1. Polariton-polariton interaction constants M. Vladimirova S. Cronenberger D. Scalbert A. Miard, A. Lemaître J. Bloch A. V. Kavokin K. V. Kavokin G. Malpuech D. Solnyshkov Groupe d’Etude des Semiconducteurs, CNRS, Montpellier, France Laboratoire de Photonique et de Nanostructures, CNRS, Marcoussis, France Physics and Astronomy School, University of Southampton, UK A. F. Ioffe Institute, St-Petersburg, Russia LASMEA, Clermont-Ferrand, France

2. UPB UPB WR LPB LPB Saturation Energy shift X C C X Energy renormalization vs saturation WR Polariton nonlinearities Energy Excitonic component is responsible for polariton non-linear effects X C WR WR WR • Interaction between excitons ↔ energy shift • Phase space filling Transmission Energy • LPB and UPB are expected to shift in the same or in the opposite direction, depending on the mechanism of the non-linearity • Experimentally : energy shift appears well before saturation k

3. a1 + a2 + + + + Polariton nonlinearities: polarization effects Interaction depends on spin energy shift depends on the spin of polaritons Energy shift in circular polarization DEC=na1 Energy shift in linear polarization DEL=n(a1+a2)/2 a>0 ↔ repulsion, blue shift a<0 ↔ attraction, red shift

4. Polariton energy shift from transmission experiments 100 fs 1 ps Babinet-Soleil compensator depolarising fiber sample demolulation T and/or Tc-Tl Spectral filtering f 10 meV 25 meV Or EOM spectrometer +PM 30 mm spot chopper GaAs l/2 cavity, In0.5Ga0.95As QW, GaAs/Ga0.9Al0.1As Bragg mirrors 23 pairs/29pairs WR=3.5 meV We look for the power dependence of transmission in linear and circular polarizations

5. “Mixed” dichroism • Corcular polarisation spectrum is blue shifte with respect to circular polarization spectrum • UPB : smaller effect, but blue shift • LPB: MC is more transparent in circular polarization! • UPB: the effect is inversed d~0 “Mixed” dichroism at very low powers : P >15 mW

6. “Mixed” dichroism : explanation Question: Why at LPB the trasmission increases with power? Answer: Because of the exciton energy shift! When exciton energy increases LPB acquire more photonic character and thus better transmitted through the sample The situation is inversed at UPB Any tiny shift of the exciton energy is accompanied by the modification of transmission This is not the saturation of absorption!

7. How to measure the power and polarization dependent polariton shift • This shift is very small • It is masked by the strong variation of intensity • We can not go up to high power • Seems to depend on the detuning and excitation type (LPB or LPB+UPB) Normalize the intensity and look at the differential spectra

8. Measuring LPB shift (T-T18 mW) / (T+T18 mW) Red → linear Black → circular Blue shift, almost no broadening in both polarizations Negligible shift and broadening in linear polarization

9. Ratio between interaction constants Red → linear Black → circular • Large dispersion=poor precision at zero and strong negative detunig • a2 and a1 have different sign • |a2| increases when detuning changes from negative to zero DEL=n(a1+a2)/2 DEC=na1

10. a1n=UCoulomb+UVdW+Uex↑↑ a2n=UCoulomb+UVdW+Uex↑↓+Ubi DEL=(a1+a2)n DEC=a1n Tentative explanation Different contribution to the interaction constants a1 (↑ ↑) and a2 (↑ ↓) • Spin independent contributions: • Mean field electrostatic energy (Repulsion) • Van-der-Waals (dipole-dipole) interaction (Attraction) • Spin dependent contributions: • Exchange interaction (Repulsion for ↑ ↑ and Attraction for ↑ ↓) • Bi-exciton state (Attraction) ↑ ↓

11. Fit of DEC a1n = UCoulomb+UVdW + Uex↑↑ measured calculated Fit of a2/a1 a2n = UCoulomb+UVdW + Uex↑↓ + Ubi Uex↑↑ UCoulomb UVdW Uex↑↓ Ubi

12. Conclusions • The question remains open, whether only 2 polariton interaction constants are sufficient. Experiment aswers YES and theory NO. • If |a2|~|a1| and a2<0 this can have important implications I. A. Shelykh et al, SST (2010)