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Fabrication and Characterization of Disordered Polymer Optical Fibers for Transverse Anderson Localization of Light

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Anderson localization of a one-dimensional quantum walker.

Stanislav Derevyanko¹

¹Department of Electrical and Computer Engineering, Ben Gurion University of the Negev, Beer Sheva, 84105, Israel. stasd@bgu.ac.il.

Scientific Reports

|January 31, 2018

Summary

We investigated quantum walks with phase disorder, finding its impact on localization length. Our study reveals how coupling and disorder interact to affect quantum system dynamics.

Area of Science:

Quantum physics
Condensed matter physics
Photonics

Background:

Quantum walks are fundamental models for quantum computation and transport.
Disorder in quantum systems can lead to localization, affecting particle or wave propagation.
Photonic mesh lattices offer a classical analogue for studying quantum phenomena.

Purpose of the Study:

To analyze the behavior of a one-dimensional quantum walk under static phase disorder.
To explore the combined effects of coupling (quantum coin bias) and disorder.
To derive analytical expressions for localization length and validate with numerical simulations.

Main Methods:

Analytical derivation of localization length for strong and weak disorder regimes.
Numerical simulations of participation ratio, Lyapunov exponent, and return probability.

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Analysis of the interplay between coupling parameter and disorder strength.

Main Results:

Exact analytical expression for localization length in limiting disorder cases.
Numerical data confirms the influence of coupling on system dynamics.
Characterization of quantum walk behavior across different coupling strengths and disorder levels.

Conclusions:

Disorder significantly impacts quantum walk evolution and localization.
The coupling parameter plays a crucial role in mitigating or enhancing disorder effects.
The model provides insights into both quantum transport and classical wave propagation in disordered media.