Dynamics and stability of Bose-Einstein condensates with attractive 1/r interaction

TL;DR

This paper investigates the dynamics and stability of Bose-Einstein condensates with attractive 1/r interactions using variational and numerical methods, revealing bifurcation phenomena and stability regimes.

Contribution

It introduces a combined variational and numerical analysis of BECs with attractive 1/r interactions, identifying bifurcation points and stability characteristics.

Findings

Existence of stable and unstable stationary states separated by a tangent bifurcation.

Stable states exhibit periodic oscillations, unstable states collapse.

No stationary solutions for sufficiently negative scattering lengths.

Abstract

The time-dependent extended Gross-Pitaevskii equation for Bose-Einstein condensates with attractive 1/r interaction is investigated with both a variational approach and numerically exact calculations. We show that these condensates exhibit signatures known from the nonlinear dynamics of autonomous Hamiltonian systems. The two stationary solutions created in a tangent bifurcation at a critical value of the scattering length are identified as elliptical and hyperbolical fixed points, corresponding to stable and unstable stationary states of the condensate. The stable stationary state is surrounded by elliptical islands, corresponding to condensates periodically oscillating in time, whereas condensate wave functions in the unstable region undergo a collapse within finite time. For negative scattering lengths below the tangent bifurcation no stationary solutions exist, i.e., the condensate is always unstable and collapses.