Effective Gaussian-state theory for Bose-Einstein condensates

The Gaussian-state theory (GST) for bosons provides an self-consistent description for the Bose-Einstein condensates with quantum fluctations. The corresponding numerical calculation for ground-state wave function requires tremendous computing resource. By noting that the Gaussian-state wave function can be factorized into the form of the multimode coherent-squeezed state, we develope an effective theory for GST by analytically deriving the imaginary-time evolution equations for the mode functions and occupation numbers. Since, in typical situations, only a limited number of squeezed modes are occupied, the effective theory may significantly reduce the requirement for computing resource in numerical computation. Finally, we validate the effective theory using self-bound dipolar droplets.