Nonlinear Spectroscopy of a Dissipative Polariton Quantum Fluid

After the observation of Bose-Einstein condensation in the solid state in 2006 and the demonstration on its superfluid character in 2009 the interest for the demonstration of the underlying elementary excitations – the Bogoliubov excitations – was growing. We dedicate this PhD thesis to the experimental study of Bogoliubov excitations in an coherent polaritons gas. This thesis initially introduces microcavity polaritons, which are quasiparticles composed by semiconductor excitons and microcavity photons. Afterwards we expose the Bogoliubov theory, which predicts sound-like excitations for a polariton quantum fluid. Thus, the excitations are no longer given by single polaritons but by collective excitations. In order to probe the Bogoliubov excitations, a heterodyne four-wave mixing (FWM) technique is used. Its theory and the experimental technique is described in this thesis. The main part of this thesis reports on the experimental study of Bogoliubov excitations in a polariton quantum fluid. First, the Bogoliubov character of the coherent polariton gas is evidenced through the observation of its normal and ghost branch emission resonances in the FWM spectrum. We then demonstrate the Bogoliubov transformation at the transition from single-particle excitation to collective excitation by increasing the polariton density. By probing the dispersion of the polariton quantum fluid, we evidence the expected linear behavior of the Bogoliubov excitations. Here, we also investigate the influence of dissipation on the Bogoliubov excitations of the coherent polariton gas. It yields a asymmetry between the Bogoliubov normal and ghost branch. However we demonstrate that, despite their dissipative character, microcavity polariton gases can be qualitatively described in the frame of Bogoliubov theory of quantum fluids. We then introduce the powerful technique of 2-dimensional Fourier transformation spectroscopy in order to analyze the different fundamental processes which are causing a FWM emission. Finally, we study the effect of polarization on the Bogoliubov excitations. The experimental findings, which are presented in this thesis, are confirmed by the theoretical predictions based on Gross-Pitaevskii calculations