Entangled phonons in atomic Bose-Einstein condensates

We theoretically propose the measurement of phonon entanglement as a tool to study the quantum dynamics of atomic Bose-Einstein condensates. In particular, we show that nonseparability of the phonon modes offers a unambiguous signature of the quantum origin of the phonon emission by analog Hawking and dynamical Casimir processes. The method is numerically validated by applying a generalized Peres-Horodecki criterion to a truncated Wigner description of the condensate. Viable strategies to implement the proposed scheme in state-of-the-art experiments are discussed.