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

TL;DR

This paper presents a theoretical framework for generating highly directional, coherent matter beams from Bose-Einstein condensates via dynamical instabilities, extending analysis methods with Floquet theory and explaining experimental observations.

Contribution

It introduces a Floquet-based analytical approach to study dynamical instabilities in two-state BECs, enabling prediction of directional matter beams and their entanglement properties.

Findings

Dynamical instabilities lead to oppositely-propagating coherent matter beams.

The Floquet approach provides analytical insights into time-dependent BEC systems.

The theory explains experimental beam profiles and predicts EPR entanglement of paired particles.

Abstract

We present a theoretical analysis of a coupled, two-state Bose-Einstein condensate with non-equal 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 of Dall et al. [Phys. Rev. A 79, 011601(R) (2009)] and show it explains the anomalous beam profiles they observed. Finally we demonstrate the paired particle beams will be EPR-entangled on formation.