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Silicon is the most scalable optoelectronic material, and it has revolutionized our lives in many ways. The prospect of quantum optics in silicon is an exciting avenue because it has the potential to address the scaling and integration challenges, the most pressing questions facing quantum science and technology. We report the first all-silicon quantum light source based on a single atomic emissive center embedded in a silicon-based nanophotonic cavity. We observe a more than 30-fold enhancement of luminescence, a near unity atom-cavity coupling efficiency, and an 8-fold acceleration of the emission from the quantum center. Our work opens avenues for large-scale integrated all-silicon cavity quantum electrodynamics and quantum photon interfaces with applications in quantum communication, sensing, imaging, and computing.

The study of defect centers in silicon has been recently reinvigorated by their potential applications in optical quantum information processing. A number of silicon defect centers emit single photons in the telecommunication $O$-band, making them promising building blocks for quantum networks between computing nodes. The two-carbon G-center, self-interstitial W-center, and spin-$1/2$ T-center are the most intensively studied silicon defect centers, yet despite this, there is no consensus on the precise configurations of defect atoms in these centers, and their electronic structures remain ambiguous. Here we employ \textit{ab initio} density functional theory to characterize these defect centers, providing insight into the relaxed structures, bandstructures, and photoluminescence spectra, which are compared to experimental results. Motivation is provided for how these properties are intimately related to the localization of electronic states in the defect centers. In particular, we present the calculation of the zero-field splitting for the excited triplet state of the G-center defect as the structure is transformed from the A-configuration to the B-configuration, showing a sudden increase in the magnitude of the $D_{zz}$ component of the zero-field splitting tensor. By performing projections onto the local orbital states of the defect, we analyze this transition in terms of the symmetry and bonding character of the G-center defect which sheds light on its potential application as a spin-photon interface., Comment: 11 pages, 6 figures

A previous paper studied the so-called borderline curves of the Kac--Murdock--Szeg\H{o} matrix $K_{n}(\rho)=\left[\rho^{|j-k|}\right]_{j,k=1}^{n}$, where $\rho\in\mathbb{C}$. These are the level curves (contour lines) in the complex-$\rho$ plane on which $K_n(\rho)$ has a type-1 or type-2 eigenvalue of magnitude $n$, where $n$ is the matrix dimension. Those curves have cusps at all critical points $\rho=\rho_c$ at which multiple (double) eigenvalues occur. The present paper determines corresponding curves pertaining to eigenvalues of magnitude $N\ne n$. We find that these curves no longer present cusps; and that, when $N

There is considerable interest in predicting the efficiency of Quantum Key Distribution (QKD) protocols when one of their implementation quantities is modified. One significant imperfection that affects the efficiency of the setup is the afterpulse phenomenon which consists in the spontaneous detections triggered by trapped carriers after previous avalanches at the detectors. While it is widely studied in bibliography for various QKD protocols, it has been reported much more scarcely for the well-known decoy-state QKD protocols and for dual detectors only. We develop a theoretical analysis of afterpulsing effect on the decoy-state QKD protocols for multiple detectors, delivering results which can be used as a guide for every practical decoy-state QKD protocol implementation in real-world deployments. A new formula connecting the baseline system error rate and the afterpulse probability is derived which may hold for all protocols as it is consisted of only setup-related quantities. Numerical simulations addressing the significance of breaking down the quantities pertaining to the decoy-state QKD protocols are being made, focusing on the weak+vacuum decoy-state QKD protocol as a characteristic subcase., Comment: 8 pages, 3 figures

We study the way that chromatic dispersion affects the visibility and the synchronization on Quantum Key Distribution (QKD) protocols in a widely-used setup based on the use of two fiber-based Mach-Zehnder (MZ) interferometers at transmitter/receiver stations. We identify the necessary conditions for the path length difference between the two arms of the interferometers for achieving the desired visibility given the transmission distance -- where the form of the detector's window can be considered. We also associate the above limitations with the maximum detection rate that can be recorded in our setup, including the quantum non-linearity phenomenon, and to the maximum time window of the detector's gate. Exploiting our results we provide two methods, depending on the clock rate of the setup, to perform chromatic dispersion compensation techniques to the signal for keeping the correct order of the transmitted symbols. At the end, we apply our theoretical outcomes in a more realistic QKD deployment, considering the case of phase-encoding BB84 QKD protocol, which is widely used. Our proposed methods, depending on the transmission distance and on the photon emission rate at transmitter station, can be easily generalized to every fiber-optic QKD protocol, for which the discrimination of each symbol is crucial., Comment: 14 pages, 12 figures