  We show how to generate bilinear (quadratic) Hamiltonians in cavity quantum
electrodynamics (QED) through the interaction of a single driven three-level
atom with two (one) cavity modes. With this scheme it is possible to generate
one-mode mesoscopic squeezed superpositions, two-mode entanglements, and
two-mode squeezed vacuum states (such the original EPR state), without the need
for Ramsey zones and external parametric amplification. The degree of squeezing
achieved is up to 99% with currently feasible experimental parameters and the
errors due to dissipative mechanisms become practically negligible.
