Variational Adiabatic Hyperspherical Treatment of Bose-Einstein Condensates

Novel tools are developed for understanding the fundamental properties of few and many bosons with low-energy s-wave interactions, combining the variational principle and the adiabatic hyperspherical formalism. An ansatz wave function [1], constructed out of independent-particle orbitals in relation to the Gross-Pitaevskii equation, has been shown to improve upon a previous method [2] in calculating the ground-state properties of the condensate, including the monopole excitation frequencies. Interestingly, systematic differences from Bogoliubov theory emerge in those computed frequencies. For attractive condensates, the single-orbital ansatz is insufficient for accurately computing the barrier protecting the metastable system from macroscopic collapse; an inclusion of many-body correlation using multiple orbitals is necessary to reach approximate agreement with mean-field methods in predicting the critical atom number where collapse occurs. Alternative ideas, involving functions of interparticle distances symmetrized in either the Jastrow or Faddeev form, are also being explored to describe several bosons at unitarity.