Anderson localization of a one-dimensional quantum walker

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.
• 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.