Collapse and revival of oscillations in a parametrically excited Bose-Einstein condensate in combined harmonic and optical lattice trap

In this work, we study parametric resonances in an elongated cigar-shaped BEC in a combined harmonic trap and a time dependent optical lattice by using numerical and analytical techniques. We show that there exists a relative competition between the harmonic trap which tries to spatially localize the BEC and the time varying optical lattice which tries to delocalize the BEC. This competition gives rise to parametric resonances (collapse and revival of the oscillations of the BEC width). Parametric resonances disappear when one of the competing factors i.e strength of harmonic trap or the strength of optical lattice dominates. Parametric instabilities (exponential growth of Bogoliubov modes) arise for large variations in the strength of the optical lattice.Comment: 9 pages, 20 figure

Stability and collisions of moving semi-gap solitons in Bragg cross-gratings

We report results of a systematic study of one-dimensional four-wave moving solitons in a recently proposed model of the Bragg cross-grating in planar optical waveguides with the Kerr nonlinearity; the same model applies to a fiber Bragg grating (BG) carrying two polarizations of light. We concentrate on the case when the system's spectrum contains no true bandgap, but only semi-gaps (which are gaps only with respect to one branch of the dispersion relation), that nevertheless support soliton families. Solely zero-velocity solitons were previously studied in this system, while current experiments cannot generate solitons with the velocity smaller than half the maximum group velocity. We find the semi-gaps for the moving solitons in an analytical form, and demonstrated that they are completely filled with (numerically found) solitons. Stability of the moving solitons is identified in direct simulations. The stability region strongly depends on the frustration parameter, which controls the difference of the present system from the usual model for the single BG. A completely new situation is possible, when the velocity interval for stable solitons is limited not only from above, but also from below. Collisions between stable solitons may be both elastic and strongly inelastic. Close to their instability border, the solitons collide elastically only if their velocities c1 and c2 are small; however, collisions between more robust solitons are elastic in a strip around c1=-c2.Comment: 16 pages, 7 figures, Physics Letters A, in pres

Symmetry-breaking Effects for Polariton Condensates in Double-Well Potentials

We study the existence, stability, and dynamics of symmetric and anti-symmetric states of quasi-one-dimensional polariton condensates in double-well potentials, in the presence of nonresonant pumping and nonlinear damping. Some prototypical features of the system, such as the bifurcation of asymmetric solutions, are similar to the Hamiltonian analog of the double-well system considered in the realm of atomic condensates. Nevertheless, there are also some nontrivial differences including, e.g., the unstable nature of both the parent and the daughter branch emerging in the relevant pitchfork bifurcation for slightly larger values of atom numbers. Another interesting feature that does not appear in the atomic condensate case is that the bifurcation for attractive interactions is slightly sub-critical instead of supercritical. These conclusions of the bifurcation analysis are corroborated by direct numerical simulations examining the dynamics of the system in the unstable regime.MICINN (Spain) project FIS2008- 0484

Matter-wave vortices and solitons in anisotropic optical lattices

Using numerical methods, we construct families of vortical, quadrupole, and fundamental solitons in a two-dimensional (2D) nonlinear-Schrodinger/Gross-Pitaevskii equation Which models Bose-Einstein condensates (BECs) or photonic crystals. The equation includes the attractive or repulsive cubic nonlinearity and an anisotropic periodic potential. Two types of anisotropy are considered, accounted for by the difference in the strengths of the I D sublattices, or by a difference in their periods. The limit case of the quasi-1D optical lattice (OL), when one sublattice is missing, is included too. By means of systematic simulations, we identify stability limits for two species of vortex solitons and quadrupoles, of the rhombus and square types. In the attraction model, rhombic vortices and quadrupoles remain stable up to the limit case of the quasi-1D lattice. In the same model, finite stability limits are found for vortices and quadrupoles of the Square type, in terms of the anisotropy parameter. In the repulsion model, rhombic vortices and quadrupoles are stable in large parts of the first finite bandgap (FBG). Another species of partly stable anisotropic states is found in the second FBG, subfundamental dipoles, each squeezed into a single cell of the OL. Square-shaped quadrupoles are completely unstable in the repulsion model, while vortices of the same type are stable only in weakly anisotropic OL potentials