Fig. 1
From: Dispersion relation of the collective excitations in a resonantly driven polariton fluid
Illustration of the different fluid components and of the detection scheme. a The polariton condensate (red spot) of wavefunction \({\psi }_{0}\), and of radiative loss rate \({\gamma }_{{\rm{c}}}\) is resonantly excited by the laser of power P. An illustration of the condensate excitations \(\delta \psi ({\bf{k}},\omega )\) is shown in yellow in the dispersion plane, with its typical dispersion relation (DR) \(\omega (\vert {\bf{k}}\vert )\) shown in a black dashed line. The bare quantum well excitonic transition energy \(\hslash {\omega }_{{\rm{X}}}\) is shown as a green dashed line. An illustration of the typical quantum well excitonic density of state \({\rho }_{{\rm{R}}}(\omega )\) is shown as a purple line in b. Owing to their effective mass differences, \({\rho }_{{\rm{R}}}\)’s peak value exceeds the polaritonic density-of-state by 5 orders of magnitude. The low-energy tail of \({\rho }_{{\rm{R}}}(\omega )\) originates from disorder in the quantum well, and can accommodate a reservoir (green spot) of long-lived excitons (loss rate \({\gamma }_{{\rm{R}}}\), fluctuations \(\delta {n}_{{\rm{R}}}\) represented in light green). Interconversion of polaritons into reservoir excitons and back by optical absorption or scattering, occur at rates \({\gamma }_{{\rm{i}}n}\) and \({\gamma }_{{\rm{b}}k}\), respectively. c Sketch of the experimental setup used to measure the DR. The excitation laser light is linearly polarized by a Glan–Thompson polarizer (GT) and passed through a beam splitter (BS) to excite resonantly the polariton fluid. The cross-polarized reflected signal is selected by another GT and passed through a monochromator (M). The polariton emission at the laser frequency is further rejected by a metallic filter playing the role of notch filter (NF), and the remaining EPL is detected on a CCD camera. Some optical elements are omitted, that provide resolution on the EPL emission angle \(\theta \), and thus on its in-plane wavevector \(\vert {\bf{k}}\vert =(\omega /c)\sin (\theta )\) (\(\hslash \omega \) is the photon energy, and \(c\) the speed of light in vacuum)
