Complex scaling approach to the decay of Bose-Einstein condensates

TL;DR

This paper introduces a complex scaling method to quantitatively analyze the decay and tunneling dynamics of Bose-Einstein condensates trapped in finite potentials, providing accurate lifetime and chemical potential calculations.

Contribution

The study applies complex scaling to the Gross-Pitaevskii equation, enabling precise computation of decay rates and quasibound states of BECs in realistic trapping potentials.

Findings

Accurate calculation of BEC lifetimes and chemical potentials.

Good agreement with alternative decay modeling methods.

Application to a 1D harmonic-Gaussian trapping potential.

Abstract

The mean-field dynamics of a Bose-Einstein condensate is studied in presence of a microscopic trapping potential from which the condensate can escape via tunneling through finite barriers. We show that the method of complex scaling can be used to obtain a quantitative description of this decay process. A real-time propagation approach that is applied to the complex-scaled Gross-Pitaevskii equation allows us to calculate the chemical potentials and lifetimes of the metastably trapped Bose-Einstein condensate. The method is applied to a one-dimensional harmonic confinement potential combined with a Gaussian envelope, for which we compute the lowest symmetric and antisymmetric quasibound states of the condensate. A comparison with alternative approaches using absorbing boundary conditions as well as complex absorbing potentials shows good agreement.