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 Physics and Astronomy School, University of Southampton, UK Laboratoire de Photonique et de Nanostructures, CNRS, Marcoussis, France A. F. Ioffe Institute, St-Petersburg, Russia LASMEA, Clermont-Ferrand, France

2. Energy Polariton nonlinearities Interaction between excitons ↔ energy shift Phase space filling C X RR Energy Transmission UPB LPB RR UPB LPB k Excitonic component is responsible for polariton non-linear effects RR RR X C C X RR Energy renormalization vs saturation Energy shift Saturation 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

3. Polariton nonlinearities: polarization effects Energy shift in linear polarization  E L =n(  1 +  2 )/2 Interaction depends on spin energy shift depends on the spin of polaritons Energy shift in circular polarization  E C =n  1  >0 ↔ repulsion, blue shift  <0 ↔ attraction, red shift + 11 + 22 + + +

4. Polariton energy shift from transmission experiments 100 fs Spectral filtering sample f demolulation 10 meV 25 meV Babinet- Soleil compensator spectrometer +PM 1 ps chopper depolarising fiber We look for the power dependence of transmission in linear and circular polarizations Or EOM T and/or T c -T l GaAs  cavity, In 0.5 Ga 0.95 As QW, GaAs/Ga 0.9 Al 0.1 As Bragg mirrors 23 pairs/29pairs  R =3.5 meV 30  m spot

5. “Mixed” dichroism  ~0 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 “Mixed” dichroism at very low powers : P >15  W

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 Blue shift, almost no broadening in both polarizations Negligible shift and broadening in linear polarization Red → linear Black → circular (T-T 18  W ) / (T+T 18  W )

9. Ratio between interaction constants  Large dispersion=poor precision at zero and strong negative detunig   2 and  1 have different sign  |  2 | increases when detuning changes from negative to zero Red → linear Black → circular  E L =n(  1 +  2 )/2  E C =n  1

10. Tentative explanation Different contribution to the interaction constants  1 (↑ ↑) and  2 (↑ ↓) Spin independent contributions: 1)Mean field electrostatic energy (Repulsion) 2)Van-der-Waals (dipole-dipole) interaction (Attraction) Spin dependent contributions: 1)Exchange interaction (Repulsion for ↑ ↑ and Attraction for ↑ ↓) 2)Bi-exciton state (Attraction) ↑ ↓  1 n=U Coulomb +U VdW +U ex↑↑  2 n=U Coulomb +U VdW +U ex↑↓ +U bi EC=1nEC=1n  E L =(  1 +  2 )n

11. U Coulomb U bi U ex↑↓ U VdW U ex↑↑  2 n = U Coulomb +U VdW + U ex↑↓ + U bi  1 n = U Coulomb +U VdW + U ex↑↑ calculated Fit of  E C measured Fit of    

12. Conclusions The question remains open, whether only 2 polariton interaction constants are sufficient. Experiment aswers YES and theory NO. If |  2 |~|  1 | and  2 <0 this can have important implications I. A. Shelykh et al, SST (2010)