Stationary Quantum Vortex Street in a Driven-Dissipative Quantum Fluid of Light

We investigate the formation of a new class of density-phase defects in a resonantly driven 2D quantum fluid of light. The system bistability allows the formation of low-density regions containing density-phase singularities confined between high-density regions. We show that, in 1D channels, an odd (1 or 3) or even (2 or 4) number of dark solitons form parallel to the channel axis in order to accommodate the phase constraint induced by the pumps in the barriers. These soliton molecules are typically unstable and evolve toward stationary symmetric or antisymmetric arrays of vortex streets straightforwardly observable in cw experiments. The flexibility of this photonic platform allows implementing more complicated potentials such as mazelike channels, with the vortex streets connecting the entrances and thus solving the maze.

Figure 1

(a) Polariton bistability: density as a function of the pump (red, green); DW velocity (black, right $Y$ axis). (b) Inhomogeneous pump: profile of the laser intensity (red curve), polariton density (black curve).

Figure 2

Modulational instability of guided solitons. $L=25\mu \mathrm{m}$. $S=0.25S_c$, $P=1.25$, $2S_c$ (top, bottom). Columns: (1) Stationary solution with even number of solitons between the high-density walls. (2) Imaginary part of the energy of weak excitations of the stationary solution from the first column as a function of $k_y$. (3),(4) Stationary solution after the development of the modulational instability (density, phase) in the presence of weak disorder. Frame colors correspond to the color of points in Fig. 3.

Figure 3

Phase diagram vs support $S$ and pump $P$. The color shows the maximal instability wave vector $k_y^{*}$. Green tones are for long-period antisymmetric excitations (snakes) and orange and red tones are for symmetric excitations with a shorter period. The lower left corner separated by the blue curve corresponds to the four-soliton initial state. The dark gray area is for oscillating in time solitons and violet is for high density in channels (no solitons). Colored dots correspond to the panels in the boxes of the same color in Fig. 2. The blue dot is for the maze pathfinding regime (Fig. 4). (Insets) Transverse profiles of unperturbed density in the channel.

Figure 4

Maze solving. (a) Initial moments: soliton heads repelled from dead-ends. (b) Stationary final distribution (maze solved). (c) DW repelled from the dead-end: confinement and particle flows. (d) Support threshold vs channel width for dead-end (blue) and open end (red).