Casimir forces between defects in one-dimensional quantum liquids

TL;DR

This paper explores the effective interactions between localized defects in one-dimensional quantum liquids, revealing a transition from Friedel oscillations to a universal Casimir-type interaction in repulsive fermionic systems, with implications for quantum information and cold atom experiments.

Contribution

It demonstrates that in 1D interacting fermionic systems, the defect interactions transition from Friedel oscillations to a universal Casimir-type form at long distances, depending only on sound velocity.

Findings

Friedel oscillations in non-interacting fermions lead to RKKY interactions.

In repulsive Luttinger liquids, interactions decay as a universal Casimir force inversely with separation.

Implications for long-range coupling of quantum dots in ultracold Fermi gases.

Abstract

We discuss the effective interactions between two localized perturbations in one-dimensional (1D) quantum liquids. For non-interacting fermions, the interactions exhibit Friedel oscillations, giving rise to a RKKY-type interaction familiar from impurity spins in metals. In the interacting case, at low energies, a Luttinger liquid description applies. In the case of repulsive fermions, the Friedel oscillations of the interacting system are replaced, at long distances, by a universal Casimir-type interaction which depends only on the sound velocity and decays inversely with the separation. The Casimir-type interaction between localized perturbations embedded in a fermionic environment gives rise to a long range coupling between quantum dots in ultracold Fermi gases, opening a novel alternative to couple qubits with neutral atoms. We also briefly discuss the case of bosonic quantum liquids in which the interaction between weak impurities turns out to be short ranged, decaying exponentially on the scale of the healing length.