Polariton pumping and decay

Peter et al. (2005) anticrossing at resonance is asymmetric (Fig. 1.11). As is the case with quantum wells, the experimental situation may be privileging one polariton branch over the other. For a more complete fitting expression of the spectra, Lindblad terms for polariton decay $\mathcal{L}^{u},\mathcal{L}^{l}$ and pump $\mathcal{L}^{\ud{u}},\mathcal{L}^{\ud{l}}$ could be included in the master Eq. (2.71). The parameters, $\gamma_\mathrm{U},\gamma_\mathrm{L}$ and $P_\mathrm{U},P_\mathrm{L}$ , respectively would also be variables in the fit. The total master equation in terms of the photon and exciton operators would include crossed Lindblad terms defined as

$\displaystyle \mathcal{L}^{c+d}=2c\rho\ud{d}-\ud{d}c\rho-\rho\ud{d}c\,.$

(3.86)

The decay and pumping rate parameters need be recalculated summing the contributions from all kinds. This leads to asymmetric spectra at resonance, Fig. 3.20(a), for the same reason that the SE of a polariton is asymmetric in Fig. 3.5(b) when $n_{ab}(0)\neq 0$ . This is an interesting configuration to contrast with experiments. In Fig. 3.20(b)-(c), we show, for instance, how strongly some polariton pump can affect the transition into WC. In the model, the cross terms appear in the Rabi frequency as an imaginary part of the coupling, producing decoherence but also a detuning effect.

**Figure 3.20:** SS cavity spectra at resonance. (a): parameters of Peter et al. (2005) SC experiments ( $\gamma_a=0.4g$ , $\gamma_b=0.7g$ ) with some roughly estimated pumping ( and ) and a very small lower polariton contribution ( $P_\mathrm{L}=0.005g$ ). (b): Set of spectra increasing the cavity decay ( $\gamma_a=1,2,5,10$ from blue to green) with fixed $\gamma_b=0.1g$ , and . (c): Idem with some lower polariton contribution $P_\mathrm{L}=0.005g$ . Pumping the polariton does not prevent the transition into WC, but delays it.
$\includegraphics[width=0.2\linewidth]{chap3/pol/polariton-pumpa.eps}$ $\includegraphics[width=0.35\linewidth]{chap3/pol/polariton-pumpb.eps}$ $\includegraphics[width=0.35\linewidth]{chap3/pol/polariton-pumpc.eps}$