Time-delay in quantum resonant systems

R. G. Tee

Massimiliano Sassoli de Bianchi

The one-dimensional Levinson’s theorem is derived and used to study zero-energy resonances in a double-potential system. The low energy behavior of time delay is also investigated. In particular, it is shown that the quantum mechanical time delay admits a classical lower bound, in the low energy limit, if the potential has no bound-state solutions.

Philippe Martin

Sebastian A. Schulz, Davide Grassani, Ivan Cardea +5 more

All resonant systems throughout science and engineering, independent of their physical implementation have a bandwidth that is inversely related to the decay time. A similar relation exists in all slow-light systems, where the group index (and therefore the delay for a given footprint) is inversely related to the bandwidth. Therefore, resonant or slow-light systems can either store a broad signal for a short time, or a narrow signal for a long time, but cannot achieve large delay for broad bandwidth signals.Here we discuss our recent work on non-reciprocal optical systems that are not constrained by the delay-bandwidth limit. We show that large, broadband optical delay is not a pipe dream and is achievable with current optical technology. We discuss the underlying physics of delay and bandwidth in non-reciprocal optical systems and present an experimental implementation, based on a figure-9 cavity. We demonstrate a delay-bandwidth product 30 times above the seemingly fundamental time-bandwidth limit of traditional systems. Furthermore, we show that the optical pulse can be released after an arbitrary number of round trips, providing the control and tunability lacking from conventional spiral waveguide or fibre loop delay lines.

Slobodan Danko Bosanac

The time delay, as defined via phase shifts, does not apply to atom-atom collisions because of the semiclassical nature of the system. In this limit the contribution of one partial wave to the cross section is negligible. Therefore, we analyze time delay for the scattering amplitude and show that some new phenomena may occur, which cannot be explained by the time delay for a single phase shift. The time delay, which is averaged over all scattering angles, shows structure corresponding to several delay mechanisms. We also show that the lifetime of a resonance state, formed in a collision, may be considerably shorter than expected from the theory of resonance scattering.

健司 加嶋, Kenji KASHIMA, 山本, 直樹 +1 more