Transition from Resonances to Bound States in Nonlinear Systems: Application to Bose-Einstein condensates

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Abstract
We show that resonance states in Bose-Einstein condensates with attractive atomic interactions can be stabilized into bound states as the interaction strength is increased, either by increasing the number of atoms, or tuning the s-wave scattering length to be more negative. We employ a newly developed numerical method which calculates the energies and linewidths of resonances in the Gross-Pitaevskii equation. In one-, three-, and two-dimensional cases, we study the condensate in a trapping potential which has the shape of a harmonic well multiplied by a broad Gaussian envelope. Borders between the three regimes of quasi-stable resonance, stable bound states, and, in three dimensions, collapse, are identified.

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