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Squeezing and over-squeezing of triphotons

Abstract

Quantum mechanics places a fundamental limit on the accuracy of measurements. In most circumstances, the measurement uncertainty is distributed equally between pairs of complementary properties; this leads to the ‘standard quantum limit’ for measurement resolution. Using a technique known as ‘squeezing’, it is possible to reduce the uncertainty of one desired property below the standard quantum limit at the expense of increasing that of the complementary one. Squeezing is already being used to enhance the sensitivity of gravity-wave detectors1 and may play a critical role in other high precision applications, such as atomic clocks2 and optical communications3. Spin squeezing (the squeezing of angular momentum variables) is a powerful tool, particularly in the context of quantum light–matter interfaces4,5,6,7,8,9. Although impressive gains in squeezing have been made, optical spin-squeezed systems are still many orders of magnitude away from the maximum possible squeezing, known as the Heisenberg uncertainty limit. Here we demonstrate how an optical system can be squeezed essentially all the way to this fundamental bound. We construct spin-squeezed states by overlapping three indistinguishable photons in an optical fibre and manipulating their polarization (spin), resulting in the formation of a squeezed composite particle known as a ‘triphoton’. The symmetry properties of polarization imply that the measured triphoton states can be most naturally represented by quasi-probability distributions on the surface of a sphere. In this work we show that the spherical topology of polarization imposes a limit on how much squeezing can occur, leading to the quasi-probability distributions wrapping around the sphere—a phenomenon we term ‘over-squeezing’. Our observations of spin-squeezing in the few-photon regime could lead to new quantum resources for enhanced measurement, lithography and information processing that can be precisely engineered photon-by-photon.

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Figure 1: Overview of the experiment.
Figure 2: Triphoton Wigner quasi-probability distributions on the Poincaré sphere.
Figure 3: The uncertainty in the Stokes parameters and for 11 squeezed triphoton states.

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Acknowledgements

We thank S. Ghose and P. Jessen for discussions. This work was supported by the Natural Sciences and Engineering Research Council of Canada, Ontario Centres of Excellence, Canadian Institute for Photonic Innovations, Quantum Works, and the Canadian Institute for Advanced Research.

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Correspondence to L. K. Shalm.

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This file contains Supplementary Methods and Data, a Supplementary Discussion, Supplementary Table 1 and Supplementary Figures 1-2 with Legends (PDF 376 kb)

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Shalm, L., Adamson, R. & Steinberg, A. Squeezing and over-squeezing of triphotons. Nature 457, 67–70 (2009). https://doi.org/10.1038/nature07624

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