Abstract: The space-time duality between Fresnel diffraction and narrowband dispersion has been the basis for the development of successful temporal imaging systems employing “time lenses” which produce quadratic phase modulation on propagating optical wavepackets. The free-particle Schrödinger equation is also of the same form as Fresnel diffraction and narrowband dispersion and this suggests that if a suitable ‘’matter-wave’’ lens could be constructed, space-time transformations of charged-particle wavefunctions might be attained. Such transformations include, e.g., space-time magnification, demagnification and local time-reversal as analogs from conventional optical imaging. The key requirement of a matter-wave lens is the production of quadratic phase modulation of the charged-particle wavefunction. I propose that this could be accomplished by velocity-matched copropagation within the cusp of a time-harmonic scalar or vector potential; in essence a local time-varying Aharonov-Bohm interaction. I will discuss the requirements and parameters of a system that mimics simple optical imaging using an electromagnetic slow-wave structure as the matter-wave lens along with the free-particle propagation solution of the Schrödinger equation.
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Reception in the JILA h-Bar prior to the colloquium at 3:30 pm.