Instantons and radial excitations in attractive Bose-Einstein condensates

In this paper imaginary- and real-time versions of an equation for the condensate density, which describe dynamics and decay of any spherical Bose-Einstein condensate (BEC) within the mean-field approach, are presented. We obtain quantized energies of collective, finite-amplitude radial oscillations, and exact numerical instanton solutions, which describe quantum tunneling from both the metastable and radially excited states of the BEC of ⁷Li atoms. The mass parameter for the radial motion is found different from the Gaussian value assumed hitherto, but the effect of this difference on decay exponents is small. The collective breathing states form a slightly compressed harmonic spectrum, n=4 state lying lower than the second Bogoliubov (small amplitude) mode. The decay of these states, if excited, may simulate a shorter-than-true lifetime of the metastable state. By scaling arguments, results extend to other attractive BECs.