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Measuring Bohm Trajectories of Entangled Photons

Dylan H. Mahler, Lee A. Rozema, Kent Bonsma-Fisher, L. Vermeyden, Kevin J. Resch, Boris Braverman, Howard M. Wiseman, Aephraim M. Steinberg

Published Jan 1, 2014• 3 citations
Publisher

Abstract

We measure, using weak measurement, the Bohmian trajectories of one photon that is part of an entangled pair. Our results shed light on the nonlocality of the Bohm model, as well as its so-called “surrealism.”
DOI
10.1364/cleo_qels.2014.fw1a.1

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Weak measurement allows one to empirically determine a set of average trajectories for an ensemble of quantum particles. However, when two particles are entangled, the trajectories of the first particle can depend nonlocally on the position of the second particle. Moreover, the theory describing these trajectories, called Bohmian mechanics, predicts trajectories that were at first deemed "surreal" when the second particle is used to probe the position of the first particle. We entangle two photons and determine a set of Bohmian trajectories for one of them using weak measurements and postselection. We show that the trajectories seem surreal only if one ignores their manifest nonlocality.
Bohmian mechanics reproduces all statistical predictions of quantum mechanics, which ensures that entanglement cannot be used for superluminal signaling. However, individual Bohmian particles can experience superluminal influences. We propose to illustrate this point using a double double-slit setup with path-entangled photons. The Bohmian velocity field for one of the photons can be measured using a recently demonstrated weak-measurement technique. The found velocities strongly depend on the value of a phase shift that is applied to the other photon, potentially at spacelike separation.