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In the limit of very low temperatures and tight transverse confinement, the dynamics of dark solitons in atomic Bose-Einstein condensates are fully controlled by the longitudinal confinement. Motion of the soliton in the harmonic trap leads to sound emission, with the soliton trajectories determined fully by the subsequent interaction between the soliton and
the emitted sound. In previous work, we have shown how to modify the amplitude of soliton-sound interactions by allowing the emitted sound to de damped out [1], or 'dephased' [2], which can be achieved by engineering the geometry of the confining potential.
Even in such systems, dark solitons tend to decay, e.g. due to small thermal effects, setting an upper limit to their expected lifetime. However, experimentalists would like to be able to observe the soliton for longer times. In this work, we propose how parametric driving can be implemented in this system, to stabilize the soliton for much longer times [3]. This is achieved by the addition of periodicaly-modulated optical gaussian potentials to the edges of the harmonic trap. Such potentials induce a sound mode which can be engineered in such a way, that the dark soliton always propagates on a local density dip in the background density, thus maintaining a roughly constant depth (and hence energy) for lifetimes significantly longer than the corresponding ones in the absence of driving. The effect of the drive should be experimentally observable by monitoring the soliton oscillations in the harmonic trap. In the absence of driving, a soliton in a dissipative condensate becomes progressively shallower, reaches further out in the trap and eventually decays into a sound wave, thus exhibiting a time-varying frequency and amplitude of oscillations in the trap. In stark contrast to this, a driven soliton can be engineered to maintain a roughly constant frequency and amplitude of oscillations. Relevant experimental parameters for the realisation of such an experiment are discussed. [1] N.G. Parker, N.P. Proukakis, M. Leadbeater and C.S. Adams, Phys. Rev. Lett. 90, 220401 (2003). [2] N.P. Proukakis, N.G. Parker, D.J. Frantzeskakis and C.S. Adams, J. Opt. B 6, S380 (2004); N.G. Parker, N.P. Proukakis, C.F. Barenghi and C.S. Adams, J. Phys. B 36, 2891 (2003). [3] N.P. Proukakis, N.G. Parker, C.F. Barenghi and C.S. Adams, Phys. Rev. Lett. (At Press) [cond-mat/0403566 (2004)]. |