Strong and Weak coupling at resonance

The criteria for strong coupling is based, as in the other cases we study in this work, on the splitting of the bare excitonic energies (degenerate at resonance, when $\omega_{E1}=\omega_{E2}=0$ ) into dressed states. This is manifested in the appearance of oscillations in the two-time correlators and a splitting of the peaks that compose their spectrum. The four peaks are always positioned symmetrically in two pairs around the bare energy ( $\omega_p\neq 0$ for all ). From Eq. (4.19), we know that $\omega_p$ are given by $\pm\Re{(z_{1,2})}$ . Therefore,

$\displaystyle \Re{(z_{1})}\neq 0\quad\mathrm{and}\quad\Re{(z_{2})}\neq 0$

(4.24)

is the mathematical condition for SC in this system. Given that there are two different parameters

and

on which the condition relies, the SC/WC distinction that sufficed with bosons must be extended to cover new possibilities. Instead of one relevant parameter, $\Gamma_-/g$ , as was the case of the LM, the type of coupling between two 2LSs, depends on a set of three parameters

$\displaystyle \{\Gamma_-/g\,,\,\Gamma_+/g\,,\,G/g=D^s\}\,.$

(4.25)

Subsections