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  • Letter
  • Open Access

Reconstructing superoscillations buried deeply in noise

Derek D. White1, Shunxing Zhang1, Barbara Šoda2, Achim Kempf2,3,4,5, Daniele C. Struppa6, Andrew N. Jordan1,7,8,9, and John C. Howell1,10,*

  • 1Institute for Quantum Studies, Chapman University, Orange, California 92866, USA
  • 2Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada N2L 2Y5
  • 3Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
  • 4Department of Physics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
  • 5Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
  • 6The Donald Bren Presidential Chair in Mathematics, Chapman University, Orange, California 92866, USA
  • 7The Kennedy Chair in Physics, Chapman University, Orange, California 92866, USA
  • 8Center for Coherence and Quantum Optics, University of Rochester, Rochester, New York 14627, USA
  • 9Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA
  • 10Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel

  • *Contact author: johhowell@chapman.edu
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Phys. Rev. A 110, L061502 – Published 23 December, 2024

DOI: https://doi.org/10.1103/PhysRevA.110.L061502

Abstract

We utilize a method using frequency combs to construct waves that feature superoscillations—local regions of the wave that exhibit a change in phase that the bandlimits of the wave should not otherwise allow. This method has been shown to create superoscillating regions that mimic any analytic function—even ones well outside the bandlimits—to an arbitrary degree of accuracy. We experimentally demonstrate that these waves are extremely robust against noise, allowing for accurate reconstruction of a superoscillating target function thoroughly buried in noise. We additionally show that such a construction can be easily used to range-resolve a signal well below the commonly accepted fundamental limit.

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Phys. Rev. A 110, L061502– Published 23 December, 2024
  • Received 7 September 2024
  • Accepted 10 October 2024
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