Dynamics of Long-Range Ordering in an Exciton-Polariton Condensate

We report on time-resolved measurements of the first order spatial coherence in an exciton-polariton Bose-Einstein condensate. Long-range spatial coherence is found to set in right at the onset of stimulated scattering, on a picosecond time scale. The coherence reaches its maximum value after the population and decays slowly, staying up to a few hundred picoseconds. This behavior can be qualitatively reproduced, using a stochastic classical field model describing interaction between the polariton condensate and the exciton reservoir within a disordered potential.

Figure 1

Time integrated real space image of the exciton-polariton condensate emission at the output of the Michelson interferometer. The signal reflected by the two mirrors is marked by black circles. The doted vertical lines are guides to the eye coinciding with the minima of the interference fringes. The part of the photoluminescence in the middle of the overlapped region, at the position of the white solid line, was sent to a streak camera and resolved temporally.

Figure 2

Dynamics of first order correlation function $g^{(1)}$ between two lines of the condensate separated by $8.5\mu \mathrm{m}$ for excitation powers (a) $0.5P_0$, (b) $P_0$, (c) $1.4P_0$, and (d) $2P_0$, where $P_0$ is the threshold power. The color scale denotes the $g^{(1)}$ amplitude, white is used at the positions where the $g^{(1)}$ cannot be defined or at the position of the laser pulse at time $t=0\mathrm{ps}$.

Figure 3

Transient of population and coherence, dashed red line and black squares, respectively, for the average over $10\mu \mathrm{m}$ along the white solid line in Fig. 1, for excitation powers (a) $0.5P_0$, (b) $P_0$, (c) $1.4P_0$, and (d) $2P_0$, where $P_0$ is the threshold power. The gray line shows the estimated standard deviation of the fit coefficients obtained in the $g^{(1)}$ calculation. (e) and (f) illustrate the theoretical simulation results at and above threshold, respectively. Depicted here is the total polariton population at $-(\Delta x/2)$ and $(\Delta x/2)$ positions. The onset of the stimulated scattering is marked by the vertical dashed lines.

Figure 4

(a) Experimental and (b) theoretical results of buildup and decay of coherence as the population of polaritons is formed at threshold $P_0$ (green circles), $1.4P_0$ (blue triangles), and $2P_0$ (red squares). The time line is marked by arrows. For high excitation powers we evidence the appearance of a hysteresis between the rise and decay.