Self acceleration from spectral geometry in dissipative quantum-walk dynamics

TL;DR

This paper experimentally links the transient self acceleration in dissipative quantum walks to the spectral topology of non-Hermitian systems, revealing a universal connection between spectral geometry and dynamics.

Contribution

It demonstrates the direct correspondence between spectral topology and transient self acceleration in quantum walks, both in one and two dimensions, using experimental photonic systems.

Findings

Self acceleration proportional to spectral area in 1D quantum walks.

Self acceleration proportional to spectral volume in 2D quantum walks.

Transient acceleration transitions to constant drift velocity at long times.

Abstract

Dynamic behaviors of a physical system often originate from its spectral properties. In open systems, where the effective non-Hermitian description enables a wealth of spectral structures on the complex plane, the concomitant dynamics is significantly enriched, whereas the identification and comprehension of the underlying connections are challenging. Here we experimentally demonstrate the correspondence between the transient self acceleration of local excitations and the non-Hermitian spectral topology using lossy photonic quantum walks. Focusing first on one-dimensional quantum walks, we show that the measured short-time acceleration of the wave function is proportional to the area enclosed by the eigenspectrum. We then reveal similar correspondence in two-dimension quantum walks, where the self acceleration is proportional to the volume enclosed by the eigenspectrum in the complex parameter space. In both dimensions, the transient self acceleration crosses over to a long-time behavior dominated by a constant flow at the drift velocity. Our results unveil the universal correspondence between spectral topology and transient dynamics, and offer a sensitive probe for phenomena in non-Hermitian systems that originate from spectral geometry.