Radiative coupling of quantum dots in photonic crystal structures

TL;DR

This paper develops a formalism to model the interaction between quantum dots and photon modes in photonic crystal structures, revealing how radiative coupling depends on structure and mode properties, with implications for quantum information transfer.

Contribution

It introduces a general eigenvalue-based formalism for modeling quantum dot-photon interactions in photonic crystals, including disorder effects and mode calculations, extending previous analytical results.

Findings

Inter-dot radiative coupling can reach 100 μeV in short cavities.

Coupling strength decay depends on photon group velocity and lifetime.

Transition from single-mode to multi-mode regime occurs around cavity length n=150.

Abstract

We derive a general formalism to model the polariton states resulting from the radiation-matter interaction between an arbitrary number of excitonic transitions in semiconductor quantum dots and photon modes in a photonic crystal structure in which the quantum dots are embedded. The Maxwell equations, including the linear nonlocal susceptibility of the exciton transitions in the quantum dots, are cast into an eigenvalue problem, which can be applied to any structure whose photon modes can be computed with reliable accuracy, and in addition naturally allows for disorder effects to be taken into account. We compute realistic photon modes using Bloch-mode expansion. As example systems, we study typical InGaAs quantum dots in a GaAs photonic crystal structures -- an $Ln$ cavity or a $\mathit{W1}$ waveguide. For a single dot, we reproduce known analytical results, while for the two dot case, we study the radiative excitation transfer mechanism and characterize its strength, the dependence on the detuning between quantum dot and photon modes, and the dependence on inter-dot distance. We find in particular that the inter-dot radiative coupling strength can reach $100 \mu{eV}$ in a short cavity, and its decay with distance in longer cavities and waveguides is determined by the group velocity of the exchanged photons and their radiative lifetime. We also show that, for an $Ln$ cavity of increasing length, the radiative excitation transfer mechanism is subject to a crossover from a regime where a single photon mode is dominating, to a multi-mode regime -- occurring around $\mathit{n}$ = 150 for the system under study.