# Driven quantum dot coupled to a fractional quantum Hall edge

## TL;DR

This paper investigates a driven quantum dot coupled to a fractional quantum Hall edge, analyzing the current response using bosonization and spin-boson models, highlighting the limitations of perturbative methods in capturing long-term charge quantization effects.

## Contribution

It demonstrates the equivalence of bosonization and spin-boson approaches in modeling the system and explores the validity of perturbative methods for out-of-equilibrium dynamics.

## Key findings

- Perturbative methods capture early-time physics.
- Both solution methods are equivalent.
- Long-time charge quantization is not captured by perturbation.

## Abstract

We study a model of a quantum dot coupled to a quantum Hall edge of the Laughlin state, taking into account short-range interactions between the dot and the edge. This system has been studied experimentally in electron quantum optics in the context of single particle sources. We consider driving the dot out of equilibrium by a time-dependent bias voltage. We calculate the resulting current on the edge by applying the Kubo formula to the bosonized Hamiltonian. The Hamiltonian of this system can also be mapped to the spin-boson model and in this picture, the current can be perturbatively calculated using the non-interacting blip approximation (NIBA). We show that both methods of solution are in fact equivalent. We present numerics demonstrating that the perturbative approaches capture the essential physics at early times, although they fail to capture the charge quantization (or lack thereof) in the current pulses integrated over long times.