Dark soliton oscillations in Bose-Einstein condensates with multi-body interactions

We consider the dynamics of dark matter solitons moving through non-uniform cigar-shaped Bose-Einstein condensates described by the mean field Gross-Pitaevskii equation with generalized nonlinearities, in the case when the condition for the modulation stability of the Bose-Einstein condensate is fulfilled. The analytical expression for the frequency of the oscillations of a deep dark soliton is derived for nonlinearities which are arbitrary functions of the density, while specific results are discussed for the physically relevant case of a cubic-quintic nonlinearity modeling two- and three-body interactions, respectively. In contrast to the cubic Gross-Pitaevskii equation for which the frequencies of the oscillations are known to be independent of background density and interaction strengths, we find that in the presence of a cubic-quintic nonlinearity an explicit dependence of the oscillations frequency on the above quantities appears. This dependence gives rise to the possibility of measuring these quantities directly from the dark soliton dynamics, or to manage the oscillation via the changes of the scattering lengths by means of Feshbach resonance. A comparison between analytical results and direct numerical simulations of the cubic-quintic Gross-Pitaevskii equation shows good agreement which confirms the validity of our approach.Comment: submitted in J. Phys.

Interference effects in the two-dimensional scattering of microcavity polaritons by an obstacle: phase dislocations and resonances

We consider interference effects within the linear description of the scattering of two-dimensional microcavity polaritons by an obstacle. The polariton wave may exhibit phase dislocations created by the interference of the incident and the scattered fields. We describe these structures within the general framework of singular optics. We also discuss another type of interference effects appearing due to the formation of (quasi)resonances in the potential of a repulsive obstacle with sharp boundaries. We discuss the relevance of our approach for the description of recent experimental results and propose a criterion for evaluating the importance of nonlinear effects.Comment: 11 pages, 9 figure