Self-trapped quantum walks
A. R. C. Buarque, Wandearley S. Dias · Physical Review A · 2020
We study the existence and characterization of self-trapping phenomena in discrete-time quantum walks. By considering a Kerr-like nonlinearity, we associate an acquisition of the intensity-dependent phase with the walker while it propagates on the lattice. Adjusting the nonlinear parameter $\ensuremath{\chi}$ and the quantum gates $\ensuremath{\theta}$, we will show the existence of different quantum walking regimes, including those with traveling solitonlike structures or localized by self-trapping. The latter scenario is absent for quantum gates close enough to the Pauli-$X$ gate. It appears for intermediate configurations and becomes predominant as quantum gates get closer to the Pauli-$Z$ gate. By using $\ensuremath{\chi}$ versus $\ensuremath{\theta}$ diagrams, we will show that the threshold between quantum walks with delocalized or localized regimes exhibits an unusual aspect in which an increment of the nonlinear strength can induce the system to transition from a localized to a delocalized regime.