Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Squeezing and over-squeezing of triphotons


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.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

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.


  1. Goda, K. et al. A quantum-enhanced prototype gravitational-wave detector. Nature Phys. 4, 472–476 (2008)

    Article  ADS  CAS  Google Scholar 

  2. Ye, J., Kimble, H. & Katori, H. Quantum state engineering and precision metrology using state-insensitive light traps. Science 320, 1734–1738 (2008)

    Article  ADS  CAS  Google Scholar 

  3. Furusawa, A. et al. Unconditional quantum teleportation. Science 282, 706–709 (1998)

    Article  ADS  CAS  Google Scholar 

  4. Hald, J., Sørensen, J. & Polzik, E. Spin squeezed atoms: A macroscopic entangled ensemble created by light. Phys. Rev. Lett. 83, 1319–1322 (1999)

    Article  ADS  Google Scholar 

  5. Bowen, W., Schnabel, R., Bachor, H.-A. & Lam, P. Polarization squeezing of continuous variable Stokes parameters. Phys. Rev. Lett. 88, 093601 (2002)

    Article  ADS  Google Scholar 

  6. Heersink, J. et al. Polarization squeezing of intense pulses with a fiber-optic Sagnac interferometer. Phys. Rev. A 68, 013815 (2003)

    Article  ADS  Google Scholar 

  7. Marquardt, C. et al. Quantum reconstruction of an intense polarization squeezed optical state. Phys. Rev. Lett. 99, 220401 (2007)

    Article  ADS  Google Scholar 

  8. Chaudhury, G. et al. Quantum control of the hyperfine spin of a Cs atom ensemble. Phys. Rev. Lett. 99, 163002 (2007)

    Article  ADS  Google Scholar 

  9. Ghose, S. S., Stock, R., Jessen, P. S., Lal, R. & Silberfarb, A. Chaos, entanglement and decoherence in the quantum kicked top. Phys. Rev. A 78, 042318 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  10. Agarwal, G. Relation between atomic coherent-state representation, state multipoles, and generalized phase-space distributions. Phys. Rev. A 24, 2889–2896 (1981)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  11. Dowling, J., Agarwal, G. & Schleich, W. Wigner distribution of a general angular-momentum state: Applications to a collection of two-level atoms. Phys. Rev. A 49, 4101–4109 (1994)

    Article  ADS  CAS  Google Scholar 

  12. Stratonovich, R. L. Gauge invariant generalization of Wigner distributions. Dokl. Akad. Nauk SSSR 109, 72–75 (1956)

    MathSciNet  Google Scholar 

  13. Luis, A. Quantum polarization distributions via marginals of quadrature distributions. Phys. Rev. A 71, 053801 (2005)

    Article  ADS  Google Scholar 

  14. Luis, A. Nonclassical polarization states. Phys. Rev. A 73, 063806 (2006)

    Article  ADS  Google Scholar 

  15. Arecchi, F., Courtens, E., Gilmore, R. & Thomas, H. Atomic coherent states in quantum optics. Phys. Rev. A 6, 2211–2273 (1972)

    Article  ADS  CAS  Google Scholar 

  16. Mitchell, M. W., Lundeen, J. S. & Steinberg, A. M. Super-resolving phase measurements with a multiphoton entangled state. Nature 429, 161–164 (2004)

    Article  ADS  CAS  Google Scholar 

  17. Lee, H., Kok, P., Cerf, N. J. & Dowling, J. P. Linear optics and projective measurements alone suffice to create large photon-number path entanglement. Phys. Rev. A 65, 030101 (2002)

    Article  ADS  Google Scholar 

  18. Fiurášek, J. Conditional generation of n-photon entangled states of light. Phys. Rev. A 65, 053818 (2002)

    Article  ADS  Google Scholar 

  19. Adamson, R. B. A., Shalm, L. K., Mitchell, M. W. & Steinberg, A. M. Multiparticle state tomography: hidden differences. Phys. Rev. Lett. 98, 043601 (2007)

    Article  ADS  CAS  Google Scholar 

  20. Adamson, R. B. A., Turner, P. S., Mitchell, M. W. & Steinberg, A. M. Detecting hidden differences via permutation symmetries. Phys. Rev. A 78, 033832 (2008)

    Article  ADS  Google Scholar 

  21. Durkin, G. A. & Dowling, J. P. Local and global distinguishability in quantum interferometry. Phys. Rev. Lett. 99, 070801 (2007)

    Article  ADS  Google Scholar 

  22. Dowling, J. Correlated input-port, matter-wave interferometer: Quantum-noise limits to the atom-laser gyroscope. Phys. Rev. A 57, 4736–4746 (1998)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  23. Walther, P. et al. De Broglie wavelength of a non-local four-photon state. Nature 429, 158–161 (2004)

    Article  ADS  CAS  Google Scholar 

  24. Nagata, T., Okamoto, R., O’Brien, J., Sasaki, K. & Takeuchi, S. Beating the standard quantum limit with four-entangled photons. Science 316, 726–729 (2007)

    Article  ADS  CAS  Google Scholar 

  25. Ou, Z. Fundamental quantum limit in precision phase measurement. Phys. Rev. A 55, 2598–2609 (1997)

    Article  ADS  CAS  Google Scholar 

  26. Resch, K. J. et al. Time-reversal and super-resolving phase measurements. Phys. Rev. Lett. 98, 223601 (2007)

    Article  ADS  CAS  Google Scholar 

  27. Miranowicz, A. & Grudka, A. A comparative study of relative entropy of entanglement, concurrence and negativity. J. Opt. B 6, 542–548 (2004)

    Article  ADS  Google Scholar 

  28. Peres, A. Separability criterion for density matrices. Phys. Rev. Lett. 77, 1413–1415 (1996)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  29. Horodecki, M. Separability of mixed states: necessary and sufficient conditions. Phys. Lett. A 223, 1–8 (1996)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  30. Takeuchi, S. Beamlike twin-photon generation by use of type II parametric downconversion. Opt. Lett. 26, 843–845 (2001)

    Article  ADS  CAS  Google Scholar 

Download references


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.

Author information

Authors and Affiliations


Corresponding author

Correspondence to L. K. Shalm.

Supplementary information

Supplementary Information

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

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Shalm, L., Adamson, R. & Steinberg, A. Squeezing and over-squeezing of triphotons. Nature 457, 67–70 (2009).

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI:

This article is cited by


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing