Point 3: decoherence and saturation

**Figure 5.29:** Point 3 of Fig. 5.13. Spectral emission for the indicated electronic pumping $P_\sigma/g$ : $10^{-3}$ (1st column), $\approx0.23$ (2nd), $\approx7.56$ (3rd) and (4th, quenching), for (thick line with no coloring), $\approx0.20$ , $\approx0.81$ and $\approx1.42$ as indicated in the top left panel, and similarly for others (apart from the case , inner peaks corresponds to higher pumpings). In this system, broadening is always too high to allow any manifestation of the underlying Jaynes-Cummings structure. The structure could be mistaken for a bosonic system (or the other way around). Cavity pumping helps observation of the vacuum Rabi doublet in the same way as of the linear Rabi doublet for the LM (see Fig. 5.30).
$\includegraphics[width=\linewidth]{chap5/JC/fig15-SpecPt3.ps}$

Finally, we turn to point 3 of Fig. 5.13, i.e., to the case with high dissipation rates. In this case, as shown in Fig. 5.29, the Jaynes-Cummings structure is not probed and the spectra are mere doublets closing in the WC. A small cavity pumping again helps to resolve them. The main physics at work here is the one that has been amply detailed in Chapter 3, in the LM, namely, the effective quantum state realized in the system by the interplay of pumpings and decay. In Fig. 5.30 we plot the LM spectra for the pumping cases that lead to a SS, for comparison with the first two columns in Fig. 5.29. The LM is always in SC for these $\gamma_{a,b}/g$ , and leads to a Rabi doublet in both channels of emission at all pumpings that is much better resolved in the presence of cavity pumping . In both models, therefore, photon-like quantum state has dispersive corrections that push apart the dressed states (Lorentzians) and therefore enhances the visibility and splitting of the lines.

Although the spectral features found in this system are those of the LM (doublet/singlet), the actual spectra differ greatly out of the linear regime. Increasing further brings the JCM into WC with a singlet in the emission, while it cannot induce such transition in the LM, that remains a doublet and in SC.

**Figure 5.30:** Linear model spectra for the system in Point 3 of Fig. 5.13. (a)-(b) correspond to cavity spectra and (c)-(d) to exciton spectra. The pumpings vary as in the two first columns of Fig. 5.29 for comparison with the JCM. The color code goes: blue, purple, brown and green, from low to high . Note that the spectrum changes non monotonically.
$\includegraphics[width=.45\linewidth]{chap5/JC/Sa1.eps}$ $\includegraphics[width=.45\linewidth]{chap5/JC/Sa2.eps}$ $\includegraphics[width=.45\linewidth]{chap5/JC/Sd1.eps}$ $\includegraphics[width=.45\linewidth]{chap5/JC/Sd2.eps}$

A fundamental difference between the models is that the bosonic pumps , , always reduce the total broadening of the lines ( $\Gamma_+$ ) while $P_\sigma$ increases it. The contribution of pump to the line positions differs greatly from the bosons, as not only $P_\sigma$ carries a different sign but also this contribution depends on the manifold. The statistics make also an important difference. Opposite to the wide variety of photon distributions found with a fermion model, cavity and exciton are always in a thermal state for bosons, without quenching or really lasing. The issue of the underlying statistics could therefore be settled in photon-counting experiment. Fig. 5.14 shows that such systems (especially when $\gamma_a\gg1$ and $\gamma_\sigma\rightarrow0$ ) have the advantage over better cavities that at low electronic pumping and vanishing cavity pumping, the system generates antibunched light, suitable for single-photon emitters (though not on demand).