Polariton gas excitations: from single- particle to superfluid

1. Yoan Léger Laboratory of Quantum Opto-electronics Ecole Polytechnique Fédérale de Lausanne Switzerland Polaritongas excitations:from single-particle to superfluid

4. Superfluidity & sound wave excitations Striking properties of superfluids Zero viscosity, Rollin film, foutain effect Quantized vortices…. Bogoliubov theory of the weakly interactingBose gas Elementary excitation are collective excitations! with sound wave behavior Woods et al. Rep. Prog. Phys.36 1135 (1973)

5. Superfluidity in the solid state Microcavity polaritons Momentum dispersion Cavity field UP Energy DBR Polariton UP QW Ph. Exciton X Spacing layer DBR LP LP In-plane momentum ~ Emission angle

6. Superfluidity in the solid state Microcavity polaritons Bose Einstein condensation Cavity field UP DBR Polariton QW Ph. Exciton X Spacing layer Kasprzak et al. Nature443, 409 (2006) DBR LP Coulomb interactions Polaritons should be superfluid!! Amo et al. Nat. Phys. 5, 805 (2009)

7. The superfluid dispersion Injecting polaritons at k=0 Linearization comes from the coupling of counter-propagating modes by interactions Appearance of a ghost branch

8. Naive picture of the ghost branch Sound wave in superfluid Diluted polariton gas Particle-hole superposition

9. Gross-Pitaevskii formalism Weakly interacting bosons: Normal branch Ghost branch Mean field theory: Linearization of interaction term: ωB uk2 gn=1meV εk0 vk2 k=1μm-1

10. Looking for the Ghost branch PL measurements Kind of linearization No ghost branch Utsunomiya et al. Nat. Phys. 4, 700 (2008) Accessing the ghost branch with FWM In the proposal: non-resonant condensate Wouters et al. Phys. Rev. B 79, 125311 (2009)

12. Polariton FWM Four wave mixing and selection rules Third order nonlinearity Angular selection rule Energy selection rule

13. Polariton FWM Four wave mixing and selection rules Third order nonlinearity Angular selection rule Energy selection rule Polariton FWM 2 fields : condensate field and probe field Stimulated parametric scattering of 2 polaritons from the condensate

14. Heterodyne FWM Problem: Condensate emission should largely dominate the spectrum How to extract useful signal when angular selection is not enough? Heterodyne FWM • Based on spectral interferometry • requires : • a full control of the excitation fields • Pulsed excitation to cover the full emission spectrum • provides: • best sensitivity, and selectivity • access to amplitude and phase of the nonlinear emission Heterodyne setup FWM Excitation fields Linear emission FWM

15. Coherent excitation Spectral interferometry Energy selection Pulsed resonant excitation Spectro Balanced detection AOM Pump FWM FWM 71 MHz Ref. Pump 75 MHz Ref. Trigger 79MHz 71 MHz Local Osc.. 79 MHz 75 MHz AOM AOM ω0 Trigger Trigger Sample Pump

16. Heterodyning Excitation Pulses Spectro Balanced detection AOM UP LP transmission FWM 71 MHz Ref. Pump 75 MHz Ref. Trigger 79MHz 71 MHz + local osc. @ 71MHz Local Osc.. Frequency comb: 79 MHz 75 MHz AOM AOM 80MHz pump ω0 FWM trigger NB 75MHz extracted FWM 71MHz GB Trigger Sample 79MHz Pump Energy

18. Dispersion & dissipation… Normal & ghost branch Damping of polariton density! Low density K=0 t1 NB GB t2 t3

19. Stating on the ghost branch? OPO experiment • Linear dispersion but off-resonances can always exist in FWM we have to go further! Savvidis et al. Phys. Rev. B. 64, 075311 (2001)

20. Nature of the excitations 1/2 Off-resonance or “real” ghost? Dissipative Gross-Pitaevskii equation with: Standard fluid Single particle excitations Superfluid Sound waves pump FWM trigger Always 2 energy modes: Ghost and normal branch Change of intensity and linewidth With polariton density 1/3 1

21. Nature of the excitations 2/2 Intensity dependence Redistribution of intensity Density of state on the ghost! GB k=0 NB Threshold!

23. Investigating the processes Delay dependence Th. Exp. Energy (eV) Delay between pulses (ps) pump pump Trig. Trig. FWM FWM t t Delay>0 Delay<0

24. 2D fourier transform spectroscopy Delay dependence LP UP ΩR Energy (eV) Delay between pulses (ps) Trigger energy (meV) delay pump Fourier transform on delay E(ωdet ,τ) E(ωdet , ωexc) Trig. FWM t

25. Conclusions & perspectives

26. acknowledgements To the audience! To my collaborators: Verena Kohnle, Michiel Wouters, Maxime Richard, Marcia Portella-Oberli, Benoit Deveaud-Plédran