Coexisting nonequilibrium condensates with long-range spatial coherence in semiconductor microcavities

Real- and momentum-space spectrally resolved images of microcavity polariton emission in the regime of condensation are investigated under nonresonant excitation using a laser source with reduced intensity fluctuations on the time scale of the exciton lifetime. We observe that the polariton emission consists of many macroscopically occupied modes. Lower-energy modes are strongly localized by the spatial polaritonic potential disorder on a scale of a few microns. Higher-energy modes have finite $k$ vectors and are delocalized over $10–15\mu \text{m}$. All the modes exhibit long-range spatial coherence comparable to their size. We provide a theoretical model describing the behavior of the system with the results of the simulations in good agreement with the experimental observations. We show that the multimode emission of the polariton condensate is a result of its nonequilibrium character, the interaction with the local polaritonic potential, and the reduced intensity fluctuations of the excitation laser.

Figure 1

(Color online) [(a) and (b)] Dispersion of the polariton emission below (a) and above (b) condensation threshold recorded for $X$ polarization. (c) The real-space intensity of the polariton luminescence averaged over mode size recorded for $X$ (thick line) and $Y$ (thin line) polarization above threshold and for $X$ polarization below threshold (dashed line).

Figure 2

(Color online) (a) Real-space spectrally averaged luminescence image for $X$ polarization. (b)–(f) Local spectra obtained from small regions in real space at positions shown by the arrows in panel (a).

Figure 3

(Color online) [(a)–(f)] State 1–6 momentum-space imaging at the energy of each mode.

Figure 4

(Color online) [(a)–(f)] State 1–6 real-space imaging at the energy of each mode.

Figure 5

(Color online) [(a)–(f)] Real-space imaging of the interference pattern of modes state 1–state 6.

Figure 6

(Color online) [(a)–(f)] Contrast of the interference pattern of each mode. In the blank regions, the measured intensity is very low giving a nondefined contrast.

Figure 7

(Color online) [(a) and (b)] Real-space correlation pattern. The blank regions are the regions where there is no intensity and thus the correlations lead to a high amplitude noise.

Figure 8

(Color online) (a) Disorder potential landscape used in the theoretical simulations and (b) energy spectrum from a simulation with the mean-field model (1) and (2). Multiple condensates are found in the simulation. The zero of the energy is the same as in (a). Values of parameters used in the simulations are $\hslash g=0.015\text{meV}\mu {\text{m}}^2$, $\hslash {\gamma }_c=0.5\text{meV}$, $\hslash {\gamma }_R=10\text{meV}$, $\hslash R\left[n_R\right]=\left(\text{meV}\mu {\text{m}}^2\right)\times n_R$ $\hslash g_R=0$, $\mathcal{G}=0$, and $P/P_{th}=2$.

Figure 9

(Color online) Momentum-space distribution of the polariton field at the corresponding peak frequencies in Fig. 8b.

Figure 10

(Color online) Real-space distribution of the polariton field at the corresponding peak frequencies in Fig. 8b.

Figure 11

(Color online) Real-space density of the calculated lowest-energy microcavity eigenstates that are localized within the excitation region. Modes A, B, and C can be identified with the three lowest condensate modes.

Figure 12

(Color online) Simultaneous representation of the density (height of the surface) and phase (color coding, lighter is higher phase) of the polariton condensate modes. Note that the phase difference between neighboring maxima is typically large.