Quantum weak measurements to measure nanoradians

Measuring a nanoradian corresponds to standing on the moon and determining the angle between the top and bottom of a house on earth. Such a small angle can, however, be measured if one borrows a trick from quantum measurement theory. Aharonov, Albert,  and Vaidman showed how the result of a 'measurement' of an observable, A, can be much larger than any of its eigenvalues (see figure).

This idea can be translated into optics [2] and has recently been used in the detection of the Spin Hall effect of light [3]. We are working on a slightly different implementation that can be used to dramatically increase the chiral splitting we have recently observed [4].

[1]"How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100", Phys. Rev. Lett. 60, 1351 - 1354 (1988)

[2]"Realization of a measurement of a ‘‘weak value’’", Phys. Rev. Lett. 66, 1107 - 1110 (1991)

[3] "Observation of the Spin Hall Effect of Light via Weak Measurements", Science 319 787 (2008)

[4] “Chiral Molecules Split Light: Reflection and Refraction in a Chiral Liquid”, Phys. Rev. Lett., 97, (2006), 173002. [pdf]

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