  Starting with the Hamiltonian formulation for spacetimes with two commuting
spacelike Killing vectors, we construct a midisuperspace model for linearly
polarized plane waves in vacuum gravity. This model has no constraints and its
degrees of freedom can be interpreted as an infinite and continuous set of
annihilation and creation like variables. We also consider a simplified version
of the model, in which the number of modes is restricted to a discrete set. In
both cases, the quantization is achieved by introducing a Fock representation.
We find regularized operators to represent the metric and discuss whether the
coherent states of the quantum theory are peaked around classical spacetimes.
It is shown that, although the expectation value of the metric on Killing
orbits coincides with a classical solution, its relative fluctuations become
significant when one approaches a region where null geodesics are focused. In
that region, the spacetimes described by coherent states fail to admit an
approximate classical description. This result applies as well to the vacuum of
the theory.
