  In this third of a series on quantum radiation, we explore the feasibility of
using the memories kept in a quantum field to decipher certain information
about the early universe. As a model study, we let a massless quantum field be
subjected to a parametric process for a finite time interval such that the mode
frequency of the field transits from one constant value to another. This
configuration mimics a statically-bounded universe, but not a continuously
evolving one. The field squeezed by this process should contain information of
the process itself. If an atom is coupled to the field after the parametric
process, its response will depend on the squeezing, and any quantum radiation
emitted by the atom will carry this information away so that an observer at a
much later time may still identify it. Our analyses show that 1) a remote
observer cannot measure the generated squeezing via the radiation energy flux
from the atom because the net radiation energy flux is canceled. However, 2)
there is a chance to identify squeezing by measuring the constant radiation
energy density at late times. The only restriction is that this energy density
is of the near-field nature. The second part of this paper focuses on 3) the
dependence of squeezing on the functional form of the parametric process. Via
several examples we demonstrate that the behavior of squeezing reflect
essential properties of the parametric process. In fact, striking features may
show up in complicated processes involving various scales. These analyses allow
us to establish the connection between properties of a squeezed quantum field
and the parametric process which does the squeezing. Therefore, 4) one can
construct templates to reconstitute the unknown parametric processes from the
data of measurable quantities subjected to squeezing. In a sequel paper these
results will be applied to a study of quantum radiations in cosmology.
