Quantum dot dephasing by fractional quantum Hall edge states

TL;DR

This paper investigates how fractional quantum Hall edge states induce dephasing in a nearby quantum dot, revealing an anomalous voltage dependence linked to Luttinger liquid physics and connecting dephasing to backscattering noise.

Contribution

It provides a theoretical analysis of quantum dot dephasing due to fractional quantum Hall edge states, incorporating Luttinger liquid effects and exact solutions for backscattering regimes.

Findings

Dephasing rate depends anomalously on bias voltage.

Dephasing rate is proportional to zero-frequency backscattering noise.

Exact crossover description using Bethe-Ansatz solution.

Abstract

We consider the dephasing rate of an electron level in a quantum dot, placed next to a fluctuating edge current in the fractional quantum Hall effect. Using perturbation theory, we show that this rate has an anomalous dependence on the bias voltage applied to the neighboring quantum point contact, which originates from the Luttinger liquid physics which describes the Hall fluid. General expressions are obtained using a screened Coulomb interaction. The dephasing rate is strictly proportional to the zero frequency backscattering current noise, which allows to describe exactly the weak to strong backscattering crossover using the Bethe-Ansatz solution.