The Dynamical Casimir Effect in quasi-one-dimensional Bose condensates: the breathing ring

We present a detailed investigation of one of the cleanest examples where it is possible to detect the “analog” Dynamical Casimir Effect in a Bose–Einstein condensate: an ultracold atom gas in toroidal confinement. The analytical solution of the time dependent Gross–Pitaevskii equation allows to follow the time evolution of the phonon spectrum and shows that periodic oscillations of the ring radius do not induce modulations in the density profile but give rise to the mixing of clockwise and anticlockwise modes, leading to the creation of pairs of entangled phonons in a squeezed vacuum state, if the drive frequency equals twice the frequency of the phonon mode. The Dynamical Casimir Effect is predicted to occur in the weakly interacting regime, where the Gross–Pitaevskii equation provides a faithful description of the many body dynamics. In the strong coupling limit, when the ultracold gas behaves as hard core bosons, the effect disappears and no amplification occurs. The presence of symmetry-breaking perturbations and finite temperature effects are also considered, as well as the comparison with the classical phenomenon of parametric amplification.