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

TL;DR

This paper demonstrates how resonance states in Bose-Einstein condensates with attractive interactions can be stabilized into bound states using the Gross-Pitaevskii equation, combining variational methods to analyze different regimes.

Contribution

It introduces a combined variational approach to study the transition from resonances to bound states in nonlinear Bose-Einstein condensates.

Findings

Resonance states can be stabilized into bound states.

Identified borders between resonances, bound states, and collapse regimes.

Both variational methods yield similar results.

Abstract

It is shown using the Gross-Pitaevskii equation that resonance states of Bose-Einstein condensates with attractive interactions can be stabilized into true bound states. A semiclassical variational approximation and an independent quantum variational numerical method are used to calculate the energies (chemical potentials) and linewidths of resonances of the time-independent Gross-Pitaevskii equation; both methods produce similar results. Borders between the regimes of resonances, bound states, and, in two and three dimensions, collapse, are identified.