Letter | Published:

Weak-value amplification of the nonlinear effect of a single photon

Nature Physics volume 13, pages 540544 (2017) | Download Citation

This article has been updated

Abstract

In quantum mechanics, the concept of weak measurements allows for the description of a quantum system both in terms of the initial preparation and the final state (post-selection)1. This paradigm has been extensively studied theoretically and experimentally, but almost all of weak-measurement experiments carried out to date can be understood in terms of the classical (electromagnetic wave) theory of optics. Here, we present a quantum version in which the measurement apparatus deterministically entangles two distinct optical beams. 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 opens up a new regime for the study of entanglement of optical beams, as well as further investigations of the power of weak-value amplification for the measurement of small quantities.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Change history

  • 06 March 2017

    In the version of this Letter orginally published, L. Vaidman's surname was spelled incorrectly in the second paragraph of the body text. This has now been corrected in all versions of the Letter.

References

  1. 1.

    , & 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).

  2. 2.

    Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurement. Phys. Rev. A 67, 042105 (2003).

  3. 3.

    et al. Experimental demonstration of a universally valid error–disturbance uncertainty relation in spin measurements. Nat. Phys. 8, 185–189 (2012).

  4. 4.

    et al. Violation of Heisenberg’s measurement–disturbance relationship by weak measurements. Phys. Rev. Lett. 109, 100404 (2012).

  5. 5.

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

  6. 6.

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

  7. 7.

    et al. Violation of Heisenberg’s measurement–disturbance relationship by weak measurements. Phys. Rev. Lett. 109, 100404 (2012).

  8. 8.

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

  9. 9.

    , , & Quantum state reduction and conditional time evolution of wave–particle correlations in cavity QED. Phys. Rev. Lett. 85, 3149–3152 (2000).

  10. 10.

    & Experimental joint weak measurement on a photon pair as a probe of Hardy’s paradox. Phys. Rev. Lett. 102, 020404 (2009).

  11. 11.

    , , & Direct observation of Hardy’s paradox by joint weak measurement with an entangled photon pair. New J. Phys. 11, 033011 (2009).

  12. 12.

    , , & Asking photons where they have been. Phys. Rev. Lett. 111, 240402 (2013).

  13. 13.

    et al. Experiment investigating the connection between weak values and contextuality. Phys. Rev. Lett. 116, 180401 (2016).

  14. 14.

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

  15. 15.

    et al. Observation of a quantum Cheshire cat in a matter–wave interferometer experiment. Nat. Commun. 5, 4492 (2014).

  16. 16.

    , & Weak Measurement and Feedback in Superconducting Quantum Circuits 163–185 (Springer International Publishing, 2016).

  17. 17.

    How much time does a tunneling particle spend in the barrier region? Phys. Rev. Lett. 74, 2405–2409 (1995).

  18. 18.

    , & A scheme for efficient quantum computation with linear optics. Nature 409, 46–52 (2001).

  19. 19.

    & A one-way quantum computer. Phys. Rev. Lett. 86, 5188–5191 (2001).

  20. 20.

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

  21. 21.

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

  22. 22.

    & Weak value amplified optical activity measurements. Opt. Express 19, 16508–16517 (2011).

  23. 23.

    , , & Demonstration of weak measurement based on atomic spontaneous emission. Phys. Rev. Lett. 111, 023604 (2013).

  24. 24.

    , & Observation of the Imbert–Fedorov effect via weak value amplification. Opt. Lett. 39, 2266–2269 (2014).

  25. 25.

    , , & Amplification of angular rotations using weak measurements. Phys. Rev. Lett. 112, 200401 (2014).

  26. 26.

    , , , & Measurement of sub-pulse-width temporal delays via spectral interference induced by weak value amplification. Phys. Rev. A 89, 012126 (2014).

  27. 27.

    & Information amplification via postselection: a parameter-estimation perspective. Phys. Rev. A 88, 042116 (2013).

  28. 28.

    & Weak value amplification is suboptimal for estimation and detection. Phys. Rev. Lett. 112, 040406 (2014).

  29. 29.

    , & Technical advantages for weak-value amplification: when less is more. Phys. Rev. X 4, 011031 (2014).

  30. 30.

    , , & Quantum limits on postselected, probabilistic quantum metrology. Phys. Rev. A 89, 052117 (2014).

  31. 31.

    , , , & Experimentally quantifying the advantages of weak-value-based metrology. Phys. Rev. A 92, 032127 (2015).

  32. 32.

    & How the result of a single coin toss can turn out to be 100 heads. Phys. Rev. Lett. 113, 120404 (2014).

  33. 33.

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

  34. 34.

    et al. Violation of the Leggett–Garg inequality with weak measurements of photons. Proc. Natl Acad. Sci. USA 108, 1256–1261 (2011).

  35. 35.

    et al. Partial-measurement backaction and nonclassical weak values in a superconducting circuit. Phys. Rev. Lett. 111, 090506 (2013).

  36. 36.

    , , & Observation of the nonlinear phase shift due to single post-selected photons. Nat. Phys. 11, 905–909 (2015).

  37. 37.

    et al. Experimental demonstration of the effectiveness of electromagnetically induced transparency for enhancing cross-phase modulation in the short-pulse regime. Phys. Rev. Lett. 116, 173002 (2016).

Download references

Acknowledgements

This work was funded by NSERC, CIFAR, Northrop Grumman Aerospace Systems NG Next, and the Fetzer Franklin Fund of the John E. Fetzer Memorial Trust. We would like to acknowledge A. Stummer’s design and construction of several electronic devices which were essential to this experiment.

Author information

Affiliations

  1. Centre for Quantum Information and Quantum Control and Institute for Optical Sciences, Department of Physics, University of Toronto, 60 St George Street, Toronto, Ontario M5S 1A7, Canada

    • Matin Hallaji
    • , Amir Feizpour
    • , Greg Dmochowski
    • , Josiah Sinclair
    •  & Aephraim M. Steinberg
  2. Canadian Institute For Advanced Research, 180 Dundas Street W., Toronto, Ontario M5G 1Z8, Canada

    • Aephraim M. Steinberg

Authors

  1. Search for Matin Hallaji in:

  2. Search for Amir Feizpour in:

  3. Search for Greg Dmochowski in:

  4. Search for Josiah Sinclair in:

  5. Search for Aephraim M. Steinberg in:

Contributions

All authors contributed equally to the results, interpretation and presentation of this Letter.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Matin Hallaji.

Supplementary information

PDF files

  1. 1.

    Supplementary information

    Supplementary information

About this article

Publication history

Received

Accepted

Published

DOI

https://doi.org/10.1038/nphys4040

Further reading