Nonlinear coupling between scissors modes of a Bose-Einsten condensate

Abstract

We explore the nonlinear coupling of the three scissors modes of an anisotropic Bose-Einstein condensate. We show that only when the frequency of the one of the scissors modes is twice the frequence of another scissors mode, these two modes can be resonantly coupled and a down conversion can occur. We preform the calculation variationally using a gaussian trial wave function. This enables us to obtain simple analytical results that we describe the oscillation and resonance behaviour of the two coupled modes.