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Topological transition in a non-Hermitian quantum walk
1Department of Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA.
Physical Review Letters
|March 5, 2009
Summary
We studied quantum walks on a decaying lattice, finding quantized particle displacement related to topological phases. This quantized behavior distinguishes coherent from incoherent quantum dynamics.
Area of Science:
- Quantum physics
- Condensed matter physics
- Topological phases
Background:
- Quantum walks are essential tools for quantum computation and simulation.
- Non-Hermitian systems exhibit unique phenomena not seen in Hermitian systems.
- Topological phases in quantum systems are robust and have potential applications.
Purpose of the Study:
- To analyze quantum walks on a decaying lattice.
- To investigate the role of topological phases in non-Hermitian systems.
- To explore the quantization of particle displacement and its relation to topological transitions.
Main Methods:
- Analysis of a quantum walk on a bipartite one-dimensional lattice.
- Modeling decay using a complex potential in a non-Hermitian tight-binding model.
- Definition and calculation of a winding number using Bloch eigenstates.
- Derivation of the mean particle displacement.
Main Results:
- The system exhibits two distinct topological phases characterized by a winding number.
- The mean particle displacement is quantized and directly related to the winding number.
- A topological transition occurs at a critical point, changing displacement from zero to one.
- The quantized behavior is experimentally relevant and can differentiate dynamics.
Conclusions:
- Quantum walks on decaying lattices display quantized displacement governed by topological phases.
- The winding number serves as a key indicator of topological transitions and system behavior.
- This work provides a framework for understanding and controlling quantum dynamics in non-Hermitian systems.
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