We investigate two-dimensional 2D states in Bose-Einstein condensates with self-attraction or selfrepulsion, trapped in an axially symmetric optical-lattice potential periodic along the radius. The states trapped both in the central potential well and in remote circular troughs are studied. In the repulsive mode, a new soliton species is found, in the form of radial gap solitons. The latter solitons are completely stable if they carry zero vorticity l=0, while with l0 they develop a weak azimuthal modulation, which makes them rotating patterns, that persist indefinitely long. In addition, annular gap solitons may support stable azimuthal darksoliton pairs on their crests. In remote troughs of the attractive model, stable localized states may assume a ringlike shape with weak azimuthal modulation, or shrink into solitons strongly localized in the azimuthal direction, which is explained in the framework of an averaged 1D equation with the cyclic azimuthal coordinate. Numerical simulations of the attractive model also reveal stable necklacelike patterns, built of several strongly localized peaks. Dynamics of strongly localized solitons circulating in the troughs is studied too. While the solitons with sufficiently small velocities are completely stable, fast solitons gradually decay, due to the leakage of matter into the adjacent trough, under the action of the centrifugal force. Investigation of head-on collisions between strongly localized solitons traveling in circular troughs shows that collisions between in-phase solitons in a common trough lead to collapse, while -out-of-phase solitons bounce many times, but eventually merge into a single one, without collapsing. In-phase solitons colliding in adjacent circular troughs also tend to merge into a single soliton.
Matter-wave solitons in radially periodic potentials
SALERNO, Mario
2006-01-01
Abstract
We investigate two-dimensional 2D states in Bose-Einstein condensates with self-attraction or selfrepulsion, trapped in an axially symmetric optical-lattice potential periodic along the radius. The states trapped both in the central potential well and in remote circular troughs are studied. In the repulsive mode, a new soliton species is found, in the form of radial gap solitons. The latter solitons are completely stable if they carry zero vorticity l=0, while with l0 they develop a weak azimuthal modulation, which makes them rotating patterns, that persist indefinitely long. In addition, annular gap solitons may support stable azimuthal darksoliton pairs on their crests. In remote troughs of the attractive model, stable localized states may assume a ringlike shape with weak azimuthal modulation, or shrink into solitons strongly localized in the azimuthal direction, which is explained in the framework of an averaged 1D equation with the cyclic azimuthal coordinate. Numerical simulations of the attractive model also reveal stable necklacelike patterns, built of several strongly localized peaks. Dynamics of strongly localized solitons circulating in the troughs is studied too. While the solitons with sufficiently small velocities are completely stable, fast solitons gradually decay, due to the leakage of matter into the adjacent trough, under the action of the centrifugal force. Investigation of head-on collisions between strongly localized solitons traveling in circular troughs shows that collisions between in-phase solitons in a common trough lead to collapse, while -out-of-phase solitons bounce many times, but eventually merge into a single one, without collapsing. In-phase solitons colliding in adjacent circular troughs also tend to merge into a single soliton.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
