Heralded mapping of photonic entanglement into single atoms in free space: proposal for a loophole-free Bell test

An obvious way to entangle two atoms located at remote locations is to produce a pair of entangled photons half-way between the two atoms, to send one photon to each location and to subsequently map the photonic entanglement into the atoms. The efficiency of this process is, however, fundamentally limited due to overall transmission losses. We propose a method to herald the success of the mapping operation in free space without destroying nor revealing the stored quantum state. Interestingly for a Bell test, the heralding signal does not open the detection loophole provided the measurement choice is performed once the heralding is obtained only. We show through a detailed feasibility study that this approach could provide an attractive alternative to Bell tests where the atom-atom entanglement is created from atom-photon entanglement using an entanglement swapping operation.