Parallel dark-soliton pair in a bistable two-dimensional exciton-polariton superfluid

Collective excitations, such as vortex-antivortex and dark solitons, are among the most fascinating effects of macroscopic quantum states. However, two-dimensional (2D) dark solitons are unstable and collapse into vortices due to snake instabilities. Making use of the optical bistability in exciton-polariton microcavities, we demonstrate that a pair of dark solitons can be formed in the wake of an obstacle in a polariton flow resonantly supported by a homogeneous laser beam. Unlike the purely dissipative case where the solitons are gray and spatially separate, here the two solitons are fully dark, rapidly align at a specific separation distance, and propagate parallel as long as the flow is in the bistable regime. Remarkably, the use of this regime allows us to relax the phase fixing constraints imposed by the resonant pumping and to circumvent the polariton decay. Our work opens very wide possibilities for studying new classes of phase-density defects which can form in driven-dissipative quantum fluids of light.

Figure 1

Cavity dispersion and bistability. (a) Energy dispersion of the exciton-polariton emission when the microcavity is pumped with a nonresonant cw laser at 1.54 eV. The polariton density is in logarithmic scale. The bare photon and exciton dispersions are in yellow and red curves, respectively. The white dot corresponds to the position of the pump, slightly blue detuned from the lower polariton branch. (b) Theoretical calculations of the bistability loop according to the experimental parameters given in the text. (c) Output intensity distribution in the momentum space when the system is in the lower branch of the bistability loop and with an excitation at $k=1.2\mu {\mathrm{m}}^{-1}$ and energy 1482.4 meV. The orange dashed circle depicts the Rayleigh scattering ring, which is visible for longer integration time (higher contrast). (d) Output intensity distribution in the momentum space when the system jumps to the upper branch of the bistability loop. The scattering ring is now visible and it has a smaller radius compared to the one in panel (c).

Figure 2

(a) Experiment scheme with pump and support beams. The curve sketches the laser intensity along the propagation axis. (b) Intensity map of the polariton fluid flowing across a structural defect. The turbulences generated in the wake of the defect evolve into two parallel dark solitons. The red dotted line indicates the position of the transverse section presented in the inset. (c) Interference pattern associated to panel (b), showing a phase jump close to $\pi$ across the solitons. (d) Theoretical simulations (using the driven dissipative Gross-Pitaevskii equation) of the intensity map for parameters corresponding to those used in the experiment. (e) Theoretical interference pattern corresponding to panel (d).

Figure 3

Oblique solitons. (a) Intensity map of the polariton flowing across a structural defect and excited using a semicircular shaped pump upstream to the defect. The generated solitons in the wake of the defect are gray, as shown in the inset on top corresponding to the transverse section indicated by the red dashed line, and they propagate with increasing separation distance. (b) Interference pattern associated to panel (a). The phase jump is decreasing along the propagation as the solitons vanish. [(c), (d)] Panels are the theoretical simulations of the intensity and interference maps, respectively.

Figure 4

Dark solitons separation distance for parallel (black dashed line) and oblique (orange dashed line) solitons along their in-plane propagation. The black solid line is the fitting of the parallel solitons experimental data (see main text for further details).