Finite isomorphically complete systems

AbstractIn the theory of finite automata it is an important problem to characterize such systems of automata from which any automaton can be built under a given composition and representation. Such systems are called complete with respect to the fixed composition and representation. From practical point of view, it is useful to determine those compositions and representations for which there are finite complete systems. In this paper we show that the existence of finite complete systems implies the unboundedness of the feedback dependency of the composition

Long-lived mesoscopic entanglement outside the Lamb-Dicke regime

We create entangled states of the spin and motion of a single $^{40}$Ca$^+$ ion in a linear ion trap. The motional part consists of coherent states of large separation and long coherence time. The states are created by driving the motion using counterpropagating laser beams. We theoretically study and experimentally observe the behaviour outside the Lamb-Dicke regime, where the trajectory in phase space is modified and the coherent states become squeezed. We directly observe the modification of the return time of the trajectory, and infer the squeezing. The mesoscopic entanglement is observed up to $\Delta \alpha = 5.1$ with coherence time 170 microseconds and mean phonon excitation \nbar = 16.Comment: 5 pages, 3 figures. Revised version after editor comment

Deterministic entanglement and tomography of ion spin qubits

We have implemented a universal quantum logic gate between qubits stored in the spin state of a pair of trapped calcium 40 ions. An initial product state was driven to a maximally entangled state deterministically, with 83% fidelity. We present a general approach to quantum state tomography which achieves good robustness to experimental noise and drift, and use it to measure the spin state of the ions. We find the entanglement of formation is 0.54.Comment: 3 figures, 4 pages, footnotes fixe

Keeping a Single Qubit Alive by Experimental Dynamic Decoupling

We demonstrate the use of dynamic decoupling techniques to extend the coherence time of a single memory qubit by nearly two orders of magnitude. By extending the Hahn spin-echo technique to correct for unknown, arbitrary polynomial variations in the qubit precession frequency, we show analytically that the required sequence of pi-pulses is identical to the Uhrig dynamic decoupling (UDD) sequence. We compare UDD and CPMG sequences applied to a single Ca-43 trapped-ion qubit and find that they afford comparable protection in our ambient noise environment.Comment: 5 pages, 5 figure

Time-separated entangled light pulses from a single-atom emitter

The controlled interaction between a single, trapped, laser-driven atom and the mode of a high-finesse optical cavity allows for the generation of temporally separated, entangled light pulses. Entanglement between the photon-number fluctuations of the pulses is created and mediated via the atomic center-of-mass motion, which is interfaced with light through the mechanical effect of atom-photon interaction. By means of a quantum noise analysis we determine the correlation matrix which characterizes the entanglement, as a function of the system parameters. The scheme is feasible in experimentally accessible parameter regimes. It may be easily extended to the generation of entangled pulses at different frequencies, even at vastly different wavelengths.Comment: 17 pages, 5 figures. Modified version, to appear in the New Journal of Physic

Using Sat solvers for synchronization issues in partial deterministic automata

We approach the task of computing a carefully synchronizing word of minimum length for a given partial deterministic automaton, encoding the problem as an instance of SAT and invoking a SAT solver. Our experimental results demonstrate that this approach gives satisfactory results for automata with up to 100 states even if very modest computational resources are used.Comment: 15 pages, 3 figure

Fabrication and heating rate study of microscopic surface electrode ion traps

We report heating rate measurements in a microfabricated gold-on-sapphire surface electrode ion trap with trapping height of approximately 240 micron. Using the Doppler recooling method, we characterize the trap heating rates over an extended region of the trap. The noise spectral density of the trap falls in the range of noise spectra reported in ion traps at room temperature. We find that during the first months of operation the heating rates increase by approximately one order of magnitude. The increase in heating rates is largest in the ion loading region of the trap, providing a strong hint that surface contamination plays a major role for excessive heating rates. We discuss data found in the literature and possible relation of anomalous heating to sources of noise and dissipation in other systems, namely impurity atoms adsorbed on metal surfaces and amorphous dielectrics.Comment: 17 pages, 5 figure

Pre-M Phase-promoting Factor Associates with Annulate Lamellae in Xenopus Oocytes and Egg Extracts

We have used complementary biochemical and in vivo approaches to study the compartmentalization of M phase-promoting factor (MPF) in prophase Xenopus eggs and oocytes. We first examined the distribution of MPF (Cdc2/CyclinB2) and membranous organelles in high-speed extracts of Xenopus eggs made during mitotic prophase. These extracts were found to lack mitochondria, Golgi membranes, and most endoplasmic reticulum (ER) but to contain the bulk of the pre-MPF pool. This pre-MPF could be pelleted by further centrifugation along with components necessary to activate it. On activation, Cdc2/CyclinB2 moved into the soluble fraction. Electron microscopy and Western blot analysis showed that the pre-MPF pellet contained a specific ER subdomain comprising "annulate lamellae" (AL): stacked ER membranes highly enriched in nuclear pores. Colocalization of pre-MPF with AL was demonstrated by anti-CyclinB2 immunofluorescence in prophase oocytes, in which AL are positioned close to the vegetal surface. Green fluorescent protein-CyclinB2 expressed in oocytes also localized at AL. These data suggest that inactive MPF associates with nuclear envelope components just before activation. This association may explain why nuclei and centrosomes stimulate MPF activation and provide a mechanism for targeting of MPF to some of its key substrates