Jaynes-Cummings dynamics with a matter wave oscillator

TL;DR

This paper demonstrates how two Bose-Einstein condensates in a periodic potential can be used to realize Jaynes-Cummings dynamics with matter waves, enabling quantum state engineering and tomography of atomic states.

Contribution

It introduces a novel approach to simulate Jaynes-Cummings interactions using matter wave oscillators in Bose-Einstein condensates, bridging quantum optics and atomic physics.

Findings

Quantum optical states of matter waves can be engineered.

Quantum state tomography of atomic states is feasible.

Analogies with cavity QED and trapped ions are established.

Abstract

We propose to subject two Bose-Einstein condensates to a periodic potential, so that one condensate undergoes the Mott insulator transition to a state with precisely one atom per lattice site. We show that photoassociation of heteronuclear molecules within each lattice site is described by the quantum optical Jaynes-Cummings Hamiltonian. In analogy with studies of this Hamiltonian with cavity fields and trapped ions, we are thus able to engineer quantum optical states of atomic matter wave fields and we are able to reconstruct these states by quantum state tomography.