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We present an analytic, and fully quantum theory of high harmonic generationby low frequency laser fields for a two-state hydrogenlike atom model. Themodel is valid for an arbitrary atomic potential role of dipole matrix elementsand can be generalized to describe laser fields of arbitrary polarization andincludes the depletion of states. In the case of an initial coherentsuperposition of two states, the theory clearly explains why high conversionefficiency can be obtained. Our results are based on quantum interferenceeffects in recombination via different states. We demonstrate that four quantumpaths of electron contribute in the harmonic spectrum. The harmonic conversionefficiency is directly proportional to the initial-state amplitudes anddepletion of the states (especially excited state), the remained population ofthe bound states at the time of recombination and the distinct dipolestrengths. The main contribution to high conversion efficiency is thetransition from the excited to the ground state.

Two states hydrogenlike model for High-Order Harmonic Generation and enhanced XUV Generation from a coherent superposition of bound states