  Emission of matter wave jets has been recently observed in a Bose-Einstein
condensate confined by a cylindrical box potential, induced by a periodically
modulated inter-particle interaction (Nature {\bf 551}, 356 (2017)). In this
paper we apply the time-dependent Bogoliubov theory to study the quantum
dynamics and the correlation effects observed in this highly non-equilibrium
phenomenon. Without any fitting parameter, our theoretical calculations on the
number of ejected atoms and the angular density correlations are in excellent
quantitative agreement with the experimental measurements. The exponential
growth in time of the ejected atoms can be understood in terms of a dynamical
instability associated with the modulation of the interaction. We interpret the
angular density correlation of the jets as the Hanbury-Brown-Twiss effect
between the excited quasi-particles with different angular momenta, and our
theory explains the puzzling observation of the asymmetric density correlations
between the jets with the same and opposite momenta. Our theory can also
identify the main factors that control the height and width of the peaks in the
density correlation function, which can be directly verified in future
experiments.
