Parapositronium atom in the field of annihilation and optical photons as a nonlinear quantum system

A parapositronium atom in an optical laser field is described beyond the perturbation theory framework by a closed system of Heisenberg equations on operators of atoms and photons. We consider the annihilation of the parapositronium atom, which starts from one or two quantum states; optical quantum transitions between these states are caused by one or two optical photons. Mean occupation numbers of these states are governed by a system of two nonlinear equations. We investigate particular stationary and nonstationary solutions of this system and find that annihilation photons substantially affect the annihilation process. We show that definite optical laser radiation may stabilize the parapositronium atom and make its lifetime hundreds of times longer than the lifetime of the free parapositronium atom in the $1s$ state.