  We study the entanglement dynamics in the system of coupled quantum fields.
We prove that if the coupling is linear, that is if the total Hamiltonian is a
quadratic form of field operators, entanglement can only be transferred between
the fields. We show that entanglement is produced in the model of the two-mode
self-interacting boson field with the characteristic Gaussian decay of
coherence in the limit of high number of particles. The interesting feature of
this system is that the particles in different modes become entangled even if
there is no direct interaction between the modes. We apply these results for
analysis of the entanglement dynamics in the two-mode Jaynes-Cummings model in
the limit of large number of photons. While the photon-atom interaction is
assumed to conserve helicity the photons with different polarizations still get
entangled due to an effective interaction mediated by the atom with the
characteristic entanglement time linearly increasing with the number of
photons.
