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Dimensional Effects on Solitonic Matter and Optical Waves with Normal and Anomalous Dispersion

L. Salasnich, A. Parola, L. Reatto

Published Jan 1, 2006• 5 citations
OpenAlex

Abstract

We investigate bright and dark solitons with anomalous or normal dispersion and under transverse harmonic confinement. In matter waves, positive atomic mass implies anomalous dispersion (kinetic spreading) while negative mass gives normal dispersion (kinetic shrinking). We find that, contrary to the strictly one-dimensional case, the axial and transverse profiles of these solitons crucially depend on the strength of the nonlinearity and on their dispersive properties. In particular, we show that, like bright solitons with anomalous dispersion, also dark solitons with normal dispersion disappear at a critical axial density. Our predictions are useful for the study of atomic matter waves in Bose–Einstein condensates and also for optical bullets in inhomogeneous Kerr media.

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We investigate bright and dark solitons with anomalous or normal dispersion and under transverse harmonic confinement. In matter waves, positive atomic mass implies anomalous dispersion (kinetic spreading) while negative mass gives normal dispersion (kinetic shrinking). We find that, contrary to the strictly one-dimensional case, the axial and transverse profiles of these solitons crucially depend on the strength of the nonlinearity and on their dispersive properties. In particular, we show that, like bright solitons with anomalous dispersion, also dark solitons with normal dispersion disappear at a critical axial density. Our predictions are useful for the study of atomic matter waves in Bose–Einstein condensates and also for optical bullets in inhomogeneous Kerr media.
We investigate bright and dark solitons with anomalous or normal dispersion and under transverse harmonic confinement. In matter waves, positive atomic mass implies anomalous dispersion (kinetic spreading) while negative mass gives normal dispersion (kinetic shrinking). We find that, contrary to the strictly one-dimensional case, the axial and transverse profiles of these solitons crucially depend on the strength of the nonlinearity and on their dispersive properties. In particular, we show that, like bright solitons with anomalous dispersion, also dark solitons with normal dispersion disappear at a critical axial density. Our predictions are useful for the study of atomic matter waves in Bose–Einstein condensates and also for optical bullets in inhomogeneous Kerr media.
We investigate the dynamics of Bose-Einstein condensate bright solitons made of alkali-metal atoms with negative scattering length and under harmonic confinement in the transverse direction. Contrary to the one-dimensional (1D) case, the 3D bright soliton exists only below a critical attractive interaction that depends on the extent of confinement. Such a behavior is also found in multisoliton condensates with box boundary conditions. We obtain numerical and analytical estimates of the critical strength beyond which the solitons do not exist. By using an effective 1D nonpolynomial nonlinear Schr\"odinger equation, which accurately takes into account the transverse dynamics of cigarlike condensates, we numerically simulate the dynamics of the ``soliton train'' reported in a recent experiment [Nature (London) 417, 150 (2002)]. Then, analyzing the macroscopic quantum tunneling of the bright soliton on a Gaussian barrier, we find that its interference in the tunneling region is strongly suppressed with respect to nonsolitonic case; moreover, the tunneling through a barrier breaks the shape invariance of the matter wave. Finally, we show that the collapse of the soliton is induced by the scattering on the barrier or by the collision with another matter wave when the density reaches a critical value, for which we derive an accurate analytical formula.
We develop a systematic analytical approach to consider the dynamics of linear and nonlinear excitations in trapped quasi-one-dimensional Bose-Einstein condensates with repulsive atom-atom interactions. We show that, for a condensate strongly confined in two transverse directions, the ground state of the system involves the high-order eigenmodes of the transverse confining potential in the transverse directions and effective high-order Thomas-Fermi wave functions in the axial direction. The linear excitations of the system have a Bogoliubov-type spectrum with the excitation frequency varying slowly along the axial direction. We find that, in a weak nonlinear approximation, the amplitude of a nonlinear excitation is governed by a variable coefficient Korteweg--de Vries equation with additional terms contributed from the transverse structure and the inhomogeneity in the axial direction of the condensate, which results in varying amplitude, width, and velocity for dark solitons. Because of the inhomogeneity the dark solitons undergo deformation and emit radiations when traveling along the axial direction. We finally demonstrate that a dark soliton will disintegrate into several ones plus a residual wave train when passing over a steplike potential.
We theoretically investigate the transmission dynamics of coherent matter wave pulses across finite optical lattices in both the linear and the nonlinear regimes. The shape and the intensity of the transmitted pulse are found to strongly depend on the parameters of the incident pulse, in particular its velocity and density: a clear physical picture of the main features observed in the numerical simulations is given in terms of the atomic band dispersion in the periodic potential of the optical lattice. Signatures of nonlinear effects due to the atom-atom interaction are discussed in detail, such as atom-optical limiting and atom-optical bistability. For positive scattering lengths, matter waves propagating close to the top of the valence band are shown to be subject to modulational instability. A scheme for the experimental generation of narrow bright gap solitons from a wide Bose-Einstein condensate is proposed: the modulational instability is seeded starting from the strongly modulated density profile of a standing matter wave and the solitonic nature of the generated pulses is checked from their shape and their collisional properties.
We study the reflection and transmission properties of matter wave solitons impinging on localized scattering potentials in one spatial dimension. By mean field analysis we identify regimes where the solitons behave more like waves or more like particles as a result of the interplay between the dispersive wave propagation and the attractive interactions between the atoms. For a bright soliton propagating together with a dark soliton void in a two-species Bose-Einstein condensate, we find different reflection and transmission properties of the dark and the bright components.