  In this work we first collect and generalize several existing
non-perturbative models for the interaction between a single two-level qubit
detector and a relativistic quantum scalar field in arbitrary curved
spacetimes, where the time evolution is given by simple-generated unitaries,
i.e., those generated by Schmidt rank-1 interaction Hamiltonians. We then
extend the relativistic quantum channel associated to these non-perturbative
models to include a very large class of Gaussian states of the quantum field,
that includes an arbitrary combinations of coherent and squeezing operations
(i.e., Gaussian operations) on the field. We show that all physical results
involving the non-vacuum Gaussian states can be rephrased in terms of
interaction with the vacuum state but with Gaussian operators applied to the
field operators via the adjoint channel, effectively giving a "Fourier
transformed" interpretation of the Gaussian operations in terms of the causal
propagators in spacetime. Furthermore, we show that in these non-perturbative
models it is possible to perform exact computation of the R\'enyi entropy and
hence, via the replica trick, the von Neumann entropy for the field state after
the interaction with the detector, without making any assumptions about the
purity of the joint initial states of the detector and the field. This gives us
a three-parameter family of "generalized cat states" of the field whose
entropies are finite and exactly computable.
