Mechanical resonances of mobile impurities in a one-dimensional quantum fluid

TL;DR

This paper investigates how two mobile impurities interact within a one-dimensional quantum fluid, revealing resonances and antiresonances in their mobility that could be observed in ultracold atom experiments.

Contribution

It introduces a model for impurity interactions in 1D quantum liquids and predicts observable mechanical antiresonances in impurity mobility.

Findings

Resonances and antiresonances in impurity mobility due to effective interactions.

Impurities can remain stationary at antiresonances despite external forces.

Predictions applicable to ultracold atom experiments.

Abstract

We study a one-dimensional interacting quantum liquid hosting a pair of mobile impurities causing backscattering. We determine the effective retarded interaction between the two impurities mediated by the liquid. We show that for strong backscattering this interaction gives rise to resonances and antiresonances in the finite-frequency mobility of the impurity pair. At the antiresonances, the two impurities remain at rest even when driven by a (small) external force. At the resonances, their synchronous motion follows the external drive in phase and reaches maximum amplitude. Using a perturbative renormalization group analysis in quantum tunneling across the impurities, we study the range of validity of our model. We predict that these mechanical antiresonances are observable in experiments on ultracold atom gases confined to one dimension.