Mixed symmetry localized modes and breathers in binary mixtures of Bose-Einstein condensates in optical lattices

We study localized modes in binary mixtures of Bose-Einstein condensates embedded in one-dimensional optical lattices. We report a diversity of asymmetric modes and investigate their dynamics. We concentrate on the cases where one of the components is dominant, i.e. has much larger number of atoms than the other one, and where both components have the numbers of atoms of the same order but different symmetries. In the first case we propose a method of systematic obtaining the modes, considering the "small" component as bifurcating from the continuum spectrum. A generalization of this approach combined with the use of the symmetry of the coupled Gross-Pitaevskii equations allows obtaining breather modes, which are also presented.Comment: 11 pages, 16 figure

Ratchet-like dynamics of fluxons in annular Josephson junctions driven by bi-harmonic microwave fields

Experimental observation of the unidirectional motion of a topological soliton driven by a bi-harmonic ac force of zero mean is reported. The observation is made by measuring the current-voltage characteristics for a fluxon trapped in an annular Josephson junction that was placed into a microwave field. The measured dependence of the fluxon mean velocity (rectified voltage) at zero dc bias versus the phase shift between the first and second harmonic of the driving force is in qualitative agreement with theoretical expectations.Comment: 6 figure

Quantum signatures of breather-breather interactions

The spectrum of the Quantum Discrete Nonlinear Schr\"odinger equation on a periodic 1D lattice shows some interesting detailed band structure which may be interpreted as the quantum signature of a two-breather interaction in the classical case. We show that this fine structure can be interpreted using degenerate perturbation theory.Comment: 4 pages, 4 fig

Analytical approach to soliton ratchets in asymmetric potentials

We use soliton perturbation theory and collective coordinate ansatz to investigate the mechanism of soliton ratchets in a driven and damped asymmetric double sine-Gordon equation. We show that, at the second order of the perturbation scheme, the soliton internal vibrations can couple {\it effectively}, in presence of damping, to the motion of the center of mass, giving rise to transport. An analytical expression for the mean velocity of the soliton is derived. The results of our analysis confirm the internal mode mechanism of soliton ratchets proposed in [Phys. Rev. E {\bf 65} 025602(R) (2002)].Comment: 9 figures. Submitted to Phys. Rev.

Three dimensional imaging of short pulses

We exploit a slightly noncollinear second-harmonic cross-correlation scheme to map the 3D space-time intensity distribution of an unknown complex-shaped ultrashort optical pulse. We show the capability of the technique to reconstruct both the amplitude and the phase of the field through the coherence of the nonlinear interaction down to a resolution of 10 $\mu$m in space and 200 fs in time. This implies that the concept of second-harmonic holography can be employed down to the sub-ps time scale, and used to discuss the features of the technique in terms of the reconstructed fields.Comment: 16 pages, 6 figure