Motion of a distinguishable impurity in the Bose gas: Arrested expansion without a lattice and impurity snaking

TL;DR

This paper investigates the real-time dynamics of a distinguishable impurity in a Lieb-Liniger Bose gas, revealing phenomena like arrested expansion and snaking motion due to quantum interactions.

Contribution

It provides numerical analysis of impurity dynamics in the Lieb-Liniger model, highlighting novel behaviors without relying on analytical solutions.

Findings

Impurity undergoes stuttering expansion and motion.

Stationary impurity forms a quasibound state causing arrested expansion.

Moving impurity exhibits snaking motion due to momentum exchange.

Abstract

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.