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We present a new paradigm in the field of cavity QED by bringing outremarkable features associated with the avoided crossing of the dressed statelevels of the Jaynes Cummings model. We demonstrate how the parametriccouplings, realized by a second order nonlinearity in the cavity, can turn thecrossing of dressed states into avoided crossings. We show how one can generatecoherence between the avoided crossing of dressed states. Such coherencesresult, for example, in quantum beats in the excitation probability of thequbit. The quality of quantum beats can be considerably improved byadiabatically turning on the parametric interaction. We show how these avoidedcrossings can be used to generate superpositions of even or odd Fock stateswith the remarkable property of equal weights for the states in superposition.The fidelity of generation is more than 95\%. In addition, we show strongentanglement between the cavity field and the qubit with the concurrenceparameter exceeding 90\%.

Parametric interaction induced avoided dressed state crossings in cavity  QED:generation of quantum coherence and equally weighted superposition of  Fock states