Motional sidebands and direct measurement of the cooling rate in the resonance fluorescence of a single trapped ion

Resonance fluorescence of a single trapped ion is spectrally analyzed using a heterodyne technique. Motional sidebands due to the oscillation of the ion in the harmonic trap potential are observed in the fluorescence spectrum. From the width of the sidebands the cooling rate is obtained and found to be in agreement with the theoretical prediction.Comment: 4 pages, 4 figures. Final version after minor changes, 1 figure replaced; to be published in PRL, July 10, 200

Iterated Binomial Sums and their Associated Iterated Integrals

We consider finite iterated generalized harmonic sums weighted by the binomial $\binom{2k}{k}$ in numerators and denominators. A large class of these functions emerges in the calculation of massive Feynman diagrams with local operator insertions starting at 3-loop order in the coupling constant and extends the classes of the nested harmonic, generalized harmonic and cyclotomic sums. The binomially weighted sums are associated by the Mellin transform to iterated integrals over square-root valued alphabets. The values of the sums for $N \rightarrow \infty$ and the iterated integrals at $x=1$ lead to new constants, extending the set of special numbers given by the multiple zeta values, the cyclotomic zeta values and special constants which emerge in the limit $N \rightarrow \infty$ of generalized harmonic sums. We develop algorithms to obtain the Mellin representations of these sums in a systematic way. They are of importance for the derivation of the asymptotic expansion of these sums and their analytic continuation to $N \in \mathbb{C}$. The associated convolution relations are derived for real parameters and can therefore be used in a wider context, as e.g. for multi-scale processes. We also derive algorithms to transform iterated integrals over root-valued alphabets into binomial sums. Using generating functions we study a few aspects of infinite (inverse) binomial sums.Comment: 62 pages Latex, 1 style fil

The optical calcium frequency standards of PTB and NIST

We describe the current status of the Ca optical frequency standards with laser-cooled neutral atoms realized in two different laboratories for the purpose of developing a possible future optical atomic clock. Frequency measurements performed at the Physikalisch-Technische Bundesanstalt (PTB) and the National Institute of Standards and Technology (NIST) make the frequency of the clock transition of 40Ca one of the best known optical frequencies (relative uncertainty 1.2e-14) and the measurements of this frequency in both laboratories agree to well within their respective uncertainties. Prospects for improvement by orders of magnitude in the relative uncertainty of the standard look feasible.Comment: 13 pages, 11 figures, to appear in Comptes Rendus Physiqu

Dark resonances as a probe for the motional state of a single ion

Single, rf-trapped ions find various applications ranging from metrology to quantum computation. High-resolution interrogation of an extremely weak transition under best observation conditions requires an ion almost at rest. To avoid line-broadening effects such as the second order Doppler effect or rf heating in the absence of laser cooling, excess micromotion has to be eliminated as far as possible. In this work the motional state of a confined three-level ion is probed, taking advantage of the high sensitivity of observed dark resonances to the trapped ion's velocity. Excess micromotion is controlled by monitoring the dark resonance contrast with varying laser beam geometry. The influence of different parameters such as the cooling laser intensity has been investigated experimentally and numerically

Resonance fluorescence of a trapped three-level atom

We investigate theoretically the spectrum of resonance fluorescence of a harmonically trapped atom, whose internal transitions are $\Lambda$--shaped and driven at two-photon resonance by a pair of lasers, which cool the center--of--mass motion. For this configuration, photons are scattered only due to the mechanical effects of the quantum interaction between light and atom. We study the spectrum of emission in the final stage of laser--cooling, when the atomic center-of-mass dynamics is quantum mechanical and the size of the wave packet is much smaller than the laser wavelength (Lamb--Dicke limit). We use the spectral decomposition of the Liouville operator of the master equation for the atomic density matrix and apply second order perturbation theory. We find that the spectrum of resonance fluorescence is composed by two narrow sidebands -- the Stokes and anti-Stokes components of the scattered light -- while all other signals are in general orders of magnitude smaller. For very low temperatures, however, the Mollow--type inelastic component of the spectrum becomes visible. This exhibits novel features which allow further insight into the quantum dynamics of the system. We provide a physical model that interprets our results and discuss how one can recover temperature and cooling rate of the atom from the spectrum. The behaviour of the considered system is compared with the resonance fluorescence of a trapped atom whose internal transition consists of two-levels.Comment: 11 pages, 4 Figure

