Solitons in tunnel-coupled repulsive and attractive condensates

We study solitons in the condensate trapped in a double-well potential with far-separated wells, when the s-wave scattering length has different signs in the two parts of the condensate. By employing the coupled-mode approximation it is shown that there are unusual stable bright solitons in the condensate, with the larger share of atoms being gathered in the repulsive part. Such unusual solitons derive their stability from the quantum tunneling and correspond to the strong coupling between the parts of the condensate. The ground state of the system, however, corresponds to weak coupling between the condensate parts, with the larger share of atoms being gathered in the attractive part of the condensate.Comment: LaTex, 23 pages, 6 figures; revised version; to appear in Physical Review

Zener tunneling in two-dimensional photonic lattices

We discuss the interband light tunneling in a two-dimensional periodic photonic structure, as was studied recently in experiments for optically-induced photonic lattices [H. Trompeter et al., Phys. Rev. Lett. \textbf{96}, 053903 (2006)]. We identify the Zener tunneling regime at the crossing of two Bloch bands, which occurs in a generic case of the Bragg reflection when the Bloch index crosses the edge of the irreducible Brillouin zone. Similarly, the higher-order Zener tunneling involves four Bloch bands when the Bloch index passes through a high-symmetry point on the edge of the Brillouin zone. We derive simple analytical models that describe the tunneling effect, and calculate the corresponding tunneling probabilities.Comment: 6 pages, 6 figures, submitted to Phys Rev E; changes: band structure added (fig1) and the error estimates for the Landau-Zener model (fig 6

Dynamics of Femtosecond Pulses in the Region of Zero Secoind Order Dispersion of Single Mode Optical Fibers

The evolution of femtosecond optical pulses in the region of minimum group velocity dispersion of single mode optical fibers is analyzed numerically, by means of an extended nonlinear Schrodinger equation. Besides spectral fragmentation with formation of femtosecond optical solitons and dispersive waves, the results revealed new features of the pulse evolution owing to the intrapulse stimulated Raman scattering effect. I. Introdurtion It has been shown that solitons also emerge from pulses whose central frequencies straddle the zero dispersion wavelength of an optical fiber In the process, due to the non-linearity, a portion of the pulse energy is shifted into the region of normal dispersion while the other fraction goes into the anomalous dispersive regime of the propagciion medium. As a consequence, solitary and dispersive waves evolve on passage. In an optical fiber, however, only qualitative agreement between theoreti~al[~l~I and e~~e r i m e n t a l [~~~I results related to thr pulse evolution and frequency shift of the solitary waves with pulse amplitude was obtained. The discrepsncies were mainly due to the fact that in the e~~e r i m e n t [~~~] , femtosecond input pulses were utilized, while in the t h e~r~[~l~] , a few picosecond input pulsewidths were assumed. The predictions of the nonlinear Schro'linger equation are accurate for picosecond pulses but rieed to be modified for femtosecond input pulses, as severa1 higher-order nonlinear effects become important for such short pulses. The most important among their. is intrapulse stimulated Raman scattering (ISRS)[~-~I. The motivation of this work is to show that, the inclusion of tlie intrapulse stimulated Rarnan scattering term in a gmeralized nonlinear Schrodinger equation, gives rise to new features for the evolution of femtosecond optical pulses in the region of zero second order dispersion oj'fibers and also provides much better agreement betwecn theoretical and experimental results current in the ~iterature[l-~I. Theory and Results The prorlagation of a femtosecond optical pulse envelope with carrier frequency at the zero second order dispersion wavelength in an optical fiber is described by an extended nonlinear Schrodinger equation. By using normalized coordinates one may write it in the form: where U is the normalized pulse envelope amplitude with The parameter /31 is given by ]/vg where vg is the group velocity, /33 the third order dispersion coefficient, To is the pulse width and TR = TR/To is the intrapulse stimulated Raman scattering parameter. In our calculations, typical parameters were used in eq. Equatio