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International Journal of Theoretical Physics

One-Dimensional Three-State Quantum Walk with Single-Point Phase Defects

Yongzhen Xu, Gongde Guo, Song Lin

Published May 15, 2016• 7 citations
Publisher
DOI
10.1007/s10773-016-3034-7

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Experimental observations of quantum walks in one dimension have provided many exciting applications in quantum computing, while recent theoretical investigation of single-phase defect in these system points towards interesting phenomena associated with bound states. Here we obtain analytical solutions of a quantum walk with a general quantum coin in one dimension with multiple defects, with predictions on the condition for zero reflectance for scattering state and the existence of an analogy to the Ramsauer effect for multiple defects. We also show the transition from the zero-reflectance state to the bound state can provide a method for preparing the quantum walk in a bound state. Applications to systems similar to thin film optics are suggested.
Scale-free localization is a distinctive phenomenon in non-Hermitian systems, where specific eigenstates, known as scale-free localized states (LSs), possess localization lengths that scale linearly with the system size. Here, we show that a single non-Hermitian defect in one-dimensional quantum walks (QWs) induces scale-free localization. Driven by non-Hermiticity, the QW system undergoes a pseudo-Hermitian (PH) phase transition and the PH symmetry breaking is accompanied by the emergence of scale-free localization. As non-Hermiticity is further increased, the system undergoes a second phase transition, marked by the emergence of two pairs of bound states. Crucially, we identify the critical points of both transitions using localization properties. Furthermore, we extend our investigation to two-dimensional QWs, where a single non-Hermitian defect also induces scale-free localization, thereby demonstrating the universality of this phenomenon. Our work provides a valuable perspective for further exploring defect physics and a type of novel LS in non-Hermitian quantum systems.