Superoscillations, sensing and quantum light-matter interactions

Superoscillations allow a band-limited field to display local behavior that appears to lie outside its global spectral content (i.e. oscillate faster than its faster Fourier component). After reviewing the basics, I will discuss how such effects arise near engineered destructive-interference minima, where local wave vectors, weak values quantities, and Fisher information densities can become strongly concentrated. As a specific example, I will begin with "optical ventriloquism": near a diffraction minimum, light can appear to originate from a displaced, nonexistent source, due to sharp transverse shifts of the local wave vector. I will then connect this phenomenon to sensing with dark-port interferometric encoders, where an ideal interference null can concentrate shot-noise Fisher information into a photon-poor region, while coherent leakage and stochastic phase noise reshape and ultimately limit the advantage. Finally, I will turn to quantum light-matter interactions under spectral constraints. In controlled quantum platforms, decoherence mitigation often imposes photonic bandgaps or filtered control lines. I will discuss how a superoscillatory pulse whose global spectrum avoids a two-level-system resonance can nevertheless produce a resonant-like response through a spectrally filtered multimode cavity. The central message is that superoscillations redistribute response and information in unique ways that can be useful for quantum sensing and quantum control.