## Casimir interaction between mobile impurities in quantum liquids    [PDF]

Michael Schecter, Alex Kamenev
The concept of vacuum energy has fascinated minds ever since the inception of quantum theory. Though initially thought as being an inconsequential redefinition of the ground state energy, Casimir showed in 1948 that it actually leads to important observable phenomena. He showed that vacuum fluctuations of the electromagnetic field lead to a weak attractive force between neutral conducting plates. The effect was observed by Blokland and Overbeek in 1978 and later by Lamoreaux in 1996. This discovery paved the way for studies of generalized fluctuation-induced interactions that extend beyond simple plane geometries and linear electromagnetic media. Here we show that impurities propagating in quantum liquids (\emph{e.g.}, Bose-Einstein condensates of cold atoms) experience Casimir interactions mediated by quantized Goldstone (sound) modes or phonons. Besides changing the zero-point energy, mobile impurities may absorb momentum from vacuum fluctuations. This leads to a qualitatively different Casimir potential, which in d-dimensions scales with the separation $r$ as $1/r^{2d+1}$. In one dimension the effect is strongest: the induced potential decays as $1/r^3$, much slower than the van der Waals interaction, $1/r^6$. Moreover, the proportionality coefficient is universally expressed through thermodynamic parameters and changes sign upon tuning through lines of exactly-solvable models in parameter space. We show that the effect is well within the accuracy of current experiments with atomic impurities embedded in 1d condensates.
View original: http://arxiv.org/abs/1307.4409