Dynamics of the Formation and Decay of Coherence in a Polariton Condensate

We study the dynamics of the formation and decay of a condensate of microcavity polaritons. We investigate the relationship among the number of particles, the emission linewidth, and its degree of linear polarization, which serves as the order parameter. Tracking the condensate formation, we show that coherence is not determined only by occupation of the ground state, bringing new insights into the determining factors for Bose-Einstein condensation.

Figure 1

Experimental results on the dynamics of BEC formation after the arrival of the nonresonant pulse. (a) Emission energy from the ground state ($k=0$) as a function of time (left) and the corresponding photoluminescence intensity (right). The color code goes from black, no emission, to red, intense emission, saturating in a black central region. (b) Spectral line shapes extracted from (a). (c) In blue dots, average condensate population $n_0$ (normalized photoluminescence intensity); in purple squares, linewidth ${\kappa }_0$ (meV) of the emission peak, limited by the spectral resolution of $\sim 0.1\mathrm{meV}$; in brown rhombus, degree of linear polarization $D_l$. Times for coherence buildup ($t_1$), maximum population ($t_2$), and coherence ($t_3$) are marked with dashed lines. Inset: Polarization polar plot at $t=t_3$ with maximum coherence for the present case (I) and for a second point in the sample (II).

Figure 2

Hysteresis in $D_l$ (a) and ${\kappa }_0$ (c) as a function of $n_0$, with time running in the sense of the arrows. (a) Three experiments are shown with increasing excitation powers (the one under study in brown rhombus). (b) Growth with power of the delay between maximum population and coherence for these three cases. The linewidth of Ref. 3, under cw excitation, is given in (c) (dashed green line) for comparison.

Figure 3

(a) Theoretical results: $n_0$ (blue line), $D_l$ (brown line), and ${\kappa }_0$ (purple line), as a function of time (rescaled to picoseconds for comparison). In (b), the maximum $\max (n_0)$, $\max (D_l)$, and minimum $\min ({\kappa }_0)$ values reached in the simulations as the effective pulse narrows (with increasing $1/\Delta t_{\mathrm{pulse}}$) down to the case in (a). The delay $t_3-t_2$ between $\max (n_0)$ and $\max (D_l)$ is plotted in (c).