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Jisuan wuli

Generation and Properties of Dark Solitons in Heteronuclear Two-component Bose-Einstein Condensates

Wei Han

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

Generation and properties of dark solitons are studied in detail by means of numerical simulation of quasi one-dimensional heteronuclear two-component Bose-Einstein condensates in syntonic potential.Dark solitons are only induced in one of the condensate components by modulational instability with instantaneous conversion of repulsive interspecies interaction to attraction.Solitons pass through each other periodically in syntonic potential.In addition,the number of dark solitons is affiliated with ratio of particle mass and ratio of particles numbers.

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Generation and properties of dark solitons are studied in detail by means of numerical simulation of quasi one-dimensional heteronuclear two-component Bose-Einstein condensates in syntonic potential.Dark solitons are only induced in one of the condensate components by modulational instability with instantaneous conversion of repulsive interspecies interaction to attraction.Solitons pass through each other periodically in syntonic potential.In addition,the number of dark solitons is affiliated with ratio of particle mass and ratio of particles numbers.
We have numerically studied the head-on collisions of the bright-bright solitons and bright-dark solitons with different relative phases, based on Gross-Pitaevskii(GP) equation of the quasi-one-dimensional heteronuclear two-component Bose-Einstein condensates. If there is no external potential well, the relative phase zc leads to elastic collision of the bright-bright solitons, but they collide with each other accompanied by some energy transfer for the relative phase π /2. If there is external potential well, they collide periodically with the relative phase π, but with the relative phase π /2, the two solitons combine to one soliton after collision with energy escape. For the bright-dark solitons, their bright-bright solitons in the first component collide periodically with the relative phase 0 or π. The difference of them is that the former has one collision point, the latter two collision points. Furthermore, we have found that the bright-bright solitons are always stable and the bright-dark solitons are unstable by solving its co~esponding Bogoliubov-de Gennes equations.
We investigate the combined soliton solutions of two-component Bose–Einstein condensates with external potential. The "phase diagram" is obtained for the formation regions of different combined solitons. Our results show that the intraspecies (interspecies) interaction strengths and the external trapped potential clearly affect the formation of dark-dark, bright-bright, and dark–bright soliton solutions in different regions. Especially, we find that the bright–bright (dark–dark) soliton can exist in the case of both repulsive (attractive) intraspecies interaction strengths in the presence of external potential. This novel phenomenon is completely different from the formation of soliton solution of one-component Bose–Einstein condensates without external potential, and it will be useful for the study of two-component Bose–Einstein condensates.
Wave properties of solitons in a two-component Bose–Einstein condensate are investigated in detail. We demonstrate that dark solitons in one of components admit interference and tunneling behavior, in sharp contrast to the scalar dark solitons and vector dark solitons. Analytic analyses of interference properties show that spatial interference patterns are determined by the relative velocity of solitons, while temporal interference patterns depend on the velocities and widths of two solitons, differing from the interference properties of scalar bright solitons. Especially, for an attractive interactions system, we show that interference effects between the two dark solitons can induce some short-time density humps (whose densities are higher than background density). Moreover, the maximum hump value is remarkably sensitive to the variation of the solitons’ parameters. For a repulsive interactions system, the temporal-spatial interference periods of dark–bright solitons have lower limits. Numerical simulation results suggest that interference patterns for the dark–bright solitons are more robust against noises than bright–dark solitons. These explicit interference properties can be used to measure the velocities and widths of solitons. It is expected that these interference behaviors can be observed experimentally and can be used to design matter wave soliton interferometer in vector systems.
We investigate numerically the dynamics of paired bright solitons induced by the modulational instability of two-component Bose-Einstein condensates. We derive the analytic gain spectrum by the modulational instability in terms of the interspecies and intraspecies scattering constants and classify the region where the instability occurs. The constraints on the interspecies and intraspecies scattering constants for the existence of the paired bright solitons are found. Using numerical simulations, it is shown that the paired bright solitons induced by the modulational instability exhibit complicated dynamical behaviors depending on the sign and strength of the interspecies and intraspecies scattering constants. - PACS numbers: 03.75.Fi, 05.30.Jp, 32.80Pj, 67.90.+z
We investigate the dynamics and pattern formation of two ring dark solitons in a two-dimensional binary Bose-Einstein condensate with tunable intercomponent interaction via numerical simulation of the time-dependent Gross-Pitaevskii equation. Both the black and gray ring dark solitons are considered for cases where the modulation frequency of the intercomponent interaction is resonant or nonresonant with the one of the trapping potential. Our results show that in the presence of periodic modulation of the intercomponent interaction not only are the lifetimes of the ring dark solitons largely extended but also their decaying dynamics are dramatically affected. Before snaking instability sets in, new ring dark solitons are formed, and both the numbers and depths of the ring dark solitons exhibit collective oscillations. With the development of instability, the system exhibits different decaying processes, and a variety of decay profiles, such as vortex necklace, distorted octagon, vortex-antivortex ring, and cross, are formed, showing a strong dependence on the modulation frequency of the intercomponent interaction and the initial depth of the ring dark soliton.