Macroscopic quantum escape of Bose-Einstein condensates: Analysis of experimentally realizable quasi-one-dimensional traps

Abstract

The variational-JWKB method is used to determine experimentally accessible macroscopic quantum tunneling regimes of quasi-bound Bose-Einstein condensates in two quasi one-dimensional trap configurations. The potentials can be created by magnetic and optical traps, a symmetric trap from two offset Gaussian barriers and a tilt trap from a linear gradient and Gaussian barrier. Scaling laws in barrier parameters, ranging from inverse polynomial to square root times exponential, are calculated and used to elucidate different dynamical regimes, such as when classical oscillations dominate tunneling rates in the symmetric trap. The symmetric trap is found to be versatile, with tunneling times at and below one second, able to hold $10^{3}$ to $10^{4}$ atoms, and realizable for atoms ranging from rubidium to lithium, with unadjusted scattering lengths. The tilt trap produces sub-second tunneling times, is able to hold a few hundred atoms of lighter elements like lithium, and requiring the use of Feshbach resonance to reduce scattering lengths. To explore a large parameter space, an extended Gaussian variational ansatz is used, which can approximate large traps with Thomas-Fermi profiles. Nonlinear interactions in the Gross-Pitaevskii equation are shown to produce additional effective mean-field barriers, affecting scaling laws.