35,36The experimental study of the out-of-equilibrium dynamics of a single impurity in the one-dimensional Bose gas has revealed rather rich physics: from how an impurity spreads when accelerated through a Tonks-Girardeau gas, 6 to how interactions effect oscillations in the size of a trapped out-of-e...