Nonlinear three-state quantum walks

TL;DR

This paper explores the complex dynamics of a nonlinear three-state quantum walk, revealing phenomena like self-trapping, solitons, radiation, and chaos, with a focus on metastable states and dynamical transitions.

Contribution

It introduces a nonlinear model of three-state quantum walks and uncovers novel behaviors such as metastable self-trapped states and dynamical transitions not seen in linear cases.

Findings

Metastable self-trapped wavepackets radiate with probability ∝ t^{-1/2}

Nonlinearity induces solitonic pulses and chaotic dynamics

Dynamical transition triggers radiation process in certain parameters

Abstract

The dynamics of a three-state quantum walk with amplitude-dependent phase shifts is investigated. We consider two representative inputs whose linear evolution is known to display either full dispersion of the wave packet or intrinsic localization on the initial position. The nonlinear counterpart presents much more involved dynamics featuring self-trapping, solitonic pulses, radiation, and chaotic-like behavior. We show that nonlinearity leads to a metastable self-trapped wavepacket component that radiates in the long-time regime with the survival probability $\propto t^{-1/2}$. A sudden dynamical transition from such metastable state to the point when the radiation process is triggered is found for a set of parameters.