Quantum super-oscillation of a single photon

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

[1]  Christian Kurtsiefer,et al.  High efficiency entangled photon pair collection in type II parametric fluorescence , 2001, quant-ph/0101074.

[2]  George V Eleftheriades,et al.  2D and 3D sub-diffraction source imaging with a superoscillatory filter. , 2013, Optics express.

[3]  Mark R. Dennis,et al.  Superoscillation in speckle patterns. , 2008, Optics letters.

[4]  Daniele C. Struppa,et al.  Some mathematical properties of superoscillations , 2011 .

[5]  M. Berry,et al.  Superluminal speeds for relativistic random waves , 2012 .

[6]  Dae Gwan Lee,et al.  Superoscillations With Optimum Energy Concentration , 2014, IEEE Transactions on Signal Processing.

[7]  Nikolay I Zheludev,et al.  What diffraction limit? , 2008, Nature materials.

[8]  Sandu Popescu,et al.  Evolution of quantum superoscillations, and optical superresolution without evanescent waves , 2006 .

[9]  N. Zheludev,et al.  Nanohole array as a lens. , 2008, Nano letters.

[10]  P. Dirac.  Principles of Quantum Mechanics , 1982 .

[11]  M. Berry,et al.  Quantum backflow, negative kinetic energy, and optical retro-propagation , 2010 .

[12]  T. Grosjean,et al.  Polarization filtering induced by imaging systems: effect on image structure. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  Abrams,et al.  Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit , 1999, Physical review letters.

[14]  Achim Kempf,et al.  Construction of Aharonov–Berry's superoscillations , 2007 .

[15]  Michael Beny,et al.  Faster than Fourier , 2017 .

[16]  G. Weihs,et al.  Coherence measures for heralded single-photon sources , 2008, 0807.1725.

[17]  Nikolay I. Zheludev,et al.  Point spread function of the optical needle super-oscillatory lens , 2014 .

[18]  Aephraim M. Steinberg,et al.  Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer , 2011, Science.

[19]  J. Vigoureux,et al.  Quantization of evanescent electromagnetic waves : momentum of the electromagnetic field very close to a dielectric medium Phys. Rev. A 21 p 347 (1980) , 1980 .

[20]  Mark R. Dennis,et al.  A super-oscillatory lens optical microscope for subwavelength imaging. , 2012, Nature materials.

[21]  P.J.S.G. Ferreira,et al.  Superoscillations: Faster Than the Nyquist Rate , 2006, IEEE Transactions on Signal Processing.

[22]  J. Teng,et al.  Optically reconfigurable metasurfaces and photonic devices based on phase change materials , 2015, Nature Photonics.

[23]  Vaidman,et al.  Superpositions of time evolutions of a quantum system and a quantum time-translation machine. , 1990, Physical review letters.

[24]  M. Berry,et al.  Pointer supershifts and superoscillations in weak measurements , 2012 .

[25]  Achim Kempf,et al.  Unusual properties of superoscillating particles , 2004 .

[26]  Vaidman,et al.  How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100. , 1988, Physical review letters.

[27]  Leggett.  Comment on "How the result of a measurement of a component of the spin of a spin-(1/2 particle can turn out to be 100" , 1989, Physical review letters.

[28]  Nikolay I Zheludev,et al.  Sub-wavelength focusing meta-lens. , 2013, Optics express.

[29]  Michael V Berry,et al.  A note on superoscillations associated with Bessel beams , 2013 .

[30]  Nikolay I. Zheludev,et al.  Optical super-oscillations: sub-wavelength light focusing and super-resolution imaging , 2013 .

[31]  G. Eleftheriades,et al.  Advances in Imaging Beyond the Diffraction Limit , 2012, IEEE Photonics Journal.

[32]  N. Zheludev,et al.  Optical whirlpool on an absorbing metallic nanoparticle. , 2005, Optics express.

[33]  George V. Eleftheriades,et al.  An Optical Super-Microscope for Far-field, Real-time Imaging Beyond the Diffraction Limit , 2013, Scientific Reports.

[34]  Nikolay I. Zheludev,et al.  Super-oscillatory optical needle , 2013 .

[35]  Hans J. Tiziani,et al.  Phase-singularities in 2D diffraction fields and interference microscopy , 1997 .

[36]  Nikolay I Zheludev,et al.  Super-resolution without evanescent waves. , 2008, Nano letters.

[37]  M. Berry,et al.  Typical weak and superweak values , 2010 .

[38]  Mark R. Dennis,et al.  Singular optics: optical vortices and polarization singularities , 2009 .

[39]  M. Berry,et al.  Superoscillations and supershifts in phase space: Wigner and Husimi function interpretations , 2014 .

[40]  Nikolay I. Zheludev,et al.  Planar super-oscillatory lens for sub-diffraction optical needles at violet wavelengths , 2014, Scientific Reports.

[41]  Y. Rahmat-Samii,et al.  Advances in Particle Swarm Optimization for Antenna Designs: Real-Number, Binary, Single-Objective and Multiobjective Implementations , 2007, IEEE Transactions on Antennas and Propagation.

[42]  Onur Hosten,et al.  Observation of the Spin Hall Effect of Light via Weak Measurements , 2008, Science.

[43]  Moshe Schwartz,et al.  Yield-Optimized Superoscillations , 2012, IEEE Transactions on Signal Processing.

[44]  Jari Lindberg,et al.  Mathematical concepts of optical superresolution , 2012 .

[45]  Mark R. Dennis,et al.  Natural superoscillations in monochromatic waves in D dimensions , 2009 .

[46]  M. Berry.  The Adiabatic Phase and Pancharatnam's Phase for Polarized Light , 1987 .