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Wave revivals: From imaging to number factorization and beyond

Tid: On 2023-06-14 kl 10.00

Plats: FA32

Medverkande: Professor Sergey Ponomarenko, Dalhousie University, Kanada

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Abstract: A spectacular self-imaging effect, experimentally discovered by Talbot, occurs whenever a one-dimensional spatially periodic structure is illuminated by a freely propagating paraxial optical field. The now classic eponymous effect has been found to be universal to waves of any nature and explored, besides optics, in acoustical, matter-wave, Bose-Einstein condensate, and Rydberg wave packet interferometry with numerous applications. I will briefly review the physics of wave revivals, stressing linear and nonlinear optical imaging and a fascinating link between wave physics and algebraic number theory. I will then present our results on wave revivals with coherent and random structured light and their applications to number factorization, yielding an efficient analog optical protocol to compute prime factors of large integers. I will conclude with outlining a close analogy between optical and matter wave revivals and implications of our results in optics to condensed-matter physics.