Scaling law linking field and weight dynamic ranges in superoscillation

Andrew N. Jordan, John C. Howell, A. Nick Vamivakas +1 more

Denis G. Baranov, A. P. Vinogradov, Alexander A. Lisyansky

We study counterintuitive dynamics of a two-level system (TLS) interacting with electric field superoscillating in time. We show that a TLS may be excited by an external light pulse whose spectral components are below the absorption line of the TLS. We attribute this unique dynamics to the Rabi oscillations of the TLS in a superoscillating driving field.

Achim Kempf, Ferreira, P J S G

It has been found that functions can oscillate locally much faster than their Fourier transform would suggest is possible - a phenomenon called superoscillation. Here, we consider the case of superoscillating wave functions in quantum mechanics. We find that they possess rather unusual properties which raise measurement theoretic, thermodynamic and information theoretic issues. We explicitly determine the wave functions with the most pronounced superoscillations, together with their scaling behavior. We also address the question how superoscillating wave functions could be produced.

Michael Berry

Wilhelm Brenig

Achim Kempf, Paulo J S G Ferreira

It has been found that functions can oscillate locally much faster than their Fourier transform would suggest is possible - a phenomenon called superoscillation. Here, we consider the case of superoscillating wave functions in quantum mechanics. We find that they possess rather unusual properties which raise measurement theoretic, thermodynamic and information theoretic issues. We explicitly determine the wave functions with the most pronounced superoscillations, together with their scaling behavior. We also address the question how superoscillating wave functions could be produced.