Generation of directional, coherent matter beams through dynamical instabilities in Bose-Einstein condensates

We present a theoretical analysis of a coupled, two-state Bose-Einstein condensate with nonequal scattering lengths and show that dynamical instabilities can be excited. We demonstrate that these instabilities are exponentially amplified, resulting in highly directional, oppositely propagating, coherent matter beams at specific momenta. To accomplish this we prove that the mean field of our system is periodic and extend the standard Bogoliubov approach to consider a time-dependent, but cyclic, background. This allows us to use Floquet's theorem to gain analytic insight into such systems, rather than employing the usual Bogoliubov-de Gennes approach, which is usually limited to numerical solutions. We apply our theory to the metastable helium atom laser experiment by Dall [Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.79. 011601 79, 011601(R) (2009)] and show that it explains the anomalous beam profiles they observed. Finally, we demonstrate that the paired particle beams will be Einstein-Podolsky-Rosen entangled on formation.