Statics and dynamics of a binary dipolar Bose-Einstein condensate soliton

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Self-trapping of a binary Bose-Einstein condensate induced by interspecies interaction

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Localized modes of binary mixtures of Bose-Einstein condensates in nonlinear optical lattices

The properties of the localized states of a two-component Bose-Einstein condensate confined in a nonlinear periodic potential (nonlinear optical lattice) are investigated. We discuss the existence of different types of solitons and study their stability by means of analytical and numerical approaches. The symmetry properties of the localized states with respect to nonlinear optical lattices are also investigated. We show that nonlinear optical lattices allow the existence of bright soliton modes with equal symmetry in both components and bright localized modes of mixed symmetry type, as well as dark-bright bound states and bright modes on periodic backgrounds. In spite of the quasi-one-dimensional nature of the problem, the fundamental symmetric localized modes undergo a delocalizing transition when the strength of the nonlinear optical lattice is varied. This transition is associated with the existence of an unstable solution, which exhibits a shrinking (decaying) behavior for slightly overcritical (undercritical) variations in the number of atoms.

Demixing and symmetry breaking in binary dipolar Bose-Einstein-condensate solitons

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Lattice approach to the dynamics of phase-coded soliton trains

We address the collective dynamics of a soliton train propagating in a medium described by the nonlinear Schrödinger equation. Our approach uses the reduction of train dynamics to the discrete complex Toda chain (CTC) model for the evolution of parameters for each train constituent: such a simplification allows one to carry out an approximate analysis of the dynamics of positions and phases of individual interacting pulses. Here, we employ the CTC model to the problem which has relevance to the field of fibre optics communications where each binary digit of transmitted information is encoded via the phase difference between the two adjacent solitons. Our goal is to elucidate different scenarios of the train distortions and the subsequent information garbling caused solely by the intersoliton interactions. First, we examine how the structure of a given phase pattern affects the initial stage of the train dynamics and explain the general mechanisms for the appearance of unstable collective soliton modes. Then we further discuss the nonlinear regime concentrating on the dependence of the Lax scattering matrix on the input phase distribution; this allows one to classify typical features of the train evolution and determine the distance where the soliton escapes from its slot. In both cases, we demonstrate deep mathematical analogies with the classical theory of crystal lattice dynamics.

10Gbit/s dispersion managed soliton transmission over 16,500km in standard fibre by reduction of soliton interactions

We show experimentally and numerically that in high-speed strongly dispersion-managed standard fiber soliton systems nonlinear interactions limit the propagation distance. We present results that show that the effect of these interactions can be significantly reduced by appropriate location of the amplifier within the dispersion map. Using this technique, we have been able to extend the propagation distance of 10-Gbit/s 231–1pseudorandom binary sequence soliton data to 16, 500km over standard fiber by use of dispersion compensation. To our knowledge this distance is the farthest transmission over standard fiber without active control ever reported, and it was achieved with the amplifier placed after the dispersion-compensating fiber in a recirculating loop.

Lattice approach to the dynamics of phase-coded soliton trains

We address the collective dynamics of a soliton train propagating in a medium described by the nonlinear Schrödinger equation. Our approach uses the reduction of train dynamics to the discrete complex Toda chain (CTC) model for the evolution of parameters for each train constituent: such a simplification allows one to carry out an approximate analysis of the dynamics of positions and phases of individual interacting pulses. Here, we employ the CTC model to the problem which has relevance to the field of fibre optics communications where each binary digit of transmitted information is encoded via the phase difference between the two adjacent solitons. Our goal is to elucidate different scenarios of the train distortions and the subsequent information garbling caused solely by the intersoliton interactions. First, we examine how the structure of a given phase pattern affects the initial stage of the train dynamics and explain the general mechanisms for the appearance of unstable collective soliton modes. Then we further discuss the nonlinear regime concentrating on the dependence of the Lax scattering matrix on the input phase distribution; this allows one to classify typical features of the train evolution and determine the distance where the soliton escapes from its slot. In both cases, we demonstrate deep mathematical analogies with the classical theory of crystal lattice dynamics.

10Gbit/s dispersion managed soliton transmission over 16,500km in standard fibre by reduction of soliton interactions

We show experimentally and numerically that in high-speed strongly dispersion-managed standard fiber soliton systems nonlinear interactions limit the propagation distance. We present results that show that the effect of these interactions can be significantly reduced by appropriate location of the amplifier within the dispersion map. Using this technique, we have been able to extend the propagation distance of 10-Gbit/s 231–1pseudorandom binary sequence soliton data to 16, 500km over standard fiber by use of dispersion compensation. To our knowledge this distance is the farthest transmission over standard fiber without active control ever reported, and it was achieved with the amplifier placed after the dispersion-compensating fiber in a recirculating loop.

Design of experiments for bivariate binary responses modelled by Copula functions

Optimal design for generalized linear models has primarily focused on univariate data. Often experiments are performed that have multiple dependent responses described by regression type models, and it is of interest and of value to design the experiment for all these responses. This requires a multivariate distribution underlying a pre-chosen model for the data. Here, we consider the design of experiments for bivariate binary data which are dependent. We explore Copula functions which provide a rich and flexible class of structures to derive joint distributions for bivariate binary data. We present methods for deriving optimal experimental designs for dependent bivariate binary data using Copulas, and demonstrate that, by including the dependence between responses in the design process, more efficient parameter estimates are obtained than by the usual practice of simply designing for a single variable only. Further, we investigate the robustness of designs with respect to initial parameter estimates and Copula function, and also show the performance of compound criteria within this bivariate binary setting.