Quantum Theory of Atomic Four-Wave Mixing in Bose-Einstein Condensates

TL;DR

This paper provides an exact quantum mechanical analysis of four-wave mixing in multicomponent Bose-Einstein condensates, revealing entanglement, mode build-up, and dynamic atom exchange phenomena.

Contribution

It introduces a novel quantum approach using angular momentum operators to analyze multicomponent BEC four-wave mixing, highlighting entanglement and dynamic effects.

Findings

Strong quantum entanglement between hyperfine states

Build-up of matter-wave side-modes from noise

Periodic collapses and revivals in atom exchange

Abstract

We present an exact quantum mechanical analysis of collinear four-wave mixing in a multicomponent Bose-Einstein condensate consisting of sodium atoms in the F=1 ground state. Technically, this is achieved by taking advantage of the conservation laws of the system to represent its Hamiltonian in terms of angular momentum operators. We discuss explicitly the build-up of matter-wave side-modes from noise, as well as the correlations between these modes. We show the appearance of a strong quantum entanglement between hyperfine states. We also demonstrate that for finite atomic numbers, the system exhibits periodic collapses and revivals in the exchange of atoms between different spin states.