Stability of Solution of the Nonlinear Schr\"odinger Equation for the Bose-Einstein Condensation

TL;DR

This paper analyzes the stability of Bose-Einstein condensates with negative scattering lengths at zero temperature, introducing a new equation to determine the critical atom number for metastability, validated against experimental data.

Contribution

It presents a novel exact equation for calculating the critical atom number in BECs with negative scattering lengths, enhancing stability predictions.

Findings

Derived a new equation for critical atom number $N_{cr}$

Calculated $N_{cr}$ for lithium BECs consistent with experiments

Improved understanding of BEC stability with negative scattering lengths

Abstract

We investigate the stability of the Bose-Einstein condensate (BEC) the case of atoms with negative scattering lengths at zero temperature using the Ginzburg-Pitaevskii-Gross (GPG) stationary theory. We have found a new exact equation for determining the upper bound of the critical numbers $N_{cr}$ of atoms for a metastable state to exist. Our calculated value of $N_{cr}$ for Bose-Einstein condensation of lithium atoms based on our new equation is in agreement with those observed in a agreement with those observed in a recent experiment.