Nonlinear coupling between scissors modes of a Bose-Einstein 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 one of the scissors modes is twice the frequency of another scissors mode, these two modes can be resonantly coupled and a down-conversion can occur. We perform the calculation variationally using a gaussian trial wave function. This enables us to obtain simple analytical results that describe the oscillation and resonance behavior of the two coupled modes.