Macroscopic Two-Dimensional Polariton Condensates

We report a record-size, two-dimensional polariton condensate of a fraction of a millimeter radius free from the presence of an exciton reservoir. This macroscopically occupied state is formed by the ballistically expanding polariton flow that relaxes and condenses over a large area outside of the excitation spot. The density of this trap-free condensate is $<1\mathrm{polariton}/\mu {\mathrm{m}}^2$, reducing the phase noise induced by the interaction energy. Moreover, the backflow effect, recently predicted for the nonparabolic polariton dispersion, is observed here for the first time in the fast-expanding wave packet.

Figure 1

(a) Energy versus real-space polariton emission along one direction, starting from the center of the pumping spot, displaying the expanding polaritons and the bottom condensate. The white-dashed line indicates the Gaussian potential induced by the excitonic repulsive interactions under the laser spot. (b) Energy-resolved reciprocal-space emission measured above the condensation threshold. The energy scale in the vertical axes is the same as in (a). (c) Two-dimensional spatial emission map at $E=0.25\mathrm{meV}$. Two random misfit dislocations, separated by about $80\mu \mathrm{m}$, appear as horizontal dark lines in the figure.

Figure 2

The propagation speeds extracted by time-resolved measurements (blue dots) are compared to the polariton velocities as calculated from the LPB (green line). Faster expansions than expected are observed for energies below $E=1.7\mathrm{meV}$ due to the prevailing effect of relaxation from higher energy state.

Figure 3

(a) Two-dimensional spatial emission at a given energy with propagation against a natural defect ($E=0.5\mathrm{meV}$). (b)–(d) Particular cases of intensity oscillations against the defect with the characteristic angle of the defect shadow for different propagation velocities [$E=0.1$, 0.5, 1.1 meV in panels (b), (c), and (d), respectively]. (e) Energies versus wave vector extracted from the LPB (black line) and from the periodical spatial oscillations (blue dots). Polariton density as a function of energy is shown by the red line. (f) Intensity cross section of the emission along the white line in panel (d).

Figure 4

(a) Polariton density at a distance of $40\mu \mathrm{m}$ from the excitation spot as a function of energy for the same pump powers as in (b),(c). The threshold power is $P_{\mathrm{th}}=25\mathrm{mW}$. (b) Reciprocal-space linewidth as a function of power [same horizontal scale as in (c)]. (c) Population ratio between the lowest energy state and the whole continuum of states at $40\mu \mathrm{m}$ from the spot region, showing the nonlinear increase above the condensation threshold.

Figure 5

(a)–(c) Density in momentum space of the flow directed horizontally to the right. The excitation power increases from (a) to (c). At the inflection point, indicated by the red vertical line, the backflow appears as a polariton density whose $k$ vector is directed to the left ($k>0$). (d),(e) Real space density maps, taken as in Fig. 3, for expanding wave vectors below (d) and close (e) to the inflection point.