Dynamical instability of a dark soliton in a quasi-one-dimensional Bose-Einstein condensate perturbed by an optical lattice

The motion of a dark soliton is investigated in a one-dimensional dilute Bose-Einstein condensate confined in a harmonic trap and an optical lattice. The harmonic trap induces a dynamical instability of the soliton, culminating in sound emission. The presence of the optical lattice enhances the instability, and in addition, dephases the emitted sound waves, thus preventing stabilisation of the soliton by sound reabsorption. This instability can be probed experimentally by monitoring the soliton oscillations under various lattice configurations, which can be realised by changing the intensity and angle between the laser beams that form the lattice. For short enough times, such that the emitted sound does not reinteract with the soliton, the power emitted by the soliton is found to be proportional to the square of the local soliton acceleration, which is in turn proportional to the deformation of the soliton profile.