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Physical Review B

Classical and quantum optical correlation effects between single quantum dots: The role of the hopping photon

Stephen Hughes, Hideki Gotoh, Hidehiko Kamada

Published Sep 29, 2006• 4 citations
Publisher

Abstract

We present a theoretical study of photon-coupled single quantum dots in a semiconductor. A series of optical effects are demonstrated, including a subradiant dark resonance, superradiance, reversible spontaneous emission decay, and pronounced exciton entanglement. Both classical and quantum optical approaches are presented using a self-consistent formalism that treats real and virtual photon exchange on an equal footing and can account for different quantum dot properties, surface effects, and retardation in the dipole-dipole coupling, all of which are shown to play a non-negligible role.

DOI
10.1103/physrevb.74.115334

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The modified spontaneous emission dynamics of two photon-coupled quantum dots in a planar-photonic crystal are theoretically investigated. Based on a photon Green function technique for quantizing the electromagnetic fields in arbitrary surroundings, pronounced vacuum Rabi oscillations and dipole-dipole interactions are self-consistently incorporated and are shown to result in a high degree of quantum-bit entanglement. Quantum dots with different optical dipole moments are also found to yield a very rich display of quantum dynamics and offer several advantages over coupling identical atoms.
We employ the quantum-jump approach to study single scatterings in single semiconductor quantum dots. Two prototypical situations are investigated. First, we analyze two-photon emissions from the cascade biexciton decay of a dot where the single-exciton states exhibit a fine-structure splitting. We show that this splitting results for appropriately chosen polarization filters in an oscillatory behavior of two-photon correlations, and carefully examine the proper theoretical description of the underlying scattering processes. Second, we analyze the decay of a single-electron charged exciton in a quantum dot embedded in a field-effect structure. We show how the quantum properties of the charged exciton are transferred through tunneling and relaxation to the spin entanglement between electrons in the dot and contact, and identify the pertinent disentanglement mechanisms.
A single atom in a cavity is the model system of cavity quantum electrodynamics (CQED). The strong coupling regime between the atom and cavity-confined photon corresponds to the reversible exchange of energy between the two modes, and underpins a wide range of CQED phenomena with applications in quantum information science, including for example as quantum logic gates and as sources of entangled states. An important advance was achieved recently when strong coupling between excitons and cavity photons was reported for the first time for localized quantum dots (QDs) in micron-size solid state cavities. This has significance in terms of scalability and integration with other optical devices, and could lead to the emergence of "quantum optics on a chip" technology. However the results presented so far for quantum dots are in the linear regime, corresponding to coupling to the vacuum field (vacuum Rabi splitting); they are not a true QED effect and can equally well be described by classical physics as the coupling between two oscillators. In this paper, we present evidence for a purely quantum phenomenon for the QD/cavity photon system, namely the increase in splitting of the levels when the mean number of photons in the cavity is increased. This corresponds to non-linearities on the single-photon scale: the presence of a single excitation in the cavity changes the level structure, affecting the emission energies for a second photon. Such results are a first step in demonstrating the promise of quantum dots for CQED applications.
We derive a rigorous theory of the interaction between photons and spatially extended excitons confined in quantum dots in inhomogeneous photonic materials. We show that beyond the dipole approximation, the radiative decay rate is proportional to a nonlocal interaction function, which describes the interaction between light and spatially extended excitons. In this regime, light and matter degrees of freedom cannot be separated and a complex interplay between the nanostructured optical environment and the exciton envelope function emerges. We illustrate this by specific examples and derive a series of important analytical relations, which are useful for applying the formalism to practical problems. In the dipole limit, the decay rate is proportional to the projected local density of optical states, and we obtain the strong and weak confinement regimes as special cases.