How a Bird in the Quantum Hand Can Be Worth 1000(*) in the Bush

(* - at least in binary)

OR: How the Result of Counting One Photon Can Turn Out to Be a Value of 8

In 1988, Aharonov, Albert, and Vaidman introduced a new paradigm of quantum measurement in a paper which had the unwieldy but provocative title "How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100." This paradigm, so-called "weak measurement," has since been the subject of widespread theoretical and experimental attention, both for the perspective it offers on quantum reality and for possible applications to precision measurement. Yet almost all of the weak-measurement experiments carried out so far could be alternatively understood in terms of the classical (electro-magnetic wave) theory of optics. Here we present a truly quantum version, the first in which a measurement apparatus deterministically entangles two distinct optical beams, enabling us to experimentally ask a question directly analogous to that of the original proposal: "In a two-arm interferometer containing one photon in total, can the result of a measurement of the photon number in one arm turn out to be greater than 1?" Specifically, we show that a single photon, when properly post-selected, can have an effect equal to that of eight photons: that is, in a system where a single photon has been calibrated to write a nonlinear phase shift of φo on a probe beam, we measure phase shifts as large as 8φo for appropriately post-selected single photons. This is the first deterministic weak-value experiment in optics which defies classical explanation, and constitutes a realization of our proposal for weak-value amplification (WVA) of the small optical nonlinearity at the single-photon level.

For Further Reading

How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100, the original AAV paper (technical)

In Praise of Weakness (semi-popular introduction to the idea of weak measurement)

Shutting a New Door on Locality (a semi-popular review of another recent postselection experiment)

"How to count one photon and get a(n average) result of 1000"(slides from a talk)

"How to count one photon and get a(n average) result of 8: progress in quantum nonlinear optics and weak-value amplification" (video of another talk)

Amplifying single-photon nonlinearity using weak measurements, our WVA proposal (technical paper)

"Observation of the nonlinear phase shift due to single post-selected photons," the first observation of the nonlinear optical effect of individual postselected photons (technical paper)

"Weak-value amplification of the nonlinear effect of a single photon," the technical paper on WVA of postselected photon (here is the published Nature Physics version, but the arXiv version contains the fuller introduction, the shortening of which by the editors distressingly also occasioned the appearance of a misspelling of a researcher's name in the published article.)

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