PROBING THE BOGOLIUBOV EXCITATION SPECTRUM OF A POLARITON SUPERFLUID BY HETERODYNE FOUR-WAVE-MIXING SPECTROSCOPY Verena Kohnle, Yoan Leger, Maxime Richard, Michiel Wouters, Marcia Portella-Oberli, Benoit Deveaud-Pledran

o Introduction o strong coupling: polaritons o sample o Motivation: excitation spectrum of a polariton superfluid o Heterodyne Four Wave Mixing (FWM) experiment o Experimental Results o Conclusion Outline

Introduction Motivation FWM experiment Experimental results Conclusion/ Outlook Strong coupling regime: Polaritons Polariton: quasi particle composed by a photon coupled to an exciton Microcavity  2D system for photons; Quantum well  2D system for excitons Polaritons are the new eigenstates of the system in the strong coupling regime Picture: Kasprzak et al. Nature (2006) Polaritons are composed bosons: Photonic content: provides high degree of coherence Excitonic content: interaction between polaritons

Introduction Motivation FWM experiment Experimental results Conclusion/ Outlook Sample Substrate (GaAs) 8nm QW In 0.04 Ga 0.96 As λ -cavity bottom DBR top DBR AlAs/GaAs – cavity which contains a 8 nm In 0.04 Ga 0.96 As quantum well (QW) Bragg mirrors: contain 26.5 and 20 pairs of alternated /4 layers of AlGaAs and AlAs wedged cavity spacer layer  the resonator frequency of the resonator can be varied by moving the laser spot over the sample rabi splitting: 3.4 meV space

Polariton superfluid: Bogoliubov dispersion feature of interactions:  blueshift of dispersion  BOGOLIUBOV Dispersion: linear at small k „ghost“ branch In experiment: up to now nobody was able to show the „ghost“ branch Polaritons : weakly interacting bose gas Introduction Motivation FWM experiment Experimental results Conclusion/ Outlook

Introduction Motivation FWM experiment Experimental results Conclusion/ Outlook State of the art Utsunomiya et al. Nature, 4, 700 (2008) No Bogoliubov ghost branch observed: A proposal as an answer: Wouters et al. Phys Rev B,79, (2009)

FWM I0I0 10 I 0 energy wavevector k 0-k 0 +k 0 Introduction Motivation FWM experiment Experimental results Conclusion/ Outlook our method: using heterodyne Four-Wave-Mixing (FWM) setup fs-laser  broad energy spectrum (~12meV)  normal and gohst branch are probed with the same laser pulse

Introduction Motivation FWM experiment Experimental results Conclusion/ Outlook Heterodyne FWM setup balanced detection best sensitivity spectral interferometry – amplitude & phase resolution balanced detection – background suppression Ref (0,0) Pump (0,  1 ) Trigger (k,  2 ) FWM (-k,2  1 -  2 ) Sample 2  1 -  2 Heterodyne Channels: A (  =0) B (  =  ) Lens Pinhole Miror to CCD

Introduction Motivation FWM experiment Experimental results Conclusion/ Outlook Bogoliubov: tracking the ghost branch ghost branch normal branch k=0 k = 1 µm -1

Introduction Motivation FWM experiment Experimental results Conclusion/ Outlook Dispersion of the Bogoliubov excitations evolution in k of the different branches: (delay integration between 5 – 6 ps) Gross-Pitaevskii equations: Equation for excitons: Equation for cavity photons:  x/p = exciton/photon wavefunction g = exciton-exciton interaction potential  x/p = decay rate of excitons/photons  R = Rabi splitting F(r,t)= pump laser field

k = 1 µm -1 Arb. Int. = 16 evolution in excitation power: delay time  =5.7ps) Bogoliubov: excitation power dependence Introduction Motivation FWM experiment Experimental results Conclusion/ Outlook

Introduction Motivation FWM experiment Experimental results Conclusion/ Outlook k = 1 µm -1 Arb. Int. = 16 ng 2 ng evolution in excitation power: delay time  =5.7ps) Bogoliubov: excitation power dependence

Introduction Motivation FWM experiment Experimental results Conclusion/ Outlook k = 1 µm -1 Arb. Int. = 16 evolution in excitation power: delay time  =5.7ps) Bogoliubov: excitation power dependence

Introduction Motivation FWM experiment Experimental results Conclusion/ Outlook conclusion & outlook  Observation of the Bogoliubov excitation spectrum of a polariton superfluid using heterodyne FWM spectroscopy  we demonstrate unambigously the excistence of the negative energy „ghost“ branch Outlook: 2D FT allows to characterice th apperence of the different resonances THANK YOU !