The Casimir force in one dimension

In 1937 Fritz London showed how the van der Waals attraction between two atoms could be explained by quantum mechanical fluctuations in the ground-state positions of the molecules’ charged components (see the article by Steve Lamoreaux, Physics Today, February 2007, page 40 ). A decade later Hendrik Casimir, having cast the physics in terms of so-called vacuum fluctuations in the electromagnetic field, famously predicted that two perfectly conducting plates in a vacuum would attract each other. With real, imperfect conductors, the strength—and, in certain cases, the sign—of the interaction depends on the details of the conductors’ shape (see, for instance, Physics Today, February 2009, page 19 ). Now Ephraim Shahmoon and Gershon Kurizki (Weizmann Institute of Science) and Igor Mazets (Vienna University of Technology) have looked at the consequences of dimensionality: They examine what happens to vacuum forces between atoms in the vicinity of an electrical transmission line, such as a coaxial cable or coplanar waveguide, in which the quantum fluctuations are effectively confined to one dimension. The researchers find analytically that the fluctuation-mediated attraction between the atoms in such an environment is much stronger and longer range than in free space. When the interatomic separation z is small, the attraction decreases very slowly with z, compared with the 1/z⁶ dependence of the van der Waals attraction; at larger separations, it falls off as only 1/z³ instead of 1/z⁷. The trio predicts that even with imperfect conductors, the enhanced interactions should be observable, with potential applications in quantum information processing. (E. Shahmoon, I. Mazets, G. Kurizki, Proc. Natl. Acad. Sci. USA 111, 10485, (2014), doi:10.1073/pnas.1401346111 .)