Time-boundary scattering and topological resonant transmissions

TL;DR

This paper develops a unified scattering theory for quantum systems with time boundaries, revealing topological resonant transmissions linked to bulk invariants and their dimensional dependence.

Contribution

It introduces a Bloch-wave scattering framework for time boundaries and uncovers topological resonant transmissions with a bulk-time-boundary correspondence across all symmetry classes.

Findings

Topological resonant transmissions correspond to poles of the scattering matrix.

In 1D, the number of RTs equals the change in bulk topological invariant.

RTs are robust in even dimensions but fragile in odd dimensions due to symmetry breaking.

Abstract

Time boundaries (TBs), temporal analogues of spatial interfaces, offer a powerful handle to engineer quantum systems. However, unlike the well-developed stationary scattering theory at spatial interfaces, a unified framework for quantum scattering at TBs has been missing. Here we develop a Bloch-wave scattering theory for TBs by introducing a temporal scattering matrix $S$ between incoming and outgoing Bloch channels. We uncover topological resonant transmissions (RTs) -- poles of $S$ that yield perfect interband transmission and dynamical freezing of the quantum state. We establish a bulk-time-boundary correspondence for all integer Altland-Zirnbauer classes: the number of RTs equals the jump of the bulk topological invariant across the TB. In one dimension this gives a time-domain Levinson's theorem. A topological analysis further reveals a striking dimensional dependence. In even dimensions RTs are robust to temporal modulations and disorder, whereas in odd dimensions they can be destroyed by dynamical symmetry breaking. Our work places temporal and spatial scattering on the same footing and opens new avenues for engineering and probing quantum dynamics.