Entangling photons via the quantum Zeno effect

Abstract

The quantum Zeno effect describes the inhibition of quantum evolution by frequent measurements. Here, we propose a scheme for entangling two given photons based on this effect. We consider a linear-optics set-up with an absorber medium whose two-photon absorption rate \(\xi_{2\gamma}\) exceeds the one-photon loss rate \(\xi_{1\gamma}\). In order to reach an error probability \(P_{\rm error}\), we need \(\xi_{1\gamma}/\xi_{2\gamma}<2P_{\rm error}^2/\pi^2\), which is a factor of 64 better than previous approaches (e.g., by Franson et al). Since typical media have \(\xi_{2\gamma}<\xi_{1\gamma}\), we discuss three mechanisms for enhancing two-photon absorption as compared to one-photon loss. The first mechanism again employs the quantum Zeno effect via self-interference effects when sending two photons repeatedly through the same absorber. The second mechanism is based on coherent excitations of many atoms and exploits the fact that \(\xi_{2\gamma}\) scales with the number of excitations but \(\xi_{1\gamma}\) does not. The third mechanism envisages three-level systems where the middle level is meta-stable (\(\Lambda\)-system). In this case, \(\xi_{1\gamma}\) is more strongly reduced than \(\xi_{2\gamma}\) and thus it should be possible to achieve \(\xi_{2\gamma}/\xi_{1\gamma}\gg1\). In conclusion, although our scheme poses challenges regarding the density of active atoms/molecules in the absorber medium, their coupling constants and the detuning, etc., we find that a two-photon gate with an error probability \(P_{\rm error}\) below 25% might be feasible using present-day technology.