Abstract:
Process calculi and graph transformation systems provide models of reactive systems with labelled transition semantics (LTS). While the semantics for process calculi is compositional, this is not the case for graph transformation systems, in general. Hence, the goal of this article is to obtain a compositional semantics for graph transformation system in analogy to the structural operational semantics (SOS) for Milner's Calculus of Communicating Systems (CCS). The paper introduces an SOS style axiomatization of the standard labelled transition semantics for graph transformation systems that is based on the idea of minimal reaction contexts as labels, due to Leifer and Milner. In comparison to previous work on inductive definitions of similarly derived LTSs, the main feature of the proposed axiomatization is a composition rule that captures the communication of sub-systems so that it can feature as a counterpart to the communication rule of CCS.

Abstract:
Inspired by decomposition problems in rule-based formalisms in Computational Systems Biology and recent work on compositionality in graph transformation, this paper proposes to use arbitrary colimits to "deconstruct" models of reactions in which states are represented as objects of adhesive categories. The fundamental problem is the decomposition of complex reactions of large states into simpler reactions of smaller states. The paper defines the local decomposition problem for transformations. To solve this problem means to "reconstruct" a given transformation as the colimit of "smaller" ones where the shape of the colimit and the decomposition of the source object of the transformation are fixed in advance. The first result is the soundness of colimit decomposition for arbitrary double pushout transformations in any category, which roughly means that several "local" transformations can be combined into a single "global" one. Moreover, a solution for a certain class of local decomposition problems is given, which generalizes and clarifies recent work on compositionality in graph transformation.

Abstract:
Semiconductor quantum dots are considered to be the leading venue for fabricating on-demand sources of single photons. However, the generation of long-lived dark excitons imposes significant limits on the efficiency of these sources. We demonstrate a technique that optically pumps the dark exciton population and converts it to a bright exciton population, using intermediate excited biexciton states. We show experimentally that our method considerably reduces the DE population while doubling the triggered bright exciton emission, approaching thereby near-unit fidelity of quantum dot depletion.

Abstract:
Process calculi and graph transformation systems provide models of reactive systems with labelled transition semantics. While the semantics for process calculi is compositional, this is not the case for graph transformation systems, in general. Hence, the goal of this article is to obtain a compositional semantics for graph transformation system in analogy to the structural operational semantics (SOS) for Milner's Calculus of Communicating Systems (CCS). The paper introduces an SOS style axiomatization of the standard labelled transition semantics for graph transformation systems. The first result is its equivalence with the so-called Borrowed Context technique. Unfortunately, the axiomatization is not compositional in the expected manner as no rule captures "internal" communication of sub-systems. The main result states that such a rule is derivable if the given graph transformation system enjoys a certain property, which we call "complementarity of actions". Archetypal examples of such systems are interaction nets. We also discuss problems that arise if "complementarity of actions" is violated.

Abstract:
Colimits that satisfy the Van Kampen condition have interesting exactness properties. We show that the elementary presentation of the Van Kampen condition is actually a characterisation of a universal property in the associated bicategory of spans. The main theorem states that Van Kampen cocones are precisely those diagrams in a category that induce bicolimit diagrams in its associated bicategory of spans, provided that the category has pullbacks and enough colimits.

Abstract:
We report on the deterministic fabrication of sub-um mesa structures containing single quantum dots by in-situ electron-beam lithography. The fabrication method is based on a two-step lithography process using a low-temperature cathodoluminescence (CL) spectroscopy setup. In the first step the position and spectral features of single InGaAs quantum dots (QDs) are detected by CL. Then circular sub-um mesa-structures are exactly defined by high-resolution electron-beam lithography and subsequent etching in the second step. CL spectroscopy and micro-photoluminscence spectroscopy demonstrate the high optical quality of the single-QD mesa-structures with emission linewidths below 15 ueV and g(2)(0) = 0.04. Our lithography method allows for an alignment precision better than 100 nm which paves the way for a fully-deterministic device technology using in-situ CL lithography.

Abstract:
We investigate the power-dependent photoluminescence spectra from a strongly coupled quantum dot-cavity system using a quantum master equation technique that accounts for incoherent pumping, pure dephasing, and fermion or boson statistics. Analytical spectra at the one-photon correlation level and the numerically exact multi-photon spectra for fermions are presented. We compare to recent experiments on a quantum dot-micropiller cavity system and show that an excellent fit to the data can be obtained by varying only the incoherent pump rates in direct correspondence with the experiments. Our theory and experiments together show a clear and systematic way of studying stimulated-emission induced broadening and anharmonic cavity-QED.

Abstract:
The prospect of realizing building blocks for long-distance quantum communication is a major driving force for the development of advanced nanophotonic devices. Significant progress has been achieved in this field with respect to the fabrication of efficient quantum-dot-based single-photon sources. More recently, even spin-photon entanglement and quantum teleportation have been demonstrated in semiconductor systems. These results are considered as crucial steps towards the realization of a quantum repeater. The related work has almost exclusively been performed on self-assembled quantum dots (QDs) and random device technology. At this point it is clear that further progress in this field towards real applications will rely crucially on deterministic device technologies which will, for instance, enable the processing of bright quantum light sources with pre-defined emission energy. Here we report on enhanced photon-extraction efficiency from monolithically integrated microlenses which are coupled deterministically to single QDs. The microlenses with diameters down to 800 nm were aligned to single QDs by in-situ electron-beam lithography using a low-temperature cathodoluminescence setup. This deterministic device technology allowed us to obtain an enhancement of photon extraction efficiency for QDs integrated into microlenses as compared to QDs in unstructured surfaces. The excellent optical quality of the structures is demonstrated by cathodoluminescence and micro-photoluminescence spectroscopy. A Hong-Ou-Mandel experiment states the emission of single indistinguishable photons.

Abstract:
We report on the generation of single-photon pulse trains at a repetition rate of up to 1 GHz. We achieve this high speed by modulating the external voltage applied on an electrically contacted quantum dot microlens, which is optically excited by a continuous-wave laser. By modulating the photoluminescence of the quantum dot microlens using a square-wave voltage, single-photon emission is triggered with a response time as short as 270 ps being 6.5 times faster than the radiative lifetime of 1.75 ns. This large reduction in the characteristic emission time is enabled by a rapid capacitive gating of emission from the quantum dot placed in the intrinsic region of a p-i-n-junction biased below the onset of electroluminescence. Here, the rising edge of the applied voltage pulses triggers the emission of single photons from the optically excited quantum dot. The non-classical nature of the photon pulse train generated at GHz-speed is proven by intensity autocorrelation measurements. Our results combine optical excitation with fast electrical gating and thus show promise for the generation of indistinguishable single photons at high rates, exceeding the limitations set by the intrinsic radiative lifetime.

Abstract:
We probe the indistinguishability of photons emitted by a semiconductor quantum dot (QD) via time- and temperature- dependent two-photon interference (TPI) experiments. An increase in temporal-separation between consecutive photon emission events, reveals a decrease in TPI visibility on a nanosecond timescale, theoretically described by a non-Markovian noise process in agreement with fluctuating charge-traps in the QD's vicinity. Phonon-induced pure dephasing results in a decrease in TPI visibility from $(96\pm4)\,$\% at 10\,K to a vanishing visibility at 40\,K. In contrast to Michelson-type measurements, our experiments provide direct access to the time-dependent coherence of a quantum emitter at a nanosecond timescale.