Macroscopic quantum tunnelling of Bose-Einstein condensates in a finite potential well

TL;DR

This paper investigates macroscopic quantum tunnelling in Bose-Einstein condensates confined in a finite potential well, predicting observable tunnelling times and stability characteristics across various states and dimensions.

Contribution

It introduces a model of finite-depth traps with realistic potential shapes and analyzes tunnelling and stability of condensates using variational and WKB methods, highlighting new observable phenomena.

Findings

Tunnelling times range from 10 ms to 10 s.

Bound states can become quasi-bound due to nonlinearity.

Stability varies with state type and dimensionality.

Abstract

Bose-Einstein condensates are studied in a potential of finite depth which supports both bound and quasi-bound states. This potential, which is harmonic for small radii and decays as a Gaussian for large radii, models experimentally relevant optical traps. The nonlinearity, which is proportional to both the number of atoms and the interaction strength, can transform bound states into quasi-bound ones. The latter have a finite lifetime due to tunnelling through the barriers at the borders of the well. We predict the lifetime and stability properties for repulsive and attractive condensates in one, two, and three dimensions, for both the ground state and excited soliton and vortex states. We show, via a combination of the variational and WKB approximations, that macroscopic quantum tunnelling in such systems can be observed on time scales of 10 milliseconds to 10 seconds.