Dynamics of two-photon paired superradiance

TL;DR

This paper develops a dynamical theory for two-photon paired superradiance (PSR), demonstrating both explosive and weak phenomena through numerical simulations, and explores energy release and steady states in molecular systems.

Contribution

It introduces a semi-classical dynamical framework for PSR in dipole-forbidden transitions, including numerical demonstrations of explosive and weak superradiance phenomena.

Findings

Explosive PSR releases most stored energy in nanoseconds.

Numerical simulations show dependence on initial coherence and atom density.

System reaches a steady state with field condensates after PSR events.

Abstract

We develop for dipole-forbidden transition a dynamical theory of two-photon paired superradiance, or PSR for short. This is a cooperative process characterized by two photons back to back emitted with equal energies. By irradiation of 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 large signal of amplified output occurs with a time delay. The basic semi-classical equations in 1+1 spacetime dimensions are derived for the field plus medium system to describe the spacetime evolution of the entire system, and numerically solved to demonstrate 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 energy stored in the target. Our numerical simulations are performed using a vibrational transition $X^1\Sigma_g^+ v=1 \rightarrow 0$ of 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 of number density close to $O[10^{21}]$cm$^{-3}$ and of high initial coherence, the explosive event terminates at several nano seconds after the trigger irradiation, when the phase relaxation time of $> O[10]$ 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.