Collisions of Dark Solitons in Elongated Bose-Einstein Condensates

We present experimental data showing the head-on collision of dark solitons generated in an elongated Bose-Einstein condensate. No discernable interaction can be recorded, in full agreement with the fundamental theoretical concepts of solitons as mutually transparent quasiparticles. Our soliton generation technique allows for the creation of solitons with different depths; hence, they can be distinguished and their trajectories be followed. Simulations of the 1D-Gross-Pitaevskii equation have been performed to compare the experiment with a mean-field description.

Figure 1

(a),(b) Scheme of the phase-imprinting method. A rectangular intensity profile as shown is imaged onto the condensate (a) to generate one soliton at each intensity step of the far-detuned light field. The sign of the detuning is chosen such that the solitons propagate to the edges of the condensate. Following Eq. (3), the depths $n_s$ of the emerging solitons (b) depend on the local background density $n_0$ and are different for the asymmetric configuration. (c) Evolution of the solitons in the trap. Absorption images of the BEC are integrated in the transverse directions to obtain the density distribution along the axial coordinate. The pictures show experimental snapshots of solitons shortly after creation (i), at the edges of the condensate (ii), and shortly before (iii), at (iv), and after collision (v).

Figure 2

Space-time plots of two solitons oscillating in a confining potential. Positions are normalized to the condensate extension to correct for quadrupole oscillations, which exhibit a relative amplitude of around 0.14 but do not couple to the soliton movement [23], and to reduce influences from fluctuations of the atom number. (a) Experimental observation. Time steps of evolution of the BEC in the trap are 2.5 ms. (b) A sinusoidal fit to the soliton positions at each time step. Note that the choice of asymmetric starting points of the two solitons results in different depths and therefore allows for the “identification” of the solitons as 1 (colored red, deeper, smaller oscillation amplitude) and 2 (colored blue, shallower, larger oscillation amplitude); see the text for details. The error bars in both time and position are well within the marks. (c) Numerical simulation of the 1D-GPE set to our parameters. Additional smaller solitons, only faintly visible in (a), can also be observed [13].

Figure 3

A close-up simulation of the collision with a resolution of 0.05 ms, given in the representation of Fig. 2b. Lines indicate trajectories without interaction.