Soliton dynamics at an interface between uniform medium and nonlinear optical lattice

We study trapping and propagation of a matter-wave soliton through the interface between uniform medium and a nonlinear optical lattice (NOL). Different regimes for transmission of a broad and a narrow soliton are investigated. Reflections and transmissions of solitons are predicted as function of the lattice phase. The existence of a threshold in the amplitude of the nonlinear optical lattice, separating the transmission and reflection regimes, is verified. The localized nonlinear surface state, corresponding to the soliton trapped by the interface, is found. Variational approach predictions are confirmed by numerical simulations for the original Gross-Pitaevskii equation with nonlinear periodic potentials

Effects of quantum fluctuations on macroscopic quantum tunneling and self-trapping of BEC in a double well trap

We study the influence of quantum fluctuations on the macroscopic quantum tunneling and self-trapping of a two-component Bose-Einstein condensate in a double-well trap. Quantum fluctuations are described by the Lee-Huang-Yang term in the modified Gross-Pitaevskii equation. Employing the modified Gross-Pitaevskii equation in scalar approximation, we derive the dimer model using a two-mode approximation. The frequencies of Josephson oscillations and self-trapping conditions under quantum fluctuations are found analytically and proven by numerical simulations of the modified Gross-Pitaevskii equation. The tunneling and localization phenomena are investigated also for the case of the Lee-Huang-Yang fluid loaded in the double-well potential.Comment: 14 pages, 9 figure

Collective oscillations of a quasi one dimensional Bose condensate under damping

Influence of the damping on collective oscillations of a one-dimensional trapped Bose gas in the mean field regime has been studied. Using the phenomenological damping approach developed by L.P. Pitaevskii, modified variational equations for the parameters of the condensate wave function is derived. Analytical expressions for the condensate parameters in equilibrium state have been obtained. Bistability in nonlinear oscillations of the condensate under periodic variations of the trap potential is predicted. The predictions of the modified variational approach are confirmed by full numerical simulations of the 1D GP equation with the damping.Comment: It contains a manuscript - damp1DBC.tex and figures (fig1a - fig1a.eps, fig1b - fig1b.eps, fig2 - fig2.eps, fig3 - fig3.eps and fig4 - fig4.eps

Resonances in a trapped 3D Bose-Einstein condensate under periodically varying atomic scattering length

Nonlinear oscillations of a 3D radial symmetric Bose-Einstein condensate under periodic variation in time of the atomic scattering length have been studied analytically and numerically. The time-dependent variational approach is used for the analysis of the characteristics of nonlinear resonances in the oscillations of the condensate. The bistability in oscillations of the BEC width is invistigated. The dependence of the BEC collapse threshold on the drive amplitude and parameters of the condensate and trap is found. Predictions of the theory are confirmed by numerical simulations of the full Gross-Pitaevski equation.Comment: 17 pages, 10 figures, submitted to Journal of Physics