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arXiv:1012.0334 · Physical Review Letters

Swift Loss of Coherence of Soliton Trains in Attractive Bose-Einstein Condensates

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

Published Jun 14, 2011• 46 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.106.240401

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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 review recent experimental and theoretical work on the creation of bright matter wave solitons in Bose–Einstein condensates. In two recent experiments, solitons are formed from Bose–Einstein condensates of 7 Li by utilizing a Feshbach resonance to switch from repulsive to attractive interactions. The solitons are made to propagate in a one-dimensional potential formed by a focused laser beam. For repulsive interactions, the wavepacket undergoes dispersive wavepacket spreading, while for attractive interactions, localized solitons are formed. In our experiment, a multi-soliton train containing up to ten solitons is observed to propagate without spreading for a duration of 2 s. Adjacent solitons are found to interact repulsively, in agreement with a calculation based on the nonlinear Schrödinger equation assuming that the soliton train is formed with an alternating phase structure. The origin of this phase structure is not entirely clear.
Solitons are localized wave packets whose dispersion is compensated by a nonlinearity. Solitons are observed in many wave settings including optics, fluids, plasmas, and matter-waves. Bright matter-wave solitons were first created by quenching the interactions in a quasi-one dimensional atomic Bose-Einstein condensate (BEC) from repulsive to attractive. Under some conditions a train of up to 10 solitons was formed. Neighboring solitons were observed to repel one another, an effect that was attributed to an alternating π-0-π phase distribution. There has been a theoretical debate whether this phase structure is inherent to the formation of the train, or if it evolves through a series of mergers and annihilations between neighboring solitons that are in-phase, and hence attractive. This paper shows that the interaction quench initiates a modulation instability (MI) in which weak perturbations undergo a nonlinear amplification, resulting in their exponential growth. Results show that the number of solitons is consistent with the initial size of the condensate divided by 2πξ. Furthermore, once formed, there are few solitons lost to merger or annihilation collisions. From this, we conclude that the soliton train is created with an alternating phase structure, rather than evolving into one.
The dynamics of matter-wave solitons in Bose-Einstein condensates (BEC) is considerably affected by the presence of a thermal cloud and the dynamical depletion of the condensate. Our numerical results, based on the time-dependent Hartree-Fock-Bogoliubov theory, demonstrate the collapse of the attractively interacting BEC via collisional emission of atom pairs into the thermal cloud, which splits the (quasi-one-dimensional) BEC soliton into two partially coherent solitonic structures of opposite momenta. These incoherent matter waves are analogous to optical random-phase solitons.
The results of one experiment (Strecker et. al.), is numerically simulated to demonstrate that a mean-field approach is capable of describing an attractive condensate in an area of nonlinear behavior such as soliton creation, and to investigate the soliton interactions by extending the experimental parameters. In the experiment being studied, the released BEC formed a train of multiple solitons which oscillated collectively in a weak harmonic potential for many cycles, each soliton kept apart from its neighbor by the alternating phase structure of the ensemble. This result suggests the possibility of designing a series of self-focussing, phase-engineered coherent matter pulses as the basis of future experiments in non-linear atom optics. Experimentally, a quasi-1D condensate was formed in a box-like potential with significantly tighter confinement in the transverse than the axial dimension. Manipulation of a Feshbach resonance rapidly tuned the scattering length of the atoms from positive to negative, resulting in a condensate which became attractive at, or shortly after, its release. Most of the unconfined atoms were ejected in a burst, leaving behind a small proportion of remnant atoms as solitons. These were allowed to evolve as they propagated along the axial potential of a far red-detuned laser field for a short time before being imaged.
Strongly correlated impurities immersed in a Bose-Einstein condensate (BEC) can form a periodic structure of tightly localized single atoms due to competing inter and intraspecies interactions, leading to a self-organized pinned state. In this work, we show numerically that the impurities in the self-pinned state form a soliton-train, as a consequence of a BEC-mediated attractive self-interaction and ordering due to the exclusion principle. The dynamics of the impurities possess the characteristics of bright matter-wave soliton trains as often seen in classical fields; however, in the few impurities cases, the detailed nature of collisions is determined by their quantum statistics. Published by the American Physical Society 2024