  The entanglement entropy of a free scalar field in its ground state is
dominated by an area law term. It is noteworthy, however, that the study of
entanglement in scalar field theory has not advanced far beyond the ground
state. In this paper, we extend the study of entanglement of harmonic systems,
which include free scalar field theory as a continuum limit, to the case of the
most general Gaussian states, namely the squeezed states. We find the
eigenstates and the spectrum of the reduced density matrix and we calculate the
entanglement entropy. Finally, we apply our method to free scalar field theory
in 1+1 dimensions and show that, for very squeezed states, the entanglement
entropy is dominated by a volume term, unlike the ground-state case. Even
though the state of the system is time-dependent in a non-trivial manner, this
volume term is time-independent. We expect this behaviour to hold in higher
dimensions as well, as it emerges in a large-squeezing expansion of the
entanglement entropy for a general harmonic system.
