Spontaneous Pattern Formation in a Polariton Condensate

Exciton-polariton condensation can be regarded as a self-organization phenomenon, where phase ordering is established among particles in the system. In such condensed systems, further ordering can occur in the particle density distribution, under particular experimental conditions. In this work we report on spontaneous pattern formation in a polariton condensate under nonresonant optical pumping. The slightly elliptical ring-shaped excitation laser that we employ forces condensation to occur into a single-energy state with periodic boundary conditions, giving rise to a multilobe standing-wave patterned state.

Figure 1

(a) Experimental setup. The ring-shaped laser, obtained using an axicon lens, is focused on the sample through a 0.5 NA microscope objective. The same objective collects the PL signal, which is then sent to a modified Mach-Zehnder interferometer. The luminescence coming from the sample, shown in (b), is overlapped with a selected region of itself [marked by the red ellipse in (b) and (c]) to obtain the resulting interferogram (d). Note that the real-space density in (b) is acquired here for a pump power of $300\mu \mathrm{W}$, showing that the pattern remains identical for pump powers higher than the condensation threshold.

Figure 2

(a) Polariton density below condensation threshold under ring-shaped laser excitation. (b) Polariton density above condensation threshold. The spontaneous formation of a spatial pattern, made up of 12 lobes, can be clearly observed. (c) Phase map corresponding to the polariton density shown in (b) where a density contour plot is superimposed in order to allow identification of the density lobes in the phase structure. (d) Phase profile along the patterned density ring, where the phase jumps between successive lobes can be identified.

Figure 3

Results of the simulations performed with a generalized Gross-Pitaevskii-based model under nonresonant (slightly elliptical) ring-shaped laser excitation. (a) Polariton density of a 10-lobe spatial pattern and (b) phase distribution.