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arXiv:1203.0390 · The European Physical Journal D

Matter-wave scattering on a BEC in a double-well potential

S. Hunn, Moritz Hiller, Andreas Buchleitner, Doron Cohen, Tsampikos Kottos

Published Apr 27, 2011• 4 citations
arXivHTMLPDF
DOI
10.1140/epjd/e2011-10639-9

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We investigate the effect of the position-dependent $s$-wave scattering length (SSL) on Bose-Einstein condensate (BEC) dynamics. In particular, we study the propagation of a BEC within a finite regime where the SSL, tuned by a periodic magnetic or optical field, results in the Bragg scattering of the BEC. We have predicted a matter-wave optical limiting process and bistability, which have potential applications like a matter wave limiter, a BEC mirror or cavity, and an atomic switch. The first phenomenon is a direct result of this periodic spatial tuning, showing that the position-dependent tuning of the SSL has the potential to result in novel properties of ultracold atomic gases.

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Abstract We consider the one-dimensional (1D) cubic-quintic Gross--Pitaevskii (GP)nequation, which governs the dynamics of Bose--Einstein condensate (BEC) matter waves with time-varying scattering length and loss/gain of atoms in a harmonic trapping potential. We derive the integrability conditions and the compensation condition for the 1D GP equation and obtain, with the help of a cubic-quintic nonlinear Schr\"{o}dinger (NLS) equation with self-steepening and self-frequency shift, exact analytical solitonlike solutions with the corresponding frequency chirp which describe the dynamics of femtosecond solitons and double-kink solitons propagating on a vanishing background. Our investigation shows that under the compensation condition, the matter wave solitons maintain a constant amplitude, the amplitude of the frequency chirp depends on the scattering length, while the motion of both the matter wave solitons and the corresponding chirp depend on the external trapping potential. More interesting, the frequency chirps are localized and their feature depends on the sign of the self-steepening parameter. Our study also shows that our exact solutions can be used to describe the compression of matter wave solitons when the absolute value of the s-wave scattering length increases with time.
A BEC can be viewed as a giant matter wave, this means that it can show interference. By creating a double-well potential we can split a BEC into two parts. After turning off the potential the BEC will start to expand because of its chemical potential. As the BEC's expand and the two matter waves superpose they show an interference pattern. In this thesis it is described how to succesfully create such a double-well potential. The potential created is stable, however not symmetric. The reason why it is not symmetric is investigated and it can be concluded that for a symmetric potential an optical dipole potential with a crosssection of around 10 micrometer is preferable. A description is given of the interference pattern that arises from different expansion time and different height of the potential barrier. Because the potential is not symmetric a dependence arises that causes the interference pattern not to be constant in space as observed in previous experiments. This might be an advantage for determining the phase difference between two BEC's.
We investigate the effect of the position-dependent sss-wave scattering length (SSL) on Bose-Einstein condensate (BEC) dynamics. In particular, we study the propagation of a BEC within a finite regime where the SSL, tuned by a periodic magnetic or optical field, results in the Bragg scattering of the BEC. We have predicted a matter-wave optical limiting process and bistability, which have potential applications like a matter wave limiter, a BEC mirror or cavity, and an atomic switch. The first phenomenon is a direct result of this periodic spatial tuning, showing that the position-dependent tuning of the SSL has the potential to result in novel properties of ultracold atomic gases.