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Light’s Polarization States Measured Directly
Mar 2013
ROCHESTER, N.Y., and OTTAWA, Ontario, Canada, March 4, 2013 — There may be a way around Heisenberg’s famous Uncertainty Principle, a law of the quantum world that says precise measurement is impossible.

The solution could be a method developed at the universities of Rochester and Ottawa, which for the first time directly measures the polarization states of light. The direct measurement technique, developed in 2011 by scientists at Canada’s National Research Council, determines the wave function — a way of determining the state of a quantum system. Such direct measurement had long been believed to be impossible on the basis that you could never fully understand a quantum system through direct observation.

Now, the investigators, led by Robert Boyd, have discovered that it is possible to measure fundamental related variables, known as “conjugate” variables, of a quantum particle or state directly. The discovery is applicable to qubits, the building blocks of quantum information theory, as polarization states of light can be used to encode information.

“The ability to perform direct measurement of the quantum wave function has important future implications for quantum information science,” said Boyd, who is Canada Excellence Research Chair in Quantum Nonlinear Optics at the University of Ottawa and professor of optics and physics at the University of Rochester. “Ongoing work in our group involves applying this technique to other systems, for example measuring the form of a 'mixed' (as opposed to a pure) quantum state.”

Weak measurement: As light goes through a birefringent crystal, the horizontally and vertically polarized components of light spread out in space, but an overlap between the two components remains when they emerge. In a “strong” measurement, the two components would be fully separated.
Weak measurement: As light goes through a birefringent crystal, the horizontally and vertically polarized components of light spread out in space, but an overlap between the two components remains when they emerge. In a “strong” measurement, the two components would be fully separated. Courtesy of Jonathan Leach.

A technique called quantum tomography previously has allowed researchers to measure the information contained in these quantum states, but only indirectly. Quantum tomography requires intensive post-processing of the data, a time-consuming process that is not required in the direct measurement technique. Thus, in principle, the new technique provides the same information as quantum tomography but in significantly less time.

"The key to characterizing any quantum system is gathering information about conjugate variables," said co-author Jonathan Leach, who is now a lecturer at Heriot-Watt University in the UK. "The reason it wasn't thought possible to measure two conjugate variables directly was because measuring one would destroy the wave function before the other one could be measured."

The new method relies on a trick that “weakly” measures the first property of a system in such a way that it is not disturbed, making it possible to obtain information about the second party through “strong” measurement.

Boyd and colleagues did this by passing polarized light through two crystals of differing thicknesses: the first, a very thin crystal that “weakly” measured the horizontal and vertical polarization state; the second, a much thicker crystal that “strongly” measured the diagonal and anti-diagonal polarization state.

The position and momentum of the light were used as indicators of the polarization state. To couple the polarization to the spatial degree of freedom, the investigators used birefringent crystals: When light goes through such a crystal, there is a spatial separation introduced for different polarizations. For example, if light is made of a combination of horizontally and vertically polarized components, the positions of the individual components will spread out when it goes through the crystal according to its polarization. The thickness of the crystal can control the strength of the measurement, weak or strong, and determine the degree of separation, correspondingly small or large.

Repeating the process several times allows accurate statistics to be built up, giving a full, direct characterization of the polarization states of the light.

The work, supported by the Canada Excellence Research Chairs Program and the DARPA InPho program, was published in Nature Photonics (doi: 10.1038/nphoton.2013.24). 

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With respect to light radiation, the restriction of the vibrations of the magnetic or electric field vector to a single plane. In a beam of electromagnetic radiation, the polarization direction is the direction of the electric field vector (with no distinction between positive and negative as the field oscillates back and forth). The polarization vector is always in the plane at right angles to the beam direction. Near some given stationary point in space the polarization direction in the beam...
AmericasCanadaCanada Excellence Research Chairdirect measurementHeisenberg’s Uncertainty PrincipleJonathan LeachNew Yorkopticspolarizationquantum informationquantum tomographyqubitsResearch & TechnologyRobert Boydstrong measurementUniversity of OttawaUniversity of Rochesterweak measurement

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