Coherent superposition mediating energy flow between fundamental and third-harmonic modes

We predict a coherent superposition mediating a significant periodic energy flow between the fundamental and third-harmonic modes. It is found for the linearly polarized electromagnetic field, where a lower bound $S$ state $|g\ensuremath{\rangle}$ is coupled to an upper bound $S$ state $|b\ensuremath{\rangle}$, where the energy difference between these states is about two photons and the coupling occurs due to the above threshold ionization from these states together. Exceptional point on complex quasienergy surfaces of the dressed resonances $|g\ensuremath{\rangle}$ and $|b\ensuremath{\rangle}$ indicates coherent superposition that manifests itself dynamically as the Rabi cycle. The cycle is irreversible, being gradually quenched by the above threshold ionization while emitting strong third-harmonic and fundamental pulses. We provide a numerical evidence confirming the existence of such a process in the helium atom.