# Metastability versus collapse following a quench in attractive Bose-Einstein condensates

## TL;DR

This paper investigates the stability and collapse dynamics of attractive Bose-Einstein condensates after a sudden increase in attraction strength, identifying critical quench values and stability conditions through numerical and variational methods.

## Contribution

It introduces a combined numerical and variational approach to determine critical quench parameters and stability thresholds in attractive BECs, advancing understanding of their nonlinear dynamics.

## Key findings

- Identified critical attraction strengths leading to collapse before a single breathing cycle.
- Computed the time interval between perihelia as attraction approaches criticality.
- Provided estimates for stability thresholds useful for experimental BEC breather creation.

## Abstract

We consider a Bose-Einstein condensate (BEC) with attractive two-body interactions in a cigar-shaped trap, initially prepared in its ground state for a given negative scattering length, which is quenched to a larger absolute value of the scattering length. Using the mean-field approximation, we compute numerically, for an experimentally relevant range of aspect ratios and initial strengths of the coupling, two critical values of quench: one corresponds to the weakest attraction strength the quench to which causes the system to collapse before completing even a single return from the narrow configuration ("perihelion") in its breathing cycle. The other is a similar critical point for the occurrence of collapse before completing two returns. In the latter case, we also compute the limiting value, as we keep increasing the strength of the post-quench attraction towards its critical value, of the time interval between the first two perihelia. We also use a Gaussian variational model to estimate the critical quenched attraction strength below which the system is stable against the collapse for long times. These time intervals and critical attraction strengths---apart from being fundamental properties of nonlinear dynamics of self-attractive BECs---may provide clues to the design of upcoming experiments that are trying to create robust BEC breathers.