Light can be reflected or transmitted when it reaches an interface between two materials. Quantum waves can also encounter boundaries in time when a system's properties change. However, a unified description of scattering at these temporal interfaces has been lacking.

HU Haiping, a researcher from the Institute of Physics of the Chinese Academy of Sciences, has recently developed a framework for quantum scattering at time boundaries.

The study was published on September 18 in the Proceedings of the National Academy of Sciences (PNAS).

The framework treats a time boundary as a scattering interface between two quantum phases. It introduces a temporal scattering matrix to describe how quantum states cross the boundary, covering both abrupt changes and finite-duration modulation.

A central prediction of the study is topological resonant transmission. At resonance, a suitable state can transfer completely from the initial valence-band subspace to the final conduction-band subspace. The framework also applies to multiband systems.

According to the study, the number of protected resonances is determined by the change in band topology across the boundary. This bulk-time-boundary correspondence links the global properties of quantum phases to their temporal scattering behavior. In one dimension, a time-domain version of Levinson's theorem connects the resonance count to scattering phases.

The study also reveals that resonance stability depends on spatial dimension. In the even-dimensional classes studied, resonances survive symmetry-compatible temporal modulation; in odd dimensions, dynamical symmetry breaking can remove them. Numerical calculations also demonstrate robustness against moderate disorder.

Illustrative simulations show dynamical freezing, in which internal-state oscillations stop after the boundary, and resonant wave packets that propagate without splitting.

According to HU, these effects offer observable signatures for controlling quantum states and probing topology in ultracold atoms and photonic systems.