It is a remarkable prediction of quantum field theory that the vacuum can generate real particles when boundary conditions are suddenly changed. Thus the 'dynamical Casimir effect' results in the spontaneous generation of photon pairs in an empty cavity with nonuniformly accelerating boundaries. Recent advances have permitted the realization of this effect, or analogs to it in a variety of systems, some of which will be discussed at this workshop. Bose Einstein condensates are attractive candidates in which to study acoustic analogs to such phenomena because their low temperatures promise to reveal quantum effects. I will discuss a recent experiment in our group to realize an acoustic analog to the dynamical Casimir effect by modulating the confinement of a Bose-Einstein condensate. We observe correlated pairs of Bogoliubov quanta, both phonon-like and particle-like, are excited by this modulation in a process that formally resembles parametric down conversion. I will discuss our current ideas on how to observe and quantify the degree of entanglement in the excitations we observe.
We present a theory of the density correlations that appear in an atomic Bose-Einstein condensate as a consequence of the emission of correlated pairs of Bogoliubov phonons by a time-dependent atom-atom scattering length. This effect can be considered as a condensed matter analog of the dynamical Casimir effect of quantum field theory. Different regimes as a function of the temporal shape of the modulation are identified and a simple physical picture of the phenomenon is discussed. Analytical expressions for the density correlation function are provided for the most significant limiting cases. This theory is able to explain some unexpected features recently observed in numerical studies of analog Hawking radiation from acoustic black holes.