We review the basic light-matter interactions and optical properties of chip-based single photon sources, that are enabled by integrating single quantum dots with planar photonic crystals. A theoretical framework is presented that allows one to connect to a wide range of quantum light propagation effects in a physically intuitive and straightforward way. We focus on the important mechanisms of enhanced spontaneous emission, and efficient photon extraction, using all-integrated photonic crystal components including waveguides, cavities, quantum dots and output couplers. The limitations, challenges, and exciting prospects of developing on-chip quantum light sources using integrated photonic crystal structures are discussed.A sequence of optical pulses (top right) interacting with a single quantum dot embedded in a photonic crystal system, resulting in the emission of a train of single photons on-chip.

Employing a medium-dependent quantum optics formalism and a Green function solution of Maxwell's equations, we study the enhanced spontaneous emission factors (Purcell factors) and Lamb shifts from a quantum dot or atom near the surface of a slow-light metamaterial waveguide. Purcell factors of approximately 250 and 100 are found at optical frequencies for p−polarized and s−polarized dipoles respectively placed 28 nm (0.02 λ0) above the slab surface, including a realistic metamaterial loss factor of γ/2π = 2 THz. For smaller loss values, we demonstrate that the slowlight regime of odd metamaterial waveguide propagation modes can be observed and related to distinct resonances in the Purcell factors. Correspondingly, we predict unusually large and rich Lamb shifts of approximately −1 GHz to −6 GHz for a dipole moment of 50 Debye. We also make a direct calculation of the far field emission spectrum which contains direct measurable access to these enhanced Purcell factors and Lamb shifts.

We present a medium-dependent quantum optics approach to describe the influence of electronacoustic phonon coupling on the emission spectra of a strongly coupled quantum-dot cavity system. Using a canonical Hamiltonian for light quantization and a photon Green function formalism, phonons are included to all orders through the dot polarizability function obtained within the independent Boson model. We derive simple user-friendly analytical expressions for the linear quantum light spectrum, including the influence from both exciton and cavity-emission decay channels. In the regime of semiconductor cavity-QED, we study cavity emission for various exciton-cavity detunings and demonstrate rich spectral asymmetries as well as cavity-mode suppression and enhancement effects. Our technique is nonperturbative, and non-Markovian, and can be applied to study photon emission from a wide range of semiconductor quantum dot structures, including waveguides and coupled cavity arrays. We compare our theory directly to recent and apparently puzzling experimental data for a single site-controlled quantum dot in a photonic crystal cavity and show good agreement as a function of cavity-dot detuning and as a function of temperature.

We present and apply a medium-dependent quantum optics formalism for describing the exciton dynamics of two spatially-separated quantum dots on-chip, in the regime of coupled-cavity quantum electrodynamics. With each dot placed in a spatially-separated cavity and coupled through a periodic waveguide channel, the quantum dot excitons behave as a composite entangled pair, exhibiting pronounced entanglement over distances of 300 microm and more. The computed light spectra above the two cavities show clear signatures of pronounced photon coupling including increased vacuum Rabi splitting and cavity-induced transmission and absorption. The macroscopic entanglement is confirmed by investigating the Bell inequality, which is shown to be violated for hundreds of picoseconds.

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