Macroscopic quantum tunneling of a Bose-Einstein condensate with attractive interaction

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-c. By applying a variational method and the instanton technique to the Gross-Pitaevskii energy functional, we find analytically the frequency of the collective excitation and the rate of macroscopic quantum tunnelling. We show that near the critical point the tunneling exponent vanishes according to (1 - N-0/N-c)(5/4) and that macroscopic quantum tunneling can be a dominant decay mechanism of the condensate for N-0 very close to N-c.