The impact of the injection protocol on an impurity's stationary state

TL;DR

This paper investigates how the injection protocol influences the stationary state and end velocity of an impurity in a one-dimensional quantum gas, revealing a protocol-dependent emergent motion beyond traditional superfluidity models.

Contribution

It provides exact analytic results and numerical simulations showing the impurity's velocity depends on the injection protocol, extending understanding of impurity dynamics in quantum gases.

Findings

Impurity's end velocity ranges between zero and the speed of sound.

Injection protocol determines the impurity's stationary velocity.

Predicted phenomena are experimentally accessible in ultracold gases.

Abstract

We examine stationary state properties of an impurity particle injected into a one-dimensional quantum gas. We show that the value of the impurity's end velocity lies between zero and the speed of sound in the gas, and is determined by the injection protocol. This way, the impurity's constant motion is a dynamically emergent phenomenon whose description goes beyond accounting for the kinematic constraints of Landau approach to superfluidity. We provide exact analytic results in the thermodynamic limit, and perform finite-size numerical simulations to demonstrate that the predicted phenomena are within the reach of the existing ultracold gases experiments.