Observation of Attraction between Dark Solitons

We demonstrate a dramatic change in the interaction forces between dark solitons in nonlocal nonlinear media. We present what we believe is the first experimental evidence of attraction of dark solitons. Our results indicate that attraction should be observable in other nonlocal systems, such as Bose-Einstein condensates with repulsive long-range interparticle interaction.

Figure 1

(a) Trajectories of two attracting dark solitons separated at $60\mu \mathrm{m}$. (b) Initial intensity (solid line) and corresponding index structure (dashed line) generated by the nonlocal nonlinear response, giving rise to attractive (dashed arrows) and repulsive forces (solid arrows) on the solitons. (c) Trajectories of two closely spaced dark solitons ($20\mu \mathrm{m}$) with dominating repulsive interactions.

Figure 2

(a) Calculated output separation ($z=50\mathrm{mm}$) vs initial separation between two dark solitons for low ($I_0=0.01$—squares) and high ($I_0=0.5$—circles) intensity of the background beam. The different regimes of interaction are marked. (b), (c) Output intensity (bottom) and index (top) profiles for two different initial separations—(b) repelling solitons ($20\mu \mathrm{m}$) and (c) attracting solitons ($90\mu \mathrm{m}$).

Figure 3

Experimental setup: M, mirrors; GS, glass slides; BE, beam expander; T, imaging telescope; P, pellicle; IL, imaging lenses; A, attenuator; NLM, nonlinear medium; CCD, cameras.

Figure 4

Measured output distance between two dark solitons as a function of their initial separation. Dots—nonlinear regime (3.5 W); squares—linear propagation (10 mW). For small initial separations the output dark notches are practically not detectable in the linear regime. Inset—interferogram reflecting the initial phase and intensity profile of solitons separated by $59\mu \mathrm{m}$.

Figure 5

(a) Measured output separation of interacting nonlocal dark solitons in thermal medium as a function of the propagation distance for input separation of $117\mu \mathrm{m}$—closed circles; $101\mu \mathrm{m}$—open circles; $91\mu \mathrm{m}$—open triangles; $59\mu \mathrm{m}$—closed triangles. (b) Measured trajectories of nonlocal solitons for initial separation of $117\mu \mathrm{m}$.