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In this work we show how to engineer bilinear and quadratic Hamiltonians incavity quantum electrodynamics (QED) through the interaction of a single driventwo-level atom with cavity modes. The validity of the engineered Hamiltoniansis numerically analyzed even considering the effects of both dissipativemechanisms, the cavity field and the atom. The present scheme can be used, inboth optical and microwave regimes, for quantum state preparation, theimplementation of quantum logical operations, and fundamental tests of quantumtheory.Comment: 11 pages, 3 figure

Bilinear and quadratic Hamiltonians in two-mode cavity quantum electrodynamics