Spontaneous Coherence Buildup in a Polariton Laser

We describe theoretically the spontaneous buildup of the second-order coherence of light emitted by microcavities in the regime of polariton lasing. This effect reveals important changes in quantum statistics of exciton polaritons in the course of their condensation. The coherence may start rising even if the polaritons do not interact with each other, e.g., in a low density regime. It happens due to correlations between occupation numbers of the ground and excited states in the microcavity.

Figure 1

Time evolution of ground state population normalized to its steady state population $\langle n_{\mathbf{0}}\left(t\right)\rangle /n_{\mathrm{e}\mathrm{q}}$ (dotted line) and of coherence degree $\eta$ (solid line), for an initially empty ground state.

Figure 2

(a) Density plot of $p_{\mathbf{0}}\left(n_{\mathbf{0}}\right)$ as a function of time for an initially empty ground state. (b) Projections of $p_{\mathbf{0}}\left(n_{\mathbf{0}}\right)$ at three various times, still in a thermal state at initial times, $\approx 75\mathrm{p}\mathrm{s}$ (blue), in a fully grown coherent state in the steady state (red), and in the intermediary region where coherence is rising, $\approx 100\mathrm{p}\mathrm{s}$ (black).

Figure 3

Ground state population normalized to pump power $\langle n_{\mathbf{0}}\rangle /P$ and coherence degree $\eta$, in the steady state as a function of reduced pumping $P/P_{\mathrm{t}\mathrm{h}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{h}\mathrm{o}\mathrm{l}\mathrm{d}}$ (we find $P_{\mathrm{t}\mathrm{h}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{h}\mathrm{o}\mathrm{l}\mathrm{d}}=26\mathrm{W}/{\mathrm{c}\mathrm{m}}^{-2}$).