Realization of a measurement of a ‘‘weak value’’

TLDR

The study demonstrates the first experimental measurement of a weak value, a concept introduced by Aharonov, Albert, and Vaidman. The experiment employs a birefringent crystal to weakly separate a laser beam’s polarization components, then a strong measurement displaces the beam’s centroid by a much larger distance. Data for orthogonal pre‑ and post‑selected states, where the weak value is undefined, reveal an interference effect that could be useful for amplifying and detecting weak signals.

Abstract

We present the first realization of a measurement of a ``weak value,'' a concept recently introduced by Aharonov, Albert, and Vaidman (AAV). Our experiment uses a birefringent crystal to separate the two linear-polarization components of a laser beam by a distance small compared to the laser-beam waist. This ``weak measurement'' is followed by a strong measurement which translates the centroid of the beam by a distance far larger than the birefringence-induced separation. In addition, we present data corresponding to orthogonal initial and final states, for which the weak value is not defined. This interference effect may have application in the amplification and detection of weak effects.