We propose an experiment which demonstrates the nonlocal properties of a singe-photon field via phase-sensitive measurements. This is the first proposal which demonstrates nonlocality and a violation of Bell's inequality with a single photon rather than a correlated photon pair.
Nonlocal effects associated with quantum-mechanical states have been theoretically interesting because they emphasize the differences between classical and quantum mechanics. We describe a system in which a single input photon causes a nonlocal influence on two spatially separated homodyne detectors, as evidenced by a violation of Bell's inequalities. Unlike previous configurations for violating Bell's inequalities, the correlation is not imposed on a pair of particles that spatially separate before being detected. Rather, the correlation arises from the interaction of the local oscillators at each homodyne detector with the spatially extended field of the input photon. The above effect is only one of a class of situations in which nonlocal correlations can be imposed on separated homodyne detectors by quantum mechanical fields. By deriving the conditions for violating Bell's inequality with phase-sensitive detectors, new tests can be developed that relate to squeezed light and other nonclassical fields.
From the work by Perrie et al. [Phys. Rev. Lett. 54, 1790 (1985)], photon pairs from the 2s 1/2 → 1s 1/2 (two-photon) decay of atomic hydrogen are known to be quantum mechanically correlated. In these experiments, the polarization states of the photons emitted in back-to-back geometry were shown to violate the Bell inequality as a qualitative sign of nonlocality and entanglement. In the present contribution, we analyze how these nonlocal quantum correlations, as given by the violation of the Bell inequality, differ from the concurrence as a true entanglement measure. Results are shown for both quantifiers in dependence of the decay geometry and the initial polarization of the atoms for the 2s 1/2 → 1s 1/2 and 3d 5/2 → 1s 1/2 two-photon decay of atomic hydrogen. These results display the difference between nonlocality and entanglement and, hence, may stimulate further experiments on nonlocal quantum correlations in atomic systems.
We describe a scheme to demonstrate the nonlocal properties of a single particle by showing a violation of Bell's inequality. The scheme is experimentally achievable as the only inputs are number states and mixed states, which serve as references to 'keep track of the experiment'. These reference states are created completely independently of one another and correlated only after all the measurement results have been recorded. This means that any observed nonlocality must solely be due to the single particle state. All the techniques used are equally applicable to massive bosonic particles as to photons and as such this scheme could be used to show the nonlocality of atoms.