Quantum super-oscillation of a single photon

Guang Hui Yuan; Stefano Vezzoli; Charles Altuzarra; Edward TF Rogers; Christophe Couteau; Cesare Soci; Nikolay I Zheludev

doi:10.1038/lsa.2016.127

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Quantum super-oscillation of a single photon

Original Articles

- Quantum super-oscillation of a single photon
- Light: Science & Applications Vol. 5, Issue 3, (2016)
- Affiliations：
  
  1.The Photonics Institute, Centre for Disruptive Photonic Technologies, Nanyang Technological University, Singapore 637371, Singapore
  2.CINTRA, CNRS-NTU-Thales, CNRS UMI 3288, Singapore 637553, Singapore
  3.Optoelectronics Research Centre and Centre for Photonic Metamaterials, University of Southampton, Southampton SO17 1BJ, UK
  4.Institute for Life Sciences, University of Southampton, Southampton SO17 1BJ, UK
  5.Laboratory for Nanotechnology, Instrumentation and Optics, ICD CNRS UMR 6281, University of Technology of Troyes, Troyes 10000, France
- Author bio：
  
  NI Zheludev, Email: nzheludev@ntu.edu.sg
- Funds：
- DOI：10.1038/lsa.2016.127
  CLC：
- Published：2016-09，
  
  Published Online：08 March 2016，
  
  Received：28 December 2015，
  
  Revised：03 March 2016，
  
  Accepted：04 March 2016
- Accepted：
Scan QR Code
Yuan, G. H. et al. Quantum super-oscillation of a single photon. Light: Science & Applications, 5, e16127 (2016).
DOI：

Yuan, G. H. et al. Quantum super-oscillation of a single photon. Light: Science & Applications, 5, e16127 (2016). DOI： 10.1038/lsa.2016.127.

摘要

Abstract

Super-oscillation is a counterintuitive phenomenon describing localized fast variations of functions and fields that happen at frequencies higher than the highest Fourier component of their spectra. The physical implications of this effect have been studied in information theory and optics of classical fields

and have been used in super-resolution imaging. As a general phenomenon of wave dynamics

super-oscillations have also been predicted to exist in quantum wavefunctions. Here we report the experimental demonstration of super-oscillatory behavior of a single-quantum object

a photon. The super-oscillatory behavior is demonstrated by tight localization of the photon wavefunction after focusing with an appropriately designed slit mask to create an interference pattern with a sub-diffraction hotspot (~0.45

). Such quantum super-oscillation can be used for low-intensity far-fiel

d super-resolution imaging techniques even down to single-photon counting regime

which would be of interest to quantum physics and non-invasive and label-free biological studies.

关键词

Keywords

energy backflowsingle-photon wavefunctionsuper-oscillationsuper-resolution

references

Aharonov Y, Anandan J, Popescu S, Vaidman L. Superpositions of time evolutions of a quantum system and a quantum time-translation machine.Phys Rev Lett1990;64: 2965–2968..

Berry MV. Faster than Fourier. In: Auandan JS, Safko JL, editors.Quantum Coherence and Reality: in Celebration of the 60th Birthday of Yakir Aharonov. Singapore: World Scientific; 1994.

Kempf A, Ferreira PJSG. Unusual properties of superoscillating particles.J Phys A Math Gen2004;37: 12067–12076..

Berry MV, Popescu S. Evolution of quantum superoscillations and optical superresolution without evanescent waves.J Phys A Math Gen2006;39: 6965–6977..

Ferreira PJSG, Kempf A, Reis MJCS. Construction of Aharonov-Berry's super-oscillations.J Phys A Math Theor2007;40: 5141–5147..

Berry MV, Shukla P. Pointer supershifts and superoscillations in weak measurements.J Phys A Math Theor2012;45: 015301..

Aharonov Y, Colombo F, Sabadini I, Struppa DC, Tollaksen J. Some mathematical properties of superoscillations.J Phys A Math Theor2011;44: 365304..

Berry MV, Moiseyev N. Superoscillations and supershifts in phase space: Wigner and Husimi function interpretations.J Phys A Math Theor2014;47: 315203..

Ferreira PJSG, Kempf A. Superoscillations: faster than the Nyquist rate.IEEE Trans Signal Process2006;54: 3732–3740..

Huang FM, Zheludev NI. Super-resolution without evanescent waves.Nano Lett2009;9: 1249–1254..

Zheludev NI. What diffraction limit?Nat Mater2008;7: 420–422..

Rogers ETF, Zheludev NI. Optical super-oscillations: sub-wavelength light focusing and super-resolution imaging.J Opt2013;15: 094008..

