Phase-matched four wave mixing and quantum beam splitting of matter waves in a periodic potential

TL;DR

This paper demonstrates how an external periodic potential enables phase-matched four wave mixing in Bose-Einstein condensates, allowing efficient generation of correlated atom pairs with conserved energy and momentum.

Contribution

It introduces a method for generating correlated atom pairs via four wave mixing in a periodic potential, leveraging dispersion properties for phase matching.

Findings

Over 95% transfer of condensate into correlated pairs

Effective generation of atom pairs with specific quasi-momenta

Numerical confirmation using Gross-Pitaevskii equation

Abstract

We show that the dispersion properties imposed by an external periodic potential ensure both energy and quasi-momentum conservation such that correlated pairs of atoms can be generated by four wave mixing from a Bose-Einstein condensate moving in an optical lattice potential. In our numerical solution of the Gross-Pitaevskii equation, a condensate with initial quasi-momentum k_0 is transferred almost completely (>95%) into a pair of correlated atomic components with quasi-momenta k_1 and k_2, if the system is seeded with a smaller number of atoms with the appropriate quasi-momentum k_1.