1. Yoan Léger Laboratory of Quantum Opto-electronics Ecole Polytechnique Fédérale de Lausanne Switzerland

2. Polariton SuperfluidityHeterodyne four wave mixingFrom standard fluid to superfluidity2d fourier spectroscopy

3. Polariton SuperfluidityHeterodyne four wave mixingFrom standard fluid to superfluidity2d fourier spectroscopy

4. Superfluidity & sound wave excitations Striking properties of superfluids Zero viscosity, Rollin film, foutain effect Quantized vortices…. Bogoliubov theory of the weakly interacting Bose 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 Spacing layer X Ph. UP LP Cavity field Exciton Polariton DBR QW DBR In-plane momentum ~ Emission angle Energy LP UP Momentum dispersion

6. Superfluidity in the solid state Bose Einstein condensation Kasprzak et al. Nature 443, 409 (2006) Coulomb interactions Polaritons should be superfluid!! Amo et al. Nat. Phys. 5, 805 (2009) Spacing layer X Ph. UP LP Cavity field Exciton Polariton DBR QW DBR Microcavity polaritons

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

8. Naive picture of the ghost branch Diluted polariton gas Sound wave in superfluid

9. Gross-Pitaevskii formalism Weakly interacting bosons: Mean field theory: εk0εk0 ωBωB uk2uk2 vk2vk2 Linearization of interaction term: k=1μm -1 gn=1meV Normal branch Ghost branch

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)

11. Polariton SuperfluidityHeterodyne four wave mixingFrom standard fluid to superfluidity2d fourier spectroscopy

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

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

14. 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 FWM How to extract useful signal when angular selection is not enough? Problem: Condensate emission should largely dominate the spectrum Heterodyne FWM Heterodyne setup Excitation fields Linear emission FWM

15. Coherent excitation Spectral interferometry Energy selection Pulsed resonant excitation Pump Trigger FWM AOM Spectro AOM 75 MHz 79 MHz Trigger Pump 71 MHz ω0ω0 Local Osc.. Sample Balanced detection FWM 71 MHz Ref. Pump 75 MHz Ref. Trigger 79MHz FWM 71 MHz Ref. Pump 75 MHz Ref. Trigger 79MHz

16. Heterodyning Excitation Pulses transmission + local osc. @ 71MHz 80MHz 75MHz pump 79MHz trigger 71MHz FWM Energy Frequency comb: AOM Spectro AOM 75 MHz 79 MHz Trigger Pump 71 MHz ω0ω0 Local Osc.. Sample Balanced detection FWM 71 MHz Ref. Pump 75 MHz Ref. Trigger 79MHz FWM 71 MHz Ref. Pump 75 MHz Ref. Trigger 79MHz LP UP extracted FWM GB NB

17. Polariton SuperfluidityHeterodyne four wave mixingFrom standard fluid to superfluidity2d fourier spectroscopy

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

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

20. Nature of the excitations1/2 Off-resonance or “real” ghost? Dissipative Gross-Pitaevskii equation with: pump FWM trigger Always 2 energy modes: Ghost and normal branch Change of intensity and linewidth With polariton density 1/3 1 Standard fluid Single particle excitations Superfluid Sound waves

21. Nature of the excitations2/2 GB k=0 NB Redistribution of intensity Density of state on the ghost! Intensity dependence

22. Polariton SuperfluidityHeterodyne four wave mixingFrom standard fluid to superfluidity2d fourier spectroscopy

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

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

25. Conclusions & perspectives Ghost branch of a superfluid In solid state, for the first time Transformation of the excitations Sound like dispersion Linear for the normal branch Assymmetry due to dissipation 2D fourier transform spectroscopy Highly powerful method Starting the process investigation…

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