We consider a Bose-Einstein condensate (BEC) with attractive two-body interactions in a cigarshaped trap, initially prepared in its ground state for a given negative scattering length, which is quenched to a larger absolute value of the scattering length. Using the mean-field approximation, we compute numerically, for an experimentally relevant range of aspect ratios and initial strengths of the coupling, two critical values of quench: one corresponds to the weakest attraction strength the quench to which causes the system to collapse before completing even a single return from the narrow configuration ("pericenter") in its breathing cycle. The other is a similar critical point for the occurrence of collapse before completing two returns. In the latter case, we also compute the limiting value, as we keep increasing the strength of the post-quench attraction towards its critical value, of the time interval between the first two pericenters. We also use a Gaussian variational model to estimate the critical quenched attraction strength below which the system is stable against the collapse for long times. These time intervals and critical attraction strengths-apart from being fundamental properties of nonlinear dynamics of self-attractive BECs-may provide clues to the design of upcoming experiments that are trying to create robust BEC breathers.
In this Letter, we show that a three-dimensional Bose-Einstein solitary wave can become stable if the dispersion law is changed from quadratic to quartic. We suggest a way to realize the quartic dispersion, using shaken optical lattices.Estimates show that the resulting solitary waves can occupy as little as ∼ 1/20-th of the Brillouin zone in each of the three directions and contain as many as N = 10 3 atoms, thus representing a fully mobile macroscopic three-dimensional object.
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