Loophole-free test of the Bell inequality

An atomic cascade experiment is proposed that includes the detection of a recoil atom after the emission of two photons. This would permit testing of the Bell inequality without the need for additional assumptions, provided that the quantum efficiency of single-photon detectors exceeds a threshold of 0.92. The atomic source consists of calcium atoms, first trapped and then accelerated by gravity, whose velocity is controlled before they reach the interaction region with the two counterpropagating laser beams. The procedure allows a relatively high background in the photodetectors.