Quantized Vortices and Four-Component Superfluidity of Semiconductor Excitons

We study spatially indirect excitons of GaAs quantum wells, confined in a $10\mu \mathrm{m}$ electrostatic trap. Below a critical temperature of about 1 K, we detect macroscopic spatial coherence and quantized vortices in the weak photoluminescence emitted from the trap. These quantum signatures are restricted to a narrow range of density, in a dilute regime. They manifest the formation of a four-component superfluid, made by a low population of optically bright excitons coherently coupled to a dominant fraction of optically dark excitons.

Figure 1

(a) A 100 ns long loading laser pulse injects indirect excitons in a $10\mu \mathrm{m}$ electrostatic trap. The reemitted photoluminescence is analyzed in a 5 ns long detection window, at a variable delay to the end of the loading pulse, the sequence being repeated at 1.5 MHz for 10–20 s typical acquisition times. (b)–(e) Photoluminescence emitted from the trap, at $T_b=330\mathrm{mK}$, and for a delay of 150 ns so that the number of trapped excitons is $\sim 2\times 10^4$. Horizontal and vertical dashed lines highlight positions where we observe about 50% intensity loss along both the horizontal and vertical axis. This is shown by the profiles in (c)–(d) and (f)–(g) for the images shown in (b) and (e), respectively. Measurements have all been acquired successively for identical experimental settings, the acquisition time being 10 s.

Figure 2

Simulation of the interference pattern for a condensate with complete long-range order in the trap (a), and for a condensate constraining one quantized vortex at the center of the trap (b). Two phase singularities are observed in the latter case, on each side of a ring-shaped interference fringe. (c) Interference pattern measured when $\sim 2\times 10^4$ excitons are confined in the trap at $T_b=330\mathrm{mK}$. These experiments were realized in the same conditions as for the measurements shown in Fig. 1. (d)–(f) Red points show the interference profiles measured, as highlighted in (b), at the center of the ring (e), on its left (d) and right (f). The solid blue lines display the patterns simulated by modulating the profile of the photoluminescence intensity with an interference visibility equal to 23%, the interference contrast possibly varying from $\sim 12\%$ to 45% in our studies.

Figure 3

(a)–(c) Interference patterns measured for a decreasing exciton density in the trap at $T_b=330\mathrm{mK}$, 120 (a), 150 (b), and 200 ns (c) after extinction of the loading laser pulse. We estimate that the total number of excitons is about $4\times {10}^4$, $2\times {10}^4$, and ${10}^4$, respectively, the drawings on top illustrating the filling of the trap. The panels (d) to (f) show the corresponding interference profiles evaluated at the center of the trap (between the dashed lines). While in (d) our experiments do not reveal any interference, in (e) and (f) the interference visibility is 25% and 18%, respectively. Red points show experimental results and the blue lines the simulation obtained by modulating the intensity profile with the aforementioned visibilities.

Figure 4

Interference contrast measured at the center trap as a function of the bath temperature $T_b$. In (a) we show the visibilities measured in the regime where $2\times 10^4$ excitons occupy the trap, while the number of excitons is reduced to ${10}^4$ for the measurements shown in (b). Solid blue lines show the theoretically expected $1-(T/T_c{)}^2$ scaling of the condensate fraction, with $T_c\sim 1.3$ and 1 K for (a) and (b), respectively. In (a)–(b) the gray region marks the sensibility of our interferometric detection, i.e., the level fixed by the signal-to-noise ratio at the detection.