Influence of confining anisotropy on the unstable behavior of a Bose gas with attractive interaction

Abstract

We apply controlled perturbation theory to calculate the spectrum of the Gross-Pitaevskii equation for a system composed of attractive bosons confined in an anisotropic harmonic trap. The energy spectrum is calculated as a function of the coupling parameters for traps going from cigar to pancake shapes. The critical number of particles that ensures real values for the energy spectrum is obtained as a function of the potential anisotropic parameter, showing strong dependence of the critical number on the anisotropy of the trap. For a number of particles above the critical value the metastability of the system is characterized through the calculation of the condensate lifetime, using the imaginary part of the energy values. The obtained results are relevant for experiments where highly anisotropic traps are considered.