Dynamics of two-photon paired superradiance

We develop for dipole-forbidden transition a dynamical theory of two-photon paired superradiance (PSR). This is a cooperative process characterized by two photons emitted back to back with equal energies. By irradiating the trigger laser from two target ends, with its frequency tuned at the half energy between two levels, a macroscopically coherent state of medium and fields dynamically emerges as time evolves, and a large signal of amplified output occurs with a time delay. The basic semiclassical equations in 1 + 1 space-time dimensions are derived for the field-plus-medium system to describe the space-time evolution of the entire system and are numerically solved to demonstrate the existence of both explosive and weak PSR phenomena in the presence of relaxation terms. The explosive PSR event terminates accompanying a sudden release of most of the energy stored in the target. Our numerical simulations are performed using the vibrational transition X-1 Sigma(+)(g)upsilon = 1 -> 0 of a para-H-2 molecule and taking many different excited atom number densities and different initial coherences between the metastable and the ground states. In an example with a number density close to O(10(21) cm(-3)) and a high initial coherence, the explosive event terminates several nanoseconds after the trigger irradiation, when the phase relaxation time larger than O(10 ns) is taken. After PSR events the system is expected to follow a steady-state solution which is obtained by analytic means and is made of many objects of field condensates endowed with a topological stability.