Figure 1

(a) Momentum dispersions ${\epsilon }_B\left(\mathbf{k}\right)$ of Bogoliubov quasiparticle excitations (red plain curve) and free-particle excitations (black dashed line) of a 2D boson gas ($\frac{{\hslash }^2{k}^2}{2m}$). The transition from the phononlike (linear) to the free-particle (quadratic) regime takes place at $k\approx {\xi }^{-1}$. The excitation spectra are renormalized to the superfluid energy. (b) In the single-particle picture, Bogoliubov excitations show up as a couple of symmetric dispersions around the blue-shifted superfluid energy as a result of the Bogoliubov transformation. (c) Experimental FWM response of a quiescent ($k=0$) polariton quantum fluid after perturbation at $k=1\mu$m${}^{-1}$ (red line) revealing the normal and ghost branches of the Bogoliubov spectrum lying at $1485.1$ and $1484.2$ meV, respectively. The low-density $k=0$ resonance obtained from transmission measurements is plotted for comparison (black dotted line).Reuse & Permissions

Figure 2

Two-beam heterodyne FWM: experiment.Reuse & Permissions

Figure 3

(a) Structure of the high-quality GaAs-based microcavity sample, consisting of two AlGaAs/AlAs Bragg reflectors with an embedded InGaAs quantum well. (b) Measured anticrossing curve as a function of the cavity detuning. (c) Polariton dispersion curve obtained in photoluminescence at zero detuning.Reuse & Permissions

Figure 4

Experimental (a) and calculated (b) delay dependence of the FWM response for a perturbation of the polariton quantum fluid at $k=1$ $\mu$m${}^{-1}$ in log color scale.Reuse & Permissions

Figure 5

Delay time dependence of the spectrally resolved FWM signal without (a) and with a spectral filter centered on the LP dispersion (b).Reuse & Permissions

Figure 6

Dispersion of the polariton quantum fluid at short (0.3 ps) positive delay (black markers) and long (3.5 ps) positive delay (red open markers). The NB, ML, and GB are plotted with circles, squares, and triangles, respectively. The experimental fit of the single-particle low-density dispersion is also plotted with dashed line for comparison.Reuse & Permissions

Figure 7

Theoretical dispersion of a coherent polariton gas with and without dynamical blue-shift: Figures (a), (b), and (c) include the dynamical blue-shift and show the change to the asymmetric behavior in the dispersion with increasing damping. The upper red curve displays the NB and GB dispersions at the starting point of the time-integrated measurement $t_{int}=0$ and the lower blue curve displays the single-particle parabolic dispersion with its mirrored parabola. In (d), (e), and (f), the dispersion is shown without dynamical blue-shift for different damping rates. Here, the normal and ghost branches are symmetric and the replica have vanished. The slope of the NB in the figures without dynamical blue-shift is less steep than the corresponding one with dynamical blue-shift. The figure is taken from the additional information of Ref. 14.Reuse & Permissions