Resolved Sideband Cooling of a Micromechanical Oscillator

Micro- and nanoscale opto-mechanical systems provide radiation pressure coupling of optical and mechanical degree of freedom and are actively pursued for their ability to explore quantum mechanical phenomena of macroscopic objects. Many of these investigations require preparation of the mechanical system in or close to its quantum ground state. Remarkable progress in ground state cooling has been achieved for trapped ions and atoms confined in optical lattices. Imperative to this progress has been the technique of resolved sideband cooling, which allows overcoming the inherent temperature limit of Doppler cooling and necessitates a harmonic trapping frequency which exceeds the atomic species' transition rate. The recent advent of cavity back-action cooling of mechanical oscillators by radiation pressure has followed a similar path with Doppler-type cooling being demonstrated, but lacking inherently the ability to attain ground state cooling as recently predicted. Here we demonstrate for the first time resolved sideband cooling of a mechanical oscillator. By pumping the first lower sideband of an optical microcavity, whose decay rate is more than twenty times smaller than the eigen-frequency of the associated mechanical oscillator, cooling rates above 1.5 MHz are attained. Direct spectroscopy of the motional sidebands reveals 40-fold suppression of motional increasing processes, which could enable reaching phonon occupancies well below unity (<0.03). Elemental demonstration of resolved sideband cooling as reported here should find widespread use in opto-mechanical cooling experiments. Apart from ground state cooling, this regime allows realization of motion measurement with an accuracy exceeding the standard quantum limit.Comment: 13 pages, 5 figure

Fungal iron availability during deep seated candidiasis is defined by a complex interplay involving systemic and local events

Peer reviewedPublisher PD

In Vivo Mechanical Loading Modulates Insulin-Like Growth Factor Binding Protein-2 Gene Expression in Rat Osteocytes

Mechanical stimulation is essential for maintaining skeletal integrity. Mechanosensitive osteocytes are important during the osteogenic response. The growth hormone-insulin-like growth factor (GH-IGF) axis plays a key role during regulation of bone formation and remodeling. Insulin-like growth factor binding proteins (IGFBPs) are able to modulate IGF activity. The aim of this study was to characterize the role of IGFBP-2 in the translation of mechanical stimuli into bone formation locally in rat tibiae. Female Wistar rats were assigned to three groups (n = 5): load, sham, and control. The four-point bending model was used to induce a single period of mechanical loading on the tibial shaft. The effect on IGFBP-2 mRNA expression 6 hours after stimulation was determined with nonradioactive in situ hybridization on decalcified tibial sections. Endogenous IGFBP-2 mRNA was expressed in trabecular and cortical osteoblasts, some trabecular and subendocortical osteocytes, intracortical endothelial cells of blood vessels, and periosteum. Megakaryocytes, macrophages, and myeloid cells also expressed IGFBP-2 mRNA. Loading and sham loading did not affect IGFBP-2 mRNA expression in osteoblasts, bone marrow cells, and chondrocytes. An increase of IGFBP-2 mRNA-positive osteocytes was shown in loaded (1.68-fold) and sham-loaded (1.35-fold) endocortical tibial shaft. In conclusion, 6 hours after a single loading session, the number of IGFBP-2 mRNA-expressing osteocytes at the endosteal side of the shaft and inner lamellae was increased in squeezed and bended tibiae. Mechanical stimulation modulates IGFBP-2 mRNA expression in endocortical osteocytes. We suggest that IGFBP-2 plays a role in the lamellar bone formation process