All-optical control of quantized momenta on a polariton staircase

Here we demonstrate a simple and reconfigurable way to create a polariton condensate in well defined discrete momentum states, allowing us to manipulate the local polariton flow. To this end, we created a spatially varying potential formed in the presence of noncondensed carriers by subjecting a microcavity to spatially modulated nonresonant optical excitation. The choice of the spatial shape of this potential allows us to tailor the properties of the polariton condensate in momentum space. Our results demonstrate a way to prepare a polariton condensate in an adjustable momentum state and provide a first step toward the creation of functional all-optical elements for polaritonic logic circuits on demand by projecting circuits onto an unprocessed planar sample.

Figure 1

(a) Real-space shape of the excitation spot used. (b) Intensity profile integrated along the $y$ axis. The red line gives a three-point-smoothed guide to the eye. The blue line gives the target spatial shape of the excitation spot used as the input for the SLM. (c) Normalized real-space intensity profile integrated along the $y$ axis on a logarithmic scale. There is still a significant amount of emission up to 20 $\mu$m away from the steep edge of the staircase potential, indicating polariton expansion away from the pump spot.

Figure 2

(a) Polariton momentum-space pattern of the uncondensed lower polariton branch. (b) Polariton momentum-space pattern in the condensed regime. Discrete momentum states occur in the $k_x$ direction. (c) Intensity distribution along $k_y$ for three values of $k_x$ in the condensed regime. The line at $k_x=0.45$ $\mu$m${}^{-1}$ shows a double-peaked shape and differs significantly from the other lines. (d) Center positions of the maxima in momentum space seen in the condensed regime. The solid line gives a power-law fit unambiguously showing the square-root dependence.

Figure 3

(a)–(c) Polariton momentum-space distributions in the condensed regime at central energies of 4.2, 6.3, and 8.4 meV above the lower polariton ground state. (d) Polariton momentum-space distributions corresponding to (a) (black), (b) (red) and (c) (blue) integrated along $k_y$. Green-dashed lines indicate the maxima with index numbers 1, 4, and 6, respectively. (e), Center positions of the maxima in momentum space. The solid lines represent power-law fits.

Figure 4

Real (a) and momentum-space (b) emission pattern of a polariton condensate created by an ideal staircase-shaped pumping spot taking only geometrical broadening into account. Real- (c) and momentum-space (d) emission pattern of a polariton condensate created by an imperfect staircase-shaped pumping spot taking only geometrical broadening into account. The smoothed edge along the $y$ axis causes a large broadening in momentum space.

Figure 5

Spatially resolved real-space emission pattern emitted from the microcavity for pump densities below (left panel) and above (right panel) the transition to the weak coupling regime. The upper row shows the emission pattern at large blueshifts early in the pulse. The lower row gives the emission patterns at smaller blueshifts 90 ps (left side) or 120 ps (right side) later.