Nonlinear flip-flop quantum walks through potential barriers

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 Kerr-like 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 $\ensuremath{\varphi}\ensuremath{\rightarrow}\ensuremath{\pi}/2$. 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 ${\ensuremath{\varphi}}_{c}$ 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 ($\ensuremath{\theta}$) a nontrivial 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 $\ensuremath{\chi}\ensuremath{-}\ensuremath{\varphi}$ plane. We believe that is possible to implement and observe the proprieties of this model in an integrated photonic system.