Abstract:
A scheme for approximate generation of an N-qubit phase gate is proposed in cavity QED based on nonidentical coupling between the atoms and the cavity. The atoms interact with a highly detuned cavity-field mode, but quantum information does not transfer between the atoms and cavity field, and thus the cavity decay is negligible. The gate time does not rise with an increase in the number of qubits. With the choice of a smaller odd number l (related to atom--cavity coupling constants), the phase gate can be generated with a higher fidelity and a higher success probability in a shorter time (the gate time is much shorter than the atomic radiative lifetime and photon lifetime). When the number of qubits N exceeds certain small values, the fidelity and success probability rise slowly with an increase in the number of qubits N. When N\rightarrow\infty, the fidelity and success probability infinitely approach 1, but never exceed 1.

Abstract:
A maximal matching can be maintained in fully dynamic (supporting both addition and deletion of edges) $n$-vertex graphs using a trivial deterministic algorithm with a worst-case update time of O(n). No deterministic algorithm that outperforms the na\"{\i}ve O(n) one was reported up to this date. The only progress in this direction is due to Ivkovi\'{c} and Lloyd \cite{IL93}, who in 1993 devised a deterministic algorithm with an \emph{amortized} update time of $O((n+m)^{\sqrt{2}/2})$, where $m$ is the number of edges. In this paper we show the first deterministic fully dynamic algorithm that outperforms the trivial one. Specifically, we provide a deterministic \emph{worst-case} update time of $O(\sqrt{m})$. Moreover, our algorithm maintains a matching which is in fact a 3/2-approximate maximum cardinality matching (MCM). We remark that no fully dynamic algorithm for maintaining $(2-\eps)$-approximate MCM improving upon the na\"{\i}ve O(n) was known prior to this work, even allowing amortized time bounds and \emph{randomization}. For low arboricity graphs (e.g., planar graphs and graphs excluding fixed minors), we devise another simple deterministic algorithm with \emph{sub-logarithmic update time}. Specifically, it maintains a fully dynamic maximal matching with amortized update time of $O(\log n/\log \log n)$. This result addresses an open question of Onak and Rubinfeld \cite{OR10}. We also show a deterministic algorithm with optimal space usage, that for arbitrary graphs maintains a maximal matching in amortized $O(\sqrt{m})$ time, and uses only $O(n+m)$ space.

Abstract:
Compared to classical light sources, quantum sources based on N00N states consisting of $N$ photons achieve an $N$-times higher phase sensitivity, giving rise to super-resolution. N00N-state creation schemes based on linear optics and projective measurements only have a success probability $p$ that decreases exponentially with $N$, e.g. $p=4.4\times 10^{-14}$ for N=20. Feed-forward improves the scaling but $N$ fluctuates nondeterministically in each attempt. Schemes based on parametric down-conversion suffer from low production efficiency and low fidelity. A recent scheme based on atoms in a cavity combines deterministic time evolution, local unitary operations, and projective measurements. Here we propose a novel scheme based on the off-resonant interaction of $N$ photons with four semiconductor quantum dots (QDs) in a cavity to create N00N states deterministically with $p=1$ and fidelity above 90% for $N\lesssim 60$, without the need of any projective measurement or local unitary operation. Using our measure we obtain maximum $N$-photon entanglement $E_N=1$ for arbitrary $N$. Our method paves the way to the miniaturization of N00N-state sources to the nanoscale regime, with the possibility to integrate them on a computer chip based on semiconductor materials.

Abstract:
We present two cavity quantum electrodynamics proposals that, sharing the same basic elements, allow for the deterministic generation of entangled photons pairs by means of a three-level atom successively coupled to two single longitudinal mode high-Q optical resonators presenting polarization degeneracy. In the faster proposal, the three-level atom yields a polarization entangled photon pair via two truncated Rabi oscillations, whereas in the adiabatic proposal a counterintuitive Stimulated Raman Adiabatic Passage process is considered. Although slower than the former process, this second method is very efficient and robust under fluctuations of the experimental parameters and, particularly interesting, almost completely insensitive to atomic decay.

Abstract:
We propose an optical cavity-QED scheme for the deterministic generation of polarization entangled photon pairs that operates with high fidelity even in the bad cavity limit. The scheme is based on the interaction of an excited four-level atom with two empty optical cavity modes via an adiabatic passage process. Monte-Carlo wave function simulations are used to evaluate the fidelity of the cavity-QED source and its entanglement capability in the presence of decoherence. In the bad cavity limit, fidelities close to one are predicted for state-of-the-art experimental parameter values.

Abstract:
We propose a method for generating maximally entangled states of N two-level trapped ions. The method is deterministic and independent of the number of ions in the trap. It involves a controlled-NOT acting simultaneously on all the ions through a dispersive interaction. We explore the potential application of our scheme for high precision frequency standards.

Abstract:
We present a scheme to generate a maximally entangled state of two three-level atoms in a cavity. The success or failure of the generation of the desired entangled state can be determined by detecting the polarization of the photon leaking out of the cavity. With the use of an automatic feedback, the success probability of the scheme can be made to approach unity.

Abstract:
Individual laser cooled atoms are delivered on demand from a single atom magneto-optic trap to a high-finesse optical cavity using an atom conveyor. Strong coupling of the atom with the cavity field allows simultaneous cooling and detection of individual atoms for time scales exceeding 15 s. The single atom scatter rate is studied as a function of probe-cavity detuning and probe Rabi frequency, and the experimental results are in good agreement with theoretical predictions. We demonstrate the ability to manipulate the position of a single atom relative to the cavity mode with excellent control and reproducibility.

Abstract:
We describe and experimentally demonstrate a technique for deterministic coupling between a photonic crystal (PC) nanocavity and single emitters. The technique is based on in-situ scanning of a PC cavity over a sample and allows the positioning of the cavity over a desired emitter with nanoscale resolution. The power of the technique, which we term a Scanning Cavity Microscope (SCM), is demonstrated by coupling the PC nanocavity to a single nitrogen vacancy (NV) center in diamond, an emitter system that provides optically accessible electron and nuclear spin qubits.

Abstract:
The negatively-charged nitrogen vacancy center (NV) in diamond has generated significant interest as a platform for quantum information processing and sensing in the solid state. For most applications, high quality optical cavities are required to enhance the NV zero-phonon line (ZPL) emission. An outstanding challenge in maximizing the degree of NV-cavity coupling is the deterministic placement of NVs within the cavity. Here, we report photonic crystal nanobeam cavities coupled to NVs incorporated by a delta-doping technique that allows nanometer-scale vertical positioning of the emitters. We demonstrate cavities with Q up to ~24,000 and mode volume V ~ $0.47({\lambda}/n)^{3}$ as well as resonant enhancement of the ZPL of an NV ensemble with Purcell factor of ~20. Our fabrication technique provides a first step towards deterministic NV-cavity coupling using spatial control of the emitters.