Dynamics of dark-soliton formation in a polariton quantum fluid

Polariton fluids have revealed huge potentialities in order to investigate the properties of bosonic fluids at the quantum scale. Among those properties, the opportunity to create dark as well as bright solitons has been demonstrated recently. In the present experiments, we image the formation dynamics of oblique dark solitons. They nucleate in the wake of an engineered attractive potential that perturbs the polariton quantum fluid. Thanks to time and phase measurements, we assess quantitatively the formation process. The formation velocity is observed to increase with increasing distance between the flow injection point and the obstacle which modulates the density distribution of the polariton fluid. We propose an explanation in terms of the increased resistance to the flow and of the conditions for the convective instability of dark solitons. By using an iterative solution of the generalized Gross-Pitaevskii equation, we are able to reproduce qualitatively our experimental results.

Figure 1

Dynamics of a 2D fluid passing an obstacle in the fluid frame, showing the formation of dark solitons. The obstacle moves with ${\vec{v}}_{\text{flow}}$, leaving behind perturbations which expand as circular waves and form dark solitons by tangential interference. The latter move in the $y_s$ direction with respect to the fluid frame, whereas they grow along the $x_s$ direction in the obstacle frame.

Figure 2

(a) Time evolution of the density of a polariton wave packet scattering on an engineered circular obstacle (green circle) of 3 $\mu$m diameter. Polaritons are injected at $t=0$ ps with a 1.5 $\mu$m${}^{-1}$ initial momentum in the vicinity of the mesa. The soliton dynamics is highlighted by white arrows. (b) Phase map of the polariton fluid 7.5 ps after the polariton injection, showing phase jump typical of DSs. (c) Density profile map along the direction of soliton growth $x_s$ vs time. (d) Density profiles at different times showing the growth of the DS along $x_s$.

Figure 3

Time evolution of the ratio $\frac{n_s}{n_0}$ for different experimental conditions. The inset is the variation of the relative soliton formation velocity $\frac{v_{\text{form}}}{v_{\parallel }}$ with the distance between the laser spot and the mesa.

Figure 4

Dependence of the formation velocity on the soliton relative amplitude $\frac{n_s}{n_0}$ calculated according to the theory of Ref. 23 (red line), measured experimentally (black dots) and numerically simulated (triangles).