Figure 1

(a) Mapping of the sample reflectivity spectra as function of the radial position with respect to the center of the planar microcavity wafer. The intensity is normalized to the LP resonance absorption and given in arbitrary units. The dispersion of the coupled QW-microcavity system shows a pronounced anticrossing behavior and strong coupling associated with a vacuum Rabi splitting of 9.5 meV. (b) Time-integrated false-color images of the Fourier-space plane are presented for excitation power densities of 1.0, 1.5, and 3.5 times the threshold pump power density $P_{\mathrm{th}}$. A cross-sectional view with normalized intensity is projected (solid white line) for each excitation power density with FWHM values decreasing from 10 to 1 μm${}^{-1}$. (c) In analogy, false-color images of the real-space projection, a microscopy view on the sample surface, are displayed for the same excitation power densities. Again, cross-sectional views, both $x$ and $y$ cut, are projected (solid lines). The dotted line represents the shape at $P_{\mathrm{th}}$ for comparison. Shiny spots originate from laser back scattering.Reuse & Permissions

Figure 2

(a) Time-integrated energy-momentum dispersion of polariton modes at a detuning Δ $=$ 2.8 meV (${\left|X\right|}^2$ ≈ 64$\%$), for different threshold-normalized pump powers. Each Fourier-space spectrum (rendered with lighting) is normalized to its maximum intensity and split into two linked parts with linear (left) and logarithmic (right) intensity profiles. Projected lines show the corresponding polariton dispersion (LP, dashed, white), and a virtual cavity mode (C*, dotted, green) aligned to the ground state. Black dots mark the maximum intensities for each $k$ vector. The pump power increases from left to right. In between, 2D real-space spectra for pump densities $P/P_{\mathrm{th}}=1$.0, 1.5, and 2.0 are displayed, from left to right, with the same energy scale which show the spatial distribution of emission. (b) Pump-power-dependent first-order spatial coherence represented by interference patterns in the Fourier-space spectrum (a), which is generated by applying a double-slit corresponding to a 3-μm spatial separation in the real-space plane projection. As a guide to the eye, the LP dispersion (dashed, white) is drawn into the linear intensity profile spectra.Reuse & Permissions

Figure 3

(a) Scheme of two-spot interference indicating the slit separation in real space. (b) Representative fringes acquired from back-scattered light from the pump laser spot in the phase space ($k_x$ vs $k_y$) or $E$-$k$ diagram ($k_x$ vs $E$) with interference fringe visibility >90$\%$. (c) $k$-space-oriented ground-state cross sections of the FF double slit spectra shown in Fig. 2b. (d) First-order spatial coherence $g^{\left(1\right)}\left(r\right)$ of a polariton condensate at 1.7 and 3.5 $P_{\mathrm{th}}$. With increasing spatial separation $r$ of emitters the measured values surpass 1/e (dotted line) at 3 and 4 μm (vertical dashed lines), respectively, which represent the spatial coherence length $d_c$ at the given pump densities. Solid lines indicate the exponential decay as guides for the eye.Reuse & Permissions

Figure 4

(a) Input-output diagram showing the pump-power-dependent nonlinear increase of time-integrated emission from the LP ground state $k$ $=$ (0 ± 0.2) $\mu {\mathrm{m}}^{-1}$. Blue open circles represent the (integrated) intensities below and above threshold, normalized to the threshold value. Close to threshold individual double-mode fitting of the LP signal was necessary to match the data acquired from the pulsed signal with time integration. Data from the stronger mode associated with emission from the condensate (black) and from the uncondensed LP mode (light blue) are plotted with half-filled circles. The relative energy shift of these modes is plotted in the same diagram with triangles. (Inset) Condensate fraction $n_0/n$ vs $P/P_{\mathrm{th}}$. (b) Linewidth of the power-dependent polariton signal as a measure of first-order temporal coherence. In addition, the first-order spatial coherence $g^{\left(1\right)}\left(r\right)$ measured with the double slit corresponding to a 3-μm spatial separation [cf. Fig. 2b] is plotted in the same graph (stars, right scale).Reuse & Permissions

Figure 5

(a) Measured polariton dispersions below and above threshold corresponding to pump powers ranging from 0.05 to 4.2 $P_{\mathrm{th}}$, labeled by white open symbols. The uncondensed LP dispersion (white dotted) and a virtual cavity dispersion (C*, black dotted) as well as a broader parabola (∼$k^2$, gray/light blue dotted) aligned to the condensate ground-state are drawn into the image. (b) Linear slope $\Delta E$/$\Delta k$ extracted from the dispersion region at $k$ $=$ 1 $\mu {\mathrm{m}}^{-1}$ vs $P/P_{\mathrm{th}}$ above threshold. (c) Bare exciton and photon mode energies which allowed for best dispersion fits. (d) Effective polariton mass vs $P/P_{\mathrm{th}}$. (e) Fitted condensate dispersion for respective pump rates 1.5 and 3.0 $P_{\mathrm{th}}$ (logarithmic intensity profile). (f) Estimated polariton population $N$($k$) for the modes presented in (a) and (e) normalized to the $k$ $=$ 0 value showing a pronounced occupation of the ground state above threshold. (g) In analogy to (f), the estimated polariton population $N$($E$) with respect to the corresponding ground-state energy $E_0$ is depicted and demonstrates strong spectral narrowing of the population distribution above threshold and a transition from Maxwell-Boltzmann (MB) distribution (dotted gray line with $T_{\mathrm{LP}}=25$ K) and a Bose-Einstein-like (BE) distribution (dashed gray curve with $T$ $=$ 5.5 K and $\mu =-2.8$ μeV, cf. Ref. 36). Populations are each normalized to the ground-state value for clarity.Reuse & Permissions

Figure 6

(a) Presentation of the time-averaged second-order time correlation $G^{\left(2\right)}\left(\tau \right)$ acquisition in the Fourier-space configuration with representative FF spectrum and corresponding NF image with spatial selection of ≈20 μm. The white circle indicates the fiber aperture, which acts as an E-k filter for light analyzed by a fiber-coupled HBT. (b) Pump-power-dependent autocorrelation function $G^{\left(2\right)}(\tau =0)$ measured with an HBT setup for the pulsed polariton ground-state emission in the FF projection. (Inset) Representative correlation histogram.Reuse & Permissions