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arXiv:0812.3573 · Physical Review A

Scattering of an attractive Bose-Einstein condensate from a barrier: Formation of quantum superposition states

Alexej I. Streltsov, Ofir E. Alon, L. S. Cederbaum

Published Oct 19, 2009• 74 citations
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Abstract

Scattering in one dimension of an attractive ultracold bosonic cloud from a barrier can lead to the formation of two nonoverlapping clouds. Once formed, the clouds travel with constant velocity, in general different in magnitude from that of the incoming cloud, and do not disperse. The phenomenon and its mechanism---transformation of kinetic energy to internal energy of the scattered cloud---are obtained by solving the time-dependent many-boson Schr\"odinger equation. The analysis of the wave function shows that the object formed corresponds to a quantum superposition state of two distinct wave packets traveling through real space.

DOI
10.1103/physreva.80.043616

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Scattering in one dimension of an attractive ultracold bosonic cloud from a barrier can lead to the formation of two nonoverlapping clouds. Once formed, the clouds travel with constant velocity, in general different in magnitude from that of the incoming cloud, and do not disperse. The phenomenon and its mechanism---transformation of kinetic energy to internal energy of the scattered cloud---are obtained by solving the time-dependent many-boson Schr"odinger equation. The analysis of the wave function shows that the object formed corresponds to a quantum superposition state of two distinct wave packets traveling through real space.
The dynamics of attractive ultracold bosonic clouds in one dimension is studied by solving the many-particle time-dependent Schrödinger equation. The initially coherent wave packet can dynamically dissociate into two parts when its energy exceeds a threshold value. Noticeably, the time-dependent Gross-Pitaevskii theory does not show up the splitting. We call the split object fragmenton. It possesses remarkable properties; in particular, it is macroscopically fragmented. A simple static model predicts the existence of fragmented states responsible for the formation and dynamics of fragmentons.
Dynamics of attractive ultra-cold bosonic clouds in one dimension are studied by solving the many-particle time-dependent Schrödinger equation. The initially coherent wave-packet can dynamically dissociate into two parts when its energy exceeds a threshold value. Noticeably, the time-dependent Gross-Pitaevskii theory applied to the same initial state does not show up the splitting. We call the split object {\it fragmenton}. It possesses remarkable properties: (1) it is two-fold fragmented, i.e., not coherent; (2) it is dynamically stable, i.e., it propagates almost without dispersion; (3) it is delocalized, i.e., the two dissociated parts still communicate with one another. A simple static model predicts the existence of fragmented states which are responsible for formation and dynamics of fragmentons.
In trapped Bose-Einstein condensates (BECs), \emph{condensate growth} refers to the process in which an increasing number of quasi-particles are immediately transferred from the non-condensate state (the thermal cloud) into the condensate state following the initial formation of the BEC. Despite its physical significance, this phenomenon has not yet been studied rigorously from a mathematical standpoint. In this work, we investigate a kinetic equation whose collision operator includes three types of wave interactions: one corresponding to a 3-wave process, and two classified as 4-wave processes. This wave kinetic equation models the evolution of the density function of the thermal cloud. We establish the immediate formation of condensation in solutions to this equation, thus providing a rigorous demonstration of the condensate growth phenomenon.
Experiments on ultracold attractive Bose-Einstein condensates (BECs) have demonstrated that at low dimensions atomic clouds can form localized objects, propagating for long times without significant changes in their shapes and attributed to bright matter-wave solitons, which are coherent objects. We consider the dynamics of bright soliton trains from the perspective of many-boson physics. The fate of matter-wave soliton trains is actually to quickly lose their coherence and become macroscopically fragmented BECs. The death of the coherent matter-wave soliton trains gives birth to fragmented objects, whose quantum properties and experimental signatures differ substantially from what is currently assumed.
We investigate how Bose-Einstein condensates, whose initial state is either irrotational or contains a single vortex, scatter off a one-dimensional Gaussian tunnel barrier. We find that for low atom densities the vortex structure within the condensate is maintained during scattering, whereas at medium and high densities, multiple additional vortices can be created by the scattering process, resulting in complex dynamics and disruption of the atom cloud. This disruption originates from two different mechanisms associated, respectively, with the initial rotation of the atom cloud and the interference between the incident and reflected matter waves.