Macroscopic quantum tunneling of Bose-Einstein condensates with long-range interaction

TL;DR

This paper investigates macroscopic quantum tunneling in Bose-Einstein condensates with long-range interactions, employing advanced variational and numerical methods to accurately compute decay rates and improve upon previous models.

Contribution

It introduces an extended variational approach with coupled Gaussians and demonstrates rapid convergence to exact results, significantly enhancing decay rate predictions.

Findings

Variational approach converges quickly to numerical results.

Decay rates are improved by several orders of magnitude.

Long-range interactions significantly affect tunneling dynamics.

Abstract

The ground state of Bose-Einstein condensates with attractive particle interaction is metastable. One of the decay mechanisms of the condensate is a collapse by macroscopic quantum tunneling, which can be described by the bounce trajectory as solution of the time-dependent Gross-Pitaevskii equation in imaginary time. For condensates with an electromagnetically induced gravity-like interaction the bounce trajectory is computed with an extended variational approach using coupled Gaussian functions and simulated numerically exact within the mean-field approach on a space-time lattice. It is shown that the variational computations converge very rapidly to the numerically exact result with increasing number of Gaussians. The tunneling rate of the condensate is obtained from the classical action and additional parameters of the bounce trajectory. The converged variational and numerically exact results drastically improve by several orders of magnitude the decay rates obtained previously with a simple variational approach using a single Gaussian-type orbital for the condensate wave function.