Availability and mean time between failures of redundant systems with random maintenance of subsystems

It is shown how the availability and MTBF (Mean Time Between Failures) of a redundant system with subsystems maintenanced at the points of so-called stationary renewal processes can be determined from the distributions of the intervals between maintenance actions and of the failure-free operating intervals of the subsystems. The results make it possible, for example, to determine the frequency and duration of hidden failure states in computers which are incidentally corrected during the repair of observed failures

Panel Regression with Random Noise

The paper explores the effect of measurement errors on the estimation of a linear panel data model. The conventional fixed effects estimator, which ignores measurement errors, is biased. By correcting for the bias one can construct consistent and asymptotically normal estimators. In addition, we find estimates for the asymptotic variances of these estimators. The paper focuses on multiplicative errors, which are often deliberately added to the data in order to minimize their disclosure risk. They can be analyzed in a similar way as additive errors, but with some important and consequential differences.panel regression, multiplicative measurement errors, bias correction, asymptotic variance, disclosure control

Dynamical polarizability of atoms in arbitrary light fields: general theory and application to cesium

We present a systematic derivation of the dynamical polarizability and the ac Stark shift of the ground and excited states of atoms interacting with a far-off-resonance light field of arbitrary polarization. We calculate the scalar, vector, and tensor polarizabilities of atomic cesium using resonance wavelengths and reduced matrix elements for a large number of transitions. We analyze the properties of the fictitious magnetic field produced by the vector polarizability in conjunction with the ellipticity of the polarization of the light field.Comment: see also Supplemental Materia

Near-ground-state cooling of atoms optically trapped 300nm away from a hot surface

Laser-cooled atoms coupled to nanophotonic structures constitute a powerful research platform for the exploration of new regimes of light-matter interaction. While the initialization of the atomic internal degrees of freedom in these systems has been achieved, a full preparation of the atomic quantum state also requires controlling the center of mass motion of the atoms at the quantum level. Obtaining such control is not straightforward, due to the close vicinity of the atoms to the photonic system that is at ambient temperature. Here, we demonstrate cooling of individual neutral Cesium atoms, that are optically interfaced with light in an optical nanofiber, preparing them close to their three-dimensional motional ground state. The atoms are localized less than 300nm away from the hot fiber surface. Ground-state preparation is achieved by performing degenerate Raman cooling, and the atomic temperature is inferred from the analysis of heterodyne fluorescence spectroscopy signals. Our cooling method can be implemented either with externally applied or guided light fields. Moreover, it relies on polarization gradients which naturally occur for strongly confined guided optical fields. Thus, this method can be implemented in any trap based on nanophotonic structures. Our results provide an ideal starting point for the study of novel effects such as light-induced self-organization, the measurement of novel optical forces, and the investigation of heat transfer at the nanoscale using quantum probes

Heating in Nanophotonic Traps for Cold Atoms

Laser-cooled atoms that are trapped and optically interfaced with light in nanophotonic waveguides are a powerful platform for fundamental research in quantum optics as well as for applications in quantum communication and quantum information processing. Ever since the first realization of such a hybrid quantum nanophotonic, heating rates of the atomic motion observed in various experimental settings have typically been exceeding those in comparable free-space optical microtraps by about three orders of magnitude. This excessive heating is a roadblock for the implementation of certain protocols and devices. Its origin has so far remained elusive and, at the typical atom-surface separations of less than an optical wavelength encountered in nanophotonic traps, numerous effects may potentially contribute to atom heating. Here, we theoretically describe the effect of mechanical vibrations of waveguides on guided light fields and provide a general theory of particle-phonon interaction in nanophotonic traps. We test our theory by applying it to the case of laser-cooled cesium atoms in nanofiber-based two-color optical traps. We find excellent quantitative agreement between the predicted heating rates and experimentally measured values. Our theory predicts that, in this setting, the dominant heating process stems from the optomechanical coupling of the optically trapped atoms to the continuum of thermally occupied flexural mechanical modes of the waveguide structure. Beyond unraveling the long-standing riddle of excessive heating in nanofiber-based atom traps, we also study the dependence of the heating rates on the relevant system parameters. Our findings allow us to propose several strategies for minimizing the heating. Finally, our findings are also highly relevant for optomechanics experiments with dielectric nanoparticles that are optically trapped close to nanophotonic waveguides.Comment: Published version. 35 pages (including appendices), 7 figures, 18 tables, and 3 pages of supplemental materia