Rogers ETF, Lindberg J, Roy T, Savo S, Chad JEet al. A super-oscillatory lens optical microscope for subwavelength imaging.Nat Mater2012;11: 432–435..

Yuan GH, Rogers ETF, Roy T, Adamo G, Shen ZXet al. Planar super-oscillatory lens for sub-diffraction circular polarization optical needles at violet wavelengths.Sci Rep2014;4: 6333..

Lindberg J. Mathematical concepts of optical superresolution.J Opt2012;14: 083001..

Wong AMH, Eleftheriades GV. An optical super-microscope for far-field, real-time imaging beyond the diffraction limit.Sci Rep2013;3: 1715..

Wong AMH, Eleftheriades GV. Advances in imaging beyond the diffraction limit.IEEE Photon J2012;4: 586–589..

Berry MV. A note on superoscillations associated with Bessel beams.J Opt2013;15: 044006..

Berry MV, Dennis MR. Natural superoscillations in monochromatic waves inDdimensions.J Phys A Math Theor2009;42: 022003..

Dennis MR, Hamilton AC, Courtial J. Superoscillations in speckle patterns.Opt Lett2008;33: 2976–2978..

Huang FM, Kao TS, Fedotov VA, Chen YF, Zheludev NI. Nanohole array as a lens.Nano Lett2008;8: 2469–2472..

Rogers ETF, Savo S, Lindberg J, Roy T, Dennis MRet al. Super-oscillatory optical needle.Appl Phys Lett2013;102: 031108..

Roy T, Rogers ETF, Yuan GH, Zheludev NI. Point spread function of the optical needle super-oscillatory lens.Appl Phys Lett2014;104: 231109..

Amineh RK, Eleftheriades GV. 2D and 3D sub-diffraction source imaging with a super-oscillatory filter.Opt Express2013;21: 8142–8156..

Roy T, Rogers ETF, Zheludev NI. Sub-wavelength focusing meta-lens.Opt Express2013;21: 7577–7582..

Wang Q, Rogers ETF, Gholipour B, Wang CM, Yuan GHet al. Optically reconfigurable metasurfaces and photonic devices based on phase change materials.Nat Photonics2016;10: 60–65..

Aharonov Y, Albert DZ, Vaidman L. 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 Lett1988;60: 1351–1354..

Berry MV, Shukla P. Typical weak and superweak values.J Phys A Math Theor2010;43: 354024..

Vigoureux JM, D'Hooge L, van Labeke D. Quantization of evanescent electromagnetic waves: momentum of the electromagnetic field very close to a dielectric medium.Phys Rev A1980;21: 347–355..

Berry MV. Superluminal speeds for relativistic random waves.J Phys A Math Theor2012;45: 185308..

Hosten O, Kwiat P. Observation of the spin hall effect of light via weak measurements.Science2008;319: 787–790..

Kurtsiefer C, Oberparleiter M, Weinfurter H. High-efficiency entangled photon pair collection in type-Ⅱ parametric fluorescence.Phys Rev A2001;64: 023802..

Grosjean T, Courjon D. Polarization filtering induced by imaging system: effect on image structure.Phys Rev E2003;67: 046611..

Bocquillon E, Couteau C, Razavi M, Laflamme R, Weihs G. Coherence measures for heralded single-photon sources.Phys Rev A2009;79: 035801..

Berry MV. The adiabatic phase and Pancharatnam's phase for polarized light.J Mod Opt1987;34: 1401–1407..

Lee G, Ferreira PJSG. Superoscillations with optimum energy concentration.IEEE Trans Signal Process2014;62: 4857–4867..

Katzav E, Schwartz M. Yield-optimized superoscillations.IEEE Trans Signal Process2013;61: 3113–3118..

Dennis MR, O'Holleran K, Padgett MJ. Singular optics: optical vortices and polarization singularities.Prog Optics2009;53: 293–363..

Bashevoy MV, Fedotov VA, Zheludev NI. Optical whirlpool on an absorbing metallic nanoparticle.Opt Express2005;13: 8372–8379..

Totzeck M, Tiziani HJ. Phase-singularities in 2D diffraction fields and interference microscopy.Opt Commun1997;138: 365–382..

Berry MV. Quantum backflow, negative kinetic energy, and optical retro-propagation.J Phys A Math Theor2010;43: 415302..

Kocsis S, Braverman B, Ravets S, Stevens MJ, Mirin RPet al. Observing the average trajectories of single photons in a two-slit interferometer.Science2011;332: 1170–1173..

Dirac PAMThe Principles of Quantum Mechanics. Oxford: The Clarendon Press; 1958.

Boto AN, Kok P, Abrams DS, Braunstein SL, Williams CPet al. Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit.Phys Rev Lett2000;85: 2733–2736..

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