Measurement of a Weak Value

Weak measurements are measurements in which the coupling between the measuring device and the observable to be measured is so weak that the eigenvalues of the observable are not resolved. Under certain circumstances the corresponding eigenfunctions can be made to interfere, producing a measurement result which is outside the allowed range of the observable's eigenvalues. We present the first measurement of this so-called "weak value" using an optical experiment. In our experiment, the small displacement between the two orthogonally polarized components of a laser beam passed through a birefringence crystal is measured. We use a numerical simulation to show that this phenomenon may be practical for detecting and amplifying small effects.