Bound states of attractive Bose-Einstein condensates in shallow traps in two and three dimensions

TL;DR

This paper demonstrates the existence of stable bound states in attractive Bose-Einstein condensates within shallow, exponentially-screened traps in two and three dimensions, highlighting their nonlinear dynamics and potential for experimental realization.

Contribution

It introduces the concept of stable bound states in shallow traps for attractive BECs using variational and numerical methods, emphasizing their nonlinear properties and soliton-like behavior.

Findings

Stable bound states exist in shallow traps for attractive BECs.

Nonlinear interactions dominate the binding in these states.

Breathing oscillations exhibit highly nonlinear dynamics.

Abstract

Using variational and numerical solutions of the mean-field Gross-Pitaevskii equation for attractive interaction (with cubic or Kerr nonlinearity) we show that a stable bound state can appear in a Bose-Einstein condensate (BEC) in a localized exponentially-screened radially-symmetric harmonic potential well in two and three dimensions. We also consider an axially-symmetric configuration with zero axial trap and a exponentially-screened radial trap so that the resulting bound state can freely move along the axial direction like a soliton. The binding of the present states in shallow wells is mostly due to the nonlinear interaction with the trap playing a minor role. Hence these BEC states are more suitable to study the effect of the nonlinear force on the dynamics. We illustrate the highly nonlinear nature of breathing oscillation of these states. Such bound states could be created in BECs and studied in the laboratory with present knowhow.