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We introduce a dynamical topological order parameter (DTOP) to characterize quantum walks. This parameter reveals distinct dynamical regimes and connects to dynamical quantum phase transitions.

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Area of Science:

  • Quantum physics
  • Statistical mechanics
  • Condensed matter theory

Background:

  • Quantum walks are inherently dynamical processes that do not fit equilibrium statistical physics models.
  • Understanding the principles governing unitary quantum dynamics has been a significant challenge.

Purpose of the Study:

  • To characterize split-step quantum walks using a dynamical topological order parameter (DTOP).
  • To explore the connection between quantum walk dynamics and dynamical quantum phase transitions.

Main Methods:

  • Theoretical characterization of split-step quantum walks.
  • Experimental observation of quantum walks.
  • Definition and measurement of a time-dependent dynamical topological order parameter (DTOP).
  • Identification of an equivalent many-body problem.

Main Results:

  • Split-step quantum walks can be characterized by an integer-quantized DTOP, measuring the geometric phase winding.
  • Distinct dynamical regimes were observed in experimental quantum walks, correlating with DTOP temporal behavior.
  • Nonanalytic changes in the DTOP are linked to dynamical quantum phase transitions.

Conclusions:

  • The DTOP provides a novel framework for understanding unitary quantum dynamics in quantum walks.
  • The study reveals a direct connection between topological properties and dynamical phase transitions in quantum systems.