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Area of Science:

  • Quantum Physics
  • Non-Hermitian Systems
  • Photonic Quantum Walks

Background:

  • Dynamic behavior in physical systems is linked to spectral properties.
  • Open systems with non-Hermitian descriptions exhibit complex spectral structures.
  • Understanding the connection between spectral topology and dynamics in non-Hermitian systems is challenging.

Purpose of the Study:

  • To experimentally demonstrate the correspondence between transient self-acceleration of local excitations and non-Hermitian spectral topology.
  • To investigate this relationship in both one-dimensional (1D) and two-dimensional (2D) photonic quantum walks.

Main Methods:

  • Utilized lossy photonic quantum walks to experimentally probe non-Hermitian spectral topology.
  • Measured the short-time acceleration of the wave function in 1D and 2D quantum walks.
  • Analyzed the relationship between spectral geometry (area/volume) and wave function acceleration.

Main Results:

  • In 1D quantum walks, wave function acceleration is proportional to the area enclosed by the eigenspectrum.
  • In 2D quantum walks, self-acceleration is proportional to the volume enclosed by the eigenspectrum in complex parameter space.
  • Observed a crossover from transient self-acceleration to a long-time drift velocity in both dimensions.

Conclusions:

  • Unveiled a universal correspondence between spectral topology and transient dynamics in non-Hermitian systems.
  • Established spectral geometry as a sensitive probe for phenomena in non-Hermitian systems.
  • This work provides fundamental insights into the interplay between spectral properties and emergent dynamics.