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

## TL;DR

This paper investigates how interactions affect charge density wave splitting at topological edge state intersections, revealing phase-dependent splitting and partial decoherence, with implications for Luttinger interferometry.

## Contribution

It derives an effective impurity model for interacting edge states and analyzes phase-dependent wave packet splitting and decoherence effects.

## Key findings

- Single wave packets split into four outgoing packets with phase-dependent coefficients.
- Multiple packets exhibit phase-dependent reflection and splitting.
- Coherent packets can transform into correlated quantum noise, losing their initial coherence.

## Abstract

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.