Decoherence of charge density waves in beam splitters for interacting quantum wires

• Published in: arXiv.org
• Main Authors: Schulz, Andreas, Schneider, Imke, Anglin, James
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 15.03.2019
• Subjects: Beam splitters; Charge density waves; Coherence; Correlation; Intersections; Packet transmission; Particle interactions; Physics - Strongly Correlated Electrons; Quantum wires; Reflection; Splitting; Time dependence; Wave packets
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1903.06431

Simple intersections between one-dimensional channels can act as coherent beam splitters for non-interacting electrons. Here we examine how coherent splitting at such intersections is affected by inter-particle interactions, in the special case of an intersection of topological edge states. We derive an effective impurity model which represents the edge-state intersection within Luttinger liquid theory at low energy. For Luttinger K = 1 / 2 , we compute the exact time-dependent expectation values of the charge density as well as the density-density correlation functions. In general a single incoming charge density wave packet will split into four outgoing wave packets with transmission and reflection coefficients depending on the strengths of the tunnelling processes between the wires at the junction. We find that when multiple charge density wave packets from different directions pass through the intersection at the same time, reflection and splitting of the packets depend on the relative phases of the waves. Active use of this phase-dependent splitting of wave packets may make Luttinger interferometry possible. We also find that coherent incident packets generally suffer partial decoherence from the intersection, with some of their initially coherent signal being transferred into correlated quantum noise. In an extreme case four incident coherent wave packets can be transformed entirely into density-density correlations, with the charge density itself having zero expectation value everywhere in the final state.