  Recent experiments have employed rapidly expanding toroidal Bose-Einstein
condensates (BECs) to mimic the inflationary expansion in the early universe.
One expected signature of the expansion in such experiments is spontaneous
particle creation (of phonons) which is observable in density-density
correlations. We study entanglement of these particles, which are known to
result in a two-mode squeezed state. Using techniques for Gaussian states of
continuous variable systems, we quantify the entanglement generated in this
system, including effects such as decoherence and the use of an initially
squeezed state, which can suppress and enhance entanglement, respectively. We
also describe a protocol to experimentally measure the correlations entering
the covariance matrix, allowing an experimental quantification of the
entanglement properties of the inflationary BEC.
