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Full characterization of polarization states of light via direct measurement

Nature Photonics volume 7, pages 316321 (2013) | Download Citation

Abstract

Ascertaining the physical state of a system is vital in order to understand and predict its behaviour. However, due to their fragile nature, the direct observation of quantum states has, until recently, been elusive. Historically, determination of the quantum state has been performed indirectly through the use of tomography. We report on two experiments showing that an alternative approach can be used to determine the polarization quantum state in a simple, fast and general manner. The first experiment entails the direct measurement of the probability amplitudes describing pure polarization states of light, the first such measurement on a two-level system. The second experiment entails the direct measurement of the Dirac distribution (a phase-space quasi-probability distribution informationally equivalent to the density matrix), demonstrating that the direct measurement procedure is applicable to general (that is, potentially mixed) quantum states. Our work has applications to measurements in foundational quantum mechanics, quantum information and quantum metrology.

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References

  1. 1.

    , & Quantum tomography. Adv. Imag. Electron. Phys. 128, 205–308 (2003).

  2. 2.

    , , & Maximum-likelihood estimation of the density matrix. Phys. Rev. A 61, 010304 (1999).

  3. 3.

    , , & Exploring Hilbert space: accurate characterization of quantum information. Phys. Rev. A 65, 012301 (2001).

  4. 4.

    et al. Tomographic imaging of molecular orbitals. Nature 432, 867–871 (2004).

  5. 5.

    , & Full characterization of a three-photon Greenberger–Horne–Zeilinger state using quantum state tomography. Phys. Rev. Lett. 94, 070402 (2005).

  6. 6.

    , , , & Tomography of the quantum state of photons entangled in high dimensions. Phys. Rev. A 84, 062101 (2011).

  7. 7.

    , , , & Direct measurement of the quantum wavefunction. Nature 474, 188–191 (2011).

  8. 8.

    & Procedure for direct measurement of general quantum states using weak measurement. Phys. Rev. Lett. 108, 070402 (2012).

  9. 9.

    On the analogy between classical and quantum mechanics. Rev. Mod. Phys. 17, 195–199 (1945).

  10. 10.

    et al. Wigner–Weyl correspondence in quantum mechanics for continuous and discrete systems—a Dirac-inspired view. J. Phys. A 39, 1405–1423 (2006).

  11. 11.

    Complex joint probabilities as expressions of reversible transformations in quantum mechanics. New J. Phys. 14, 043031 (2012).

  12. 12.

    Negative probability. In Quantum Implications: Essays in Honour of David Bohm Ch. 13 (eds Healy, B. J. & Peat, F. D.) 235–248 (Routledge, 1987).

  13. 13.

    Quantum-state tomography and discrete Wigner function. Phys. Rev. Lett. 74, 4101–4105 (1995).

  14. 14.

    , , & Direct measurement of the spatial Wigner function with area-integrated detection. Opt. Lett. 28, 1317–1319 (2003).

  15. 15.

    , , , & Measurement of the transverse spatial quantum state of light at the single-photon level. Opt. Lett. 30, 3365–3367 (2005).

  16. 16.

    , & 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).

  17. 17.

    , & The sense in which a weak measurement of a spin-1/2 particle's spin component yields a value 100. Phys. Rev. D 40, 2112–2117 (1989).

  18. 18.

    & Weak easurement of photon polarization. Phys. Lett. A 143, 357–361 (1990).

  19. 19.

    , & Realization of a measurement of a weak value. Phys. Rev. Lett. 66, 1107–1110 (1991).

  20. 20.

    Weak values, quantum trajectories, and the cavity-QED experiment on wave–particle correlation. Phys. Rev. A 65, 032111 (2002).

  21. 21.

    , , , & Fast light, slow light, and phase singularities: A connection to generalized weak values. Phys. Rev. Lett. 92, 043601 (2004).

  22. 22.

    , & Experimental realization of the quantum box problem. Phys. Lett. A 324, 125–131 (2004).

  23. 23.

    Weak measurements with arbitrary probe states. Phys. Rev. Lett. 93, 120402 (2004).

  24. 24.

    , , , & Measurement of quantum weak values of photon polarization. Phys. Rev. Lett. 94, 220405 (2005).

  25. 25.

    & Observation of the spin hall effect of light via weak measurements. Science 319, 787–790 (2008).

  26. 26.

    , , & Ultrasensitive beam deflection measurement via interferometric weak value amplification. Phys. Rev. Lett. 102, 173601 (2009).

  27. 27.

    Viewpoint: weak measurements just got stronger. Physics 2, 32 (2009).

  28. 28.

    et al. Observing the average trajectories of single photons in a two-slit interferometer. Science 332, 1170–1173 (2011).

  29. 29.

    , & Amplifying single-photon nonlinearity using weak measurements. Phys. Rev. Lett. 107, 133603 (2011).

  30. 30.

    & Weak values of a quantum observable and the cross-Wigner distribution. Phys. Lett. A 376, 293–296 (2012).

  31. 31.

    et al. Imaging high-dimensional spatial entanglement with a camera. Nature Commun. 3, 984 (2012).

  32. 32.

    & Practical measurement of joint weak values and their connection to the annihilation operator. Phys. Lett. A 334, 337–344 (2005).

  33. 33.

    & Optimal state-determination by mutually unbiased measurements. Ann. Phys. 191, 363–381 (1989).

  34. 34.

    Postselected weak measurement beyond the weak value. Phys. Rev. A 81, 044102 (2010).

  35. 35.

    , & Observation of entanglement witnesses for orbital angular momentum states. Eur. Phys. J. D 66, 156 (2012).

  36. 36.

    et al. Entanglement in a solid-state spin ensemble. Nature 470, 69–72 (2011).

  37. 37.

    Quantum information storage for over 180 s using donor spins in a 28Si ‘semiconductor vacuum’. Science 336, 1280–1283 (2012).

  38. 38.

    Full counting statistics of weak-value measurement. Phys. Rev. A 85, 032106 (2012).

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Acknowledgements

The authors thank K. Piché and F. Miatto for helpful discussions, and P.B. Corkum and C. Zhang for lending us the quartz crystal. This work was supported by the Canada Excellence Research Chairs (CERC) Program. In addition, R.W.B. acknowledges support from the DARPA InPho program.

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Affiliations

  1. Department of Physics, University of Ottawa, Ottawa, Canada K1N 6N5

    • Jeff Z. Salvail
    • , Megan Agnew
    • , Allan S. Johnson
    • , Eliot Bolduc
    • , Jonathan Leach
    •  & Robert W. Boyd
  2. Institute of Optics, University of Rochester, Rochester, New York 14627, USA

    • Robert W. Boyd

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Contributions

J.Z.S. initiated the study. The experiment was designed by J.Z.S., A.S.J., E.B. and J.L. The experiment was performed by J.Z.S., M.A. and A.S.J., and data analysis was performed by J.Z.S. R.W.B. supervised all aspects of the project. All authors contributed to the text of the manuscript.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Jeff Z. Salvail.

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DOI

https://doi.org/10.1038/nphoton.2013.24

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