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Physical Review A

Publisher's Note: Oscillating Casimir force between impurities in one-dimensional Fermi liquids [Phys. Rev. A75, 043615 (2007)]

Jean-Noël Fuchs, Alessio Recati, W. Zwerger

Published May 7, 2007• 1 citation
Publisher
DOI
10.1103/physreva.75.059904

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Publisher's Note: Effect of the Casimir-Polder force on the collective oscillations of a trapped Bose-Einstein condensate [Phys. Rev. A70, 053619 (2004)]

Mauro Antezza, Лев П. Питаевский, S. Stringari

Received 2 December 2004DOI:https://doi.org/10.1103/PhysRevA.70.069901©2004 American Physical Society

Physical Review A•Dec 13, 2004•3 citations
We study the interaction of two localized impurities in a repulsive one-dimensional Fermi liquid via bosonization. In a previous paper [Phys. Rev. A 72, 023616 (2005)], it was shown that at distances much larger than the interparticle spacing the impurities interact through a Casimir-type force mediated by the zero-sound phonons of the underlying quantum liquid. Here we extend these results and show that the strength and sign of this Casimir interaction depend sensitively on the impurity separation. These oscillations in the Casimir interaction have the same period as Friedel oscillations. Their maxima correspond to tunneling resonances tuned by the impurity separation.
We discuss the effective interactions between two localized perturbations in one-dimensional quantum liquids. For noninteracting fermions, the interactions exhibit Friedel oscillations, giving rise to a Ruderman-Kittel-Kasuya-Yosida-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 an 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.