Wave packet spreading with periodic, Fibonacci quasiperiodic, and random nonlinear discrete-time quantum walks

Gong, Lei; Guo, Xuan; Sun, Jingye; Zhao, Shenghui

doi:10.1007/s11128-022-03538-1

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Nonlinear Dqw1

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2024

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Cited by 2 publications

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“…They numerically find and describe a variety of nonlinear phenomena, which were further studied in [63].…”

Section: Nonlinear Dqwmentioning

confidence: 99%

Bright and dark solitons in a photonic nonlinear quantum walk: lessons from the continuum

Anglés-Castillo,

Pérez,

Roldán

2024

New J. Phys.

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We propose a nonlinear quantum walk model inspired in a photonic implementation in which thepolarization state of the light field plays the role of the coin-qubit. In particular, we take profit of thenonlinear polarization rotation occurring in optical media with Kerr nonlinearity, which allows toimplement a nonlinear coin operator, one that depends on the state of the coin-qubit. We considerthe space-time continuum limit of the evolution equation, which takes the form of a nonlinear Diracequation. The analysis of this continuum limit allows us to gain some insight into the existenceof different solitonic structures, such as bright and dark solitons. We illustrate several propertiesof these solitons with numerical calculations, including the effect on them of an additional phasesimulating an external electric field.

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“…They numerically find and describe a variety of nonlinear phenomena, which were further studied in [63].…”

Section: Nonlinear Dqwmentioning

confidence: 99%