Minimum Detection Efficiency for a Loophole-Free Atom-Photon Bell Experiment

In Bell experiments, one problem is to achieve high enough photodetection to ensure that there is no possibility of describing the results via a local hidden-variable model. Using the Clauser-Horne inequality and a two-photon nonmaximally entangled state, a photodetection efficiency higher than 0.67 is necessary. Here we discuss atom-photon Bell experiments. We show that, assuming perfect detection efficiency of the atom, it is possible to perform a loophole-free atom-photon Bell experiment whenever the photodetection efficiency exceeds 0.50.

Figure 1

Maximum affordable background noise for a loophole-free Bell experiment as a function of the photodetection efficiency ${\eta }_B$. (a) Using the CHSH inequality with ${\eta }_A={\eta }_B$, (b) using the CHSH inequality with ${\eta }_A=1$, (c) using the CH inequality with ${\eta }_A={\eta }_B$, and (d) using the CH inequality with ${\eta }_A=1$. The cases (a) and (c) are appropriate in a photon-photon experiment and the cases (b) and (d) are appropriate in an atom-photon experiment.