Nonlinear flip-flop quantum walks through potential barriers

TL;DR

This paper explores the complex dynamics of nonlinear flip-flop quantum walks with potential barriers, revealing regimes with soliton-like structures, self-trapping, and chaos, and suggests potential implementation in photonic systems.

Contribution

It introduces a novel model of nonlinear flip-flop quantum walks with amplitude-dependent phase shifts and potential barriers, analyzing diverse dynamic regimes and their dependence on system parameters.

Findings

Existence of soliton-like and self-trapped states.

Chaotic regimes emerge at intermediate nonlinearity levels.

System behavior varies with quantum coin parameters.

Abstract

The dynamics of nonlinear flip-flop quantum walk with amplitude-dependent phase shifts with pertubing potential barrier is investigated. Through the adjustment between uniform local perturbations and a Kerrlike nonlinearity of the medium we find a rich set of dynamic profiles. We will show the existence of different Hadamard quantum walking regimes, including those with mobile soliton-like structures or self-trapped states. The latter is predominant for perturbations with amplitudes that tend to $\varphi\rightarrow \pi/2$. In this system, the qubit shows an unusual behavior as we increase the amplitudes of the potential barriers, and displays a monotonic decrease in the self-trapping $\varphi_c$ with respect to the nonlinear parameter. A chaotic-like regime becomes predominant for intermediate nonlinearity values. Furthermore, we show that by changing the quantum coins ($\theta$) a non-trivial dynamic arises, where coins close to Pauli-X drives the system to a regime with predominant soliton-like structures, while the chaotic behavior are restricted to a narrow region in the $\chi$-$\varphi$ plane. We believe that is possible to implement and observe the proprieties of this model in a integrated photonic system.