Macroscopic Quantum Tunneling of a Bose-Einstein Condensate with Attractive Interaction

TL;DR

This paper analytically investigates the macroscopic quantum tunneling of a Bose-Einstein condensate with attractive interactions, revealing how tunneling rates behave near the critical particle number and identifying MQT as a key decay process.

Contribution

The study introduces an analytical approach using variational and instanton methods to quantify MQT rates and excitation frequencies near the critical point of condensate stability.

Findings

Tunneling exponent vanishes as (1 - N_0/N_c)^{5/4} near the critical point.

MQT becomes the dominant decay mechanism close to the critical particle number.

Analytical expressions for collective excitation frequency and tunneling rate are derived.

Abstract

A Bose-Einstein condensate with attractive interaction can be metastable if it is spatially confined and if the number of condensate bosons $N_0$ is below a certain critical value $N_{\rm c}$. By applying a variational method and the instanton techinique to the Gross-Pitaevskii energy functional, we find analytically the frequency of the collective excitation and the rate of macroscopic quantum tunneling (MQT). We show that near the critical point the tunneling exponent vanishes according to $(1-N_0/N_c)^\frac{5}{4}$ and that MQT can be a dominant decay mechanism of the condensate for $N_0$ very close to $N_{\rm c}$.