Influence of exciton-exciton correlations on the polarization characteristics of polariton amplification in semiconductor microcavities

Based on a microscopic many-particle theory, we investigate the influence of excitonic correlations on the vectorial polarization state characteristics of the parametric amplification of polaritons in semiconductor microcavities. We study a microcavity with perfect in-plane isotropy. A linear stability analysis of the cavity-polariton dynamics shows that in the co-linear (TE-TE or TM-TM) pump-probe polarization state configuration, excitonic correlations diminish the parametric scattering process, whereas it is enhanced by excitonic correlations in the cross-linear (TE-TM or TM-TE) configuration. Without any free parameters, our microscopic theory gives a quantitative understanding how many-particle effects can lead to a rotation or change of the outgoing (amplified) probe signal’s vectorial polarization state relative to the incoming one’s.

Figure 1

(Color online) (a) Shown is the dependence of the cavity-polariton modes on the magnitude $k$ of the in-plane momentum. Depicted are the lower (LPB) and upper (UPB) polariton branches for TE (solid) and TM (dashed) cavity modes and the bare cavity and exciton (dotted) dispersions. For details on the modeling of the cavity modes, see Sec. 2. (b) Real and imaginary parts of the two-exciton scattering matrices $T\left(\Omega \right)$ in the co-circular (++) and counter-circular (+−) polarization state channels as defined in Appendix . [(a) and (b)] Results are shown for typical GaAs parameters (Ref. 35), as used throughout this work.

Figure 2

(Color online) Schematic of the excitation geometry. The plane of incidence is spanned by the wave vector of the incoming light field and the $z$ axis. All lines in this plane are solid. The quantum-well plane is the $x\text{−}y$ plane. All lines in this plane are broken. The figure shows the basis vectors ${\mathbf{e}}_{\mathrm{TE}}^{\text{in}-\text{plane}}$ and ${\mathbf{e}}_{\mathrm{TM}}^{\text{in}-\text{plane}}$ that span the projection of the TE-TM basis on the $x\text{−}y$ plane. The polar angle $\vartheta$ and azimuthal angle ${\phi }_{\mathbf{k}}$ are also shown. For more explanation, see text in Sec. 2.

Figure 3

(Color online) Top: coherent steady-state exciton density ${\mid p_{k_p}^Y\mid }^2$ for a fixed pump intensity of a linearly TE polarized pump as a function of the magnitude $k_p$ of the pump in-plane momentum and the pump detuning $\Delta \epsilon =\hslash {\omega }_p-{\epsilon }_0^x$ from the bare exciton resonance ${\epsilon }_0^x$. Middle and lower figures show the real part of the eigenvalue of $M_{\parallel }^{\mathrm{TE},\mathrm{TE}}$ and $M_{\perp }^{\mathrm{TE},\mathrm{TM}}$ with the largest real part in meV (maximum growth rate if larger than zero). The linear polariton dispersions are included as the dashed lines and the insets show the same data around the magic angle for pump excitation on the LPB.

Figure 4

(Color online) Same as Fig. 3 but for linearly TM polarized pump.

Figure 5

(Color online) Same as the two lower panels in Fig. 3 but without exciton-exciton scattering in the +− channel $({\tilde{\mathcal{T}}}^{+-}\equiv 0)$.