Soliton Instabilities and Vortex Street Formation in a Polariton Quantum Fluid

Exciton polaritons have been shown to be an optimal system in order to investigate the properties of bosonic quantum fluids. We report here on the observation of dark solitons in the wake of engineered circular obstacles and their decay into streets of quantized vortices. Our experiments provide a time-resolved access to the polariton phase and density, which allows for a quantitative study of instabilities of freely evolving polaritons. The decay of solitons is quantified and identified as an effect of disorder-induced transverse perturbations in the dissipative polariton gas.

Figure 1

Time evolution of density (upper panel) and phase (lower panel) of a polariton wave packet scattering on an engineered circular obstacle (solid circles) of $3\mu \mathrm{m}$ diameter. Polaritons are injected at $t=0\mathrm{ps}$ with a $1.5\mu {\mathrm{m}}^{-1}$ initial momentum and a pump power of 5 mW in the vicinity of the mesa (column I). Solitons (II) are visible few picoseconds later and are characterized by low density straight lines and a phase shift. The soliton decay (III) comes along with the breaking of the phase fronts and the formation of vortex streets (circular arrows). The latter is pointed out by the apparition of several density minima coinciding with phase singularities. The motion of vortices is tracked along the flow during polariton lifetime (IV).

Figure 2

Density map along the soliton direction $x_s$ versus time. After the pulse arrival at $t=0\mathrm{ps}$, the presence of a low density region stresses the nucleation of a soliton. Around $t=5\mathrm{ps}$ soliton decay occurs and the formation of vortices is highlighted by the appearance of periodic modulation of the density in the region previously occupied by the soliton. The inset plot shows the density and the phase profile along $y_s$ at $t=3\mathrm{ps}$ calculated at around $7\mu \mathrm{m}$ from the mesa center showing the characteristic soliton transversal shape and the phase jump across the minimum.

Figure 3

(a) Pump power versus soliton lifetime. Horizontal bars show the time window at which vortex street formation occurs. Central black spots highlight that soliton lifetime increases while decreasing the pump power. (b) Time evolution of the soliton amplitude $n_s$ over polariton fluid density $n_0$ for different pump powers. Maximum of the ratio is found in correspondence of the soliton decay into vortex streets (dashed vertical lines).

Figure 4

Snapshots of the numerical simulations, based on the generalized Gross-Pitaevskii equations for the nucleation and the decay of dark solitons. The $2\mu \mathrm{m}$ diameter negative potential of $-4\mathrm{meV}$ is indicated by a green circle. Flow direction is upstream. Random potential disorder is added in order to perturb solitons.