Loophole-free Bell test with one atom and less than one photon on average

We consider the entanglement between two internal states of a single atom and two photon number states describing either the vaccum or a single photon and thus containing, on average, less than one photon. We show that this intriguing entanglement can be characterized through substantial violations of a Bell inequality by performing homodyne detections on the optical mode. We present the experimental challenges that need to be overcome to pave the way towards a loophole-free Bell test in this setup.