On the Minimal Uncompletable Word Problem

Let S be a finite set of words over an alphabet Sigma. The set S is said to be complete if every word w over the alphabet Sigma is a factor of some element of S*, i.e. w belongs to Fact(S*). Otherwise if S is not complete, we are interested in finding bounds on the minimal length of words in Sigma* which are not elements of Fact(S*) in terms of the maximal length of words in S.Comment: 5 pages; added references, corrected typo

Coherent population trapping of a single nuclear spin under ambient conditions

Coherent control of quantum systems has far-reaching implications in quantum engineering. In this context, coherent population trapping (CPT) involving dark resonances has played a prominent role, leading to a wealth of major applications including laser cooling of atoms and molecules, optical magnetometry, light storage and highly precise atomic clocks. Extending CPT methods to individual solid-state quantum systems has been only achieved in cryogenic environments for electron spin impurities and superconducting circuits. Here, we demonstrate efficient CPT of a single nuclear spin in a room temperature solid. To this end, we make use of a three-level system with a $\Lambda$-configuration in the microwave domain, which consists of nuclear spin states addressed through their hyperfine coupling to the electron spin of a single nitrogen-vacancy defect in diamond. Dark state pumping requires a relaxation mechanism which, in atomic systems, is simply provided by spontaneous emission. In this work, the relaxation process is externally controlled through incoherent optical pumping and separated in time from consecutive coherent microwave excitations of the nuclear spin $\Lambda$-system. Such a pumping scheme with controlled relaxation allows us (i) to monitor the sequential accumulation of population into the dark state and (ii) to reach a new regime of CPT dynamics for which periodic arrays of dark resonances can be observed, owing to multiple constructive interferences. This work offers new prospects for quantum state preparation, information storage in hybrid quantum systems and metrology.Comment: 13 pages including supplementary information, links to figures correcte

Multiscale Finite Element Modeling of Nonlinear Magnetoquasistatic Problems Using Magnetic Induction Conforming Formulations

In this paper we develop magnetic induction conforming multiscale formulations for magnetoquasistatic problems involving periodic materials. The formulations are derived using the periodic homogenization theory and applied within a heterogeneous multiscale approach. Therefore the fine-scale problem is replaced by a macroscale problem defined on a coarse mesh that covers the entire domain and many mesoscale problems defined on finely-meshed small areas around some points of interest of the macroscale mesh (e.g. numerical quadrature points). The exchange of information between these macro and meso problems is thoroughly explained in this paper. For the sake of validation, we consider a two-dimensional geometry of an idealized periodic soft magnetic composite.Comment: Paper accepted for publication in the SIAM MMS journa

Coherent population trapping of a single nuclear spin under ambient conditions

Coherent control of quantum systems has far-reaching implications in quantum engineering. In this context, coherent population trapping (CPT) involving dark resonances has played a prominent role, leading to a wealth of major applications including laser cooling of atoms and molecules, optical magnetometry, light storage and highly precise atomic clocks. Extending CPT methods to individual solid-state quantum systems has been only achieved in cryogenic environments for electron spin impurities and superconducting circuits. Here, we demonstrate efficient CPT of a single nuclear spin in a room temperature solid. To this end, we make use of a three-level system with a $\Lambda$-configuration in the microwave domain, which consists of nuclear spin states addressed through their hyperfine coupling to the electron spin of a single nitrogen-vacancy defect in diamond. Dark state pumping requires a relaxation mechanism which, in atomic systems, is simply provided by spontaneous emission. In this work, the relaxation process is externally controlled through incoherent optical pumping and separated in time from consecutive coherent microwave excitations of the nuclear spin $\Lambda$-system. Such a pumping scheme with controlled relaxation allows us (i) to monitor the sequential accumulation of population into the dark state and (ii) to reach a new regime of CPT dynamics for which periodic arrays of dark resonances can be observed, owing to multiple constructive interferences. This work offers new prospects for quantum state preparation, information storage in hybrid quantum systems and metrology.Comment: 13 pages including supplementary information, links to figures correcte

Efficient single photon emission from a high-purity hexagonal boron nitride crystal

Among a variety of layered materials used as building blocks in van der Waals heterostructures, hexagonal boron nitride (hBN) appears as an ideal platform for hosting optically-active defects owing to its large bandgap ($\sim 6$ eV). Here we study the optical response of a high-purity hBN crystal under green laser illumination. By means of photon correlation measurements, we identify individual defects emitting a highly photostable fluorescence under ambient conditions. A detailed analysis of the photophysical properties reveals a high quantum efficiency of the radiative transition, leading to a single photon source with very high brightness. These results illustrate how the wide range of applications offered by hBN could be further extended to photonic-based quantum information science and metrology.Comment: 5 pages, 4 figure

Perfect preferential orientation of nitrogen-vacancy defects in a synthetic diamond sample

We show that the orientation of nitrogen-vacancy (NV) defects in diamond can be efficiently controlled through chemical vapor deposition (CVD) growth on a (111)-oriented diamond substrate. More precisely, we demonstrate that spontaneously generated NV defects are oriented with a ~ 97 % probability along the [111] axis, corresponding to the most appealing orientation among the four possible crystallographic axes. Such a nearly perfect preferential orientation is explained by analyzing the diamond growth mechanism on a (111)-oriented substrate and could be extended to other types of defects. This work is a significant step towards the design of optimized diamond samples for quantum information and sensing applications.Comment: 6 pages, 4 figure

Current non-conservation effects in ν\nuDIS diffraction

In the neutrino DIS diffraction the charged current non-conservation gives rise to sizable corrections to the longitudinal structure function, $F_L$. These corrections is a higher twist effect enhanced at small-$x$ by the rapidly growing gluon density. The phenomenon manifests itself in abundant production of charm and strangeness by longitudinally polarized W bosons of moderate virtualities Q^2\lsim m_c^2.Comment: Prepared for the Int. Workshop on Diffraction in High-Energy Physics, Diffraction 2008, La Londe-les-Maures, France, Sept. 9-14, 200