Synchronized and Desynchronized Phases of Exciton-Polariton Condensates in the Presence of Disorder

Condensation of exciton polaritons in semiconductor microcavities takes place despite in-plane disorder. Below the critical density, the inhomogeneity of the disorder limits the spatial extension of the ground state. Above the critical density, in the presence of weak disorder, this limitation is spontaneously overcome by the nonlinear interaction, resulting in an extended synchronized phase. In the case of strong disorder, several non-phase-locked condensates can be evidenced. The transition from a synchronized phase to a desynchronized phase is addressed by sampling the cavity disorder.

Figure 1

(a) Real space luminescence of one single condensate taken at position 1 and (b) three independent condensates taken at position 2.

Figure 2

(a)–(b) and (e)–(f) Spectrally resolved real space line and (c)–(d) interferogram. Horizontal axis: Energy in electron volts. Vertical axis: Real space in microns. (a) Profile along $x=0$ line in Fig. 1a (position 1), at $P=0.4P_{\mathrm{thr}}$. At the same position, the ground state energy given by the spatially integrated dispersion curve is at 1.674 33 eV (dashed-dotted vertical line). The bottleneck appears on the same dispersion curve around 1.675 54 eV (dashed line). Small vertical lines: Energy of the ground state. (b) The same at $P=3P_{\mathrm{thr}}$. (c) Spectrally resolved interferogram at $P=0.1P_{\mathrm{thr}}$ and (d) the same at $P=1.2P_{\mathrm{thr}}$. (e) Profile along $x=0$ line in Fig. 1b (position 2), at $P=0.32P_{\mathrm{thr}}$. (f) The same at $P=2.88P_{\mathrm{thr}}$.

Figure 3

Frequency detuning for different pairs of spatially separated polaritons as a function of the excitation intensity. The experimental points are connected by lines. Points 1, 2, 3, and 4 belong to a single condensate (position 1), and points $1^{\prime }$ and $2^{\prime }$ belong to independent condensates (position 2).

Figure 4

Statistical study of the frequency detuning above threshold ($\Delta \nu$) as a function of the frequency detuning well below threshold ($\Delta {\Omega }_0$). Solid line: Nonsynchronized phase $\Delta \nu =\Delta {\Omega }_0$; the synchronized phase corresponds to $\Delta \nu =0$. Dashed line: $\Delta \nu =(\Delta {\Omega }_0^2-g^2{)}^{1/2}$, with $g=850\mu \mathrm{eV}$.