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arXiv:0910.2711 · Physical Review A

Reentrant stability of Bose-Einstein-condensate standing-wave patterns

Ryan M. Kalas, Dmitry Solenov, Eddy Timmermans

Published May 20, 2010• 1 citation
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Abstract

We describe standing-wave patterns induced by an attractive finite-ranged external potential inside a large Bose-Einstein Condensate (BEC). As the potential depth increases, the time-independent Gross-Pitaevskii equation develops pairs of solutions that have nodes in their wave function. We elucidate the nature of these states and study their dynamical stability. Although we study the problem in a two-dimensional BEC subject to a cylindrically symmetric square well potential of a radius that is comparable to the coherence length of the BEC, our analysis reveals general trends that are valid in two and three dimensions, independent of the symmetry of the localized potential well, and suggestive of the behavior in general short-range and large-range potentials. One set of nodal BEC wave functions resembles the single particle $n$-node bound-state wave function of the potential well, the other wave functions resemble the $n\ensuremath{-}1$-node bound-state wave function with a kink state pinned by the potential. The second state, though corresponding to the lower free energy value of the pair of $n$-node BEC states, is always unstable, whereas the first can be dynamically stable in intervals of the potential well depth, implying that the standing-wave BEC can evolve from being dynamically unstable to stable and back to unstable as the potential well is adiabatically deepened---a phenomenon that we refer to as ``reentrant dynamical stability.''

DOI
10.1103/physreva.81.053620

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