Interaction of quantum dot molecules with multi-mode radiation fields

TL;DR

This paper models the interaction between multiple quantum dot molecules and multi-mode electromagnetic fields, providing analytical solutions and analyzing entanglement dynamics within a quantum optics framework.

Contribution

It introduces a method to analytically solve the Jaynes-Cummings-Paul model for multiple quantum dots interacting with multi-mode fields, including entanglement evolution.

Findings

Analytical solutions for single-mode interactions.

Demonstration with two quantum dots in a two-mode cavity.

Analysis of entanglement dynamics via concurrency.

Abstract

In this article, the interaction of an arbitrary number of quantum dots, behaving as artificial molecules, with different energy levels and multi-mode electromagnetic field is studied. We make the assumption that each quantum dot can be represented as an atom with zero kinetic energy, and that all excitonic effects except dipole-dipole interactions may be disregarded. We use Jaynes-Cummings-Paul model with applications to quantum systems based on a time-dependent Hamiltonian and entangled states. We obtain a system of equations describing the interaction and present a method to solve the equations analytically for a single mode field within the Rotating-Wave Approximation. As an example of the applicability of this approach, we solve the system of two two-level quantum dots in a lossless cavity with two modes of electromagnetic field. We furthermore study the evolution of entanglement by defining and computing the concurrency.