# Cavity-photon induced high order transitions between ground states of quantum dots

## TL;DR

This paper demonstrates that high-order quantum electromagnetic transitions are crucial for understanding the dynamics of a nanoscale electron system in a photon cavity, revealing a slow transition between quantum dot ground states with observable resonance features.

## Contribution

It introduces a detailed numerical approach to analyze high-order photon-induced transitions in a coupled quantum dot system within a cavity, accounting for complex interactions and geometry.

## Key findings

- Identification of a slow high-order transition between quantum dot ground states.
- Observation of a Fano-type resonance in photon-photon correlations.
- Accurate modeling of electron-electron and electron-photon interactions.

## Abstract

We show that quantum electromagnetic transitions to high orders are essential to describe the time-dependent path of a nanoscale electron system in a Coulomb blockage regime when coupled to external leads and placed in a three-dimensional rectangular photon cavity. The electronic system consists of two quantum dots embedded asymmetrically in a short quantum wire. The two lowest in energy spin degenerate electron states are mostly localized in each dot with only a tiny probability in the other dot. In the presence of the leads we identify a slow high order transition between the ground states of the two quantum dots. The Fourier power spectrum for photon-photon correlations in the steady state shows a Fano-type of a resonance for the frequency of the slow transition. Full account is taken of the geometry of the multi-level electronic system, and the electron-electron Coulomb interactions together with the para- and diamagnetic electron-photon interactions are treated with step wise exact numerical diagonalization and truncation of appropriate many-body Fock spaces. The matrix elements for all interactions are computed analytically or numerically exactly.