Casimir interaction between mobile impurities in one-dimensional quantum liquids

Michael Schecter, Dimitri M. Gangardt, Alex Kamenev

Jean-Noël Fuchs, Alessio Recati, W. Zwerger

Oleksandr Gamayun, Evgeni Burovski, Vadim Cheianov +1 more

Y. Tsukamoto, T. Fujii, N. Kawakami

Michael Schecter, Alex Kamenev

Virtual phonons of a quantum liquid scatter off impurities and mediate a long-range interaction, analogous to the Casimir effect. In one dimension the effect is universal and the induced interaction decays as 1/r3, much slower than the van der Waals interaction ∼1/r6, where r is the impurity separation. The sign of the effect is characterized by the product of impurity-phonon scattering amplitudes, which take a universal form and have been seen to vanish for several integrable impurity models. Thus, if the impurity parameters can be independently tuned to lie on opposite sides of such integrable points, one can observe an attractive interaction turned into a repulsive one.

Jean-Noël Fuchs, Alessio Recati, W. Zwerger

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.