Energetics and phasing of nonprecessing spinning coalescing black hole binaries

We present an improved numerical relativity (NR) calibration of the new effective-one-body (EOB) model for coalescing non precessing spinning black hole binaries recently introduced by Damour and Nagar [Physical Review D 90, 044018 (2014)]. We do so by comparing the EOB predictions to both the phasing and the energetics provided by two independent sets of NR data covering mass ratios $1\leq q \leq 9.989$ and dimensionless spin range $-0.95\leq \chi\leq +0.994$. One set of data is a subset of the Simulating eXtreme Spacetimes (SXS) catalog of public waveforms; the other set consists of new simulations obtained with the Llama code plus Cauchy Characteristic Evolution. We present the first systematic computation of the gauge-invariant relation between the binding energy and the total angular momentum, $E_{b}(j)$, for a large sample of, spin-aligned, SXS and Llama data. The dynamics of the EOB model presented here involves only two free functional parameters, one ($a_6^c(\nu)$) entering the non spinning sector, as a 5PN effective correction to the interaction potential, and one ($c_3(\tilde{a}_1,\tilde{a}_2,\nu))$ in the spinning sector, as an effective next-to-next-to-next-to-leading order correction to the spin-orbit coupling. These parameters are determined (together with a third functional parameter $\Delta t_{\rm NQC}(\chi)$ entering the waveform) by comparing the EOB phasing with the SXS phasing, the consistency of the energetics being checked afterwards. The quality of the analytical model for gravitational wave data analysis purposes is assessed by computing the EOB/NR faithfulness. Over the NR data sample and when varying the total mass between 20 and 200~$M_\odot$ the EOB/NR unfaithfulness (integrated over the NR frequency range) is found to vary between $99.493\%$ and $99.984\%$ with a median value of $99.944\%$.Comment: 26 pages, 27 figures, results improved with respect to first versio

Line Coupling Effects in the Isotropic Raman Spectra of N2: A Quantum Calculation at Room Temperature

We present quantum calculations of the relaxation matrix for the Q branch of N2 at room temperature using a recently proposed N2-N2 rigid rotor potential. Close coupling calculations were complemented by coupled states studies at high energies and provide about 10200 two-body state-to state cross sections from which the needed one-body cross-sections may be obtained. For such temperatures, convergence has to be thoroughly analyzed since such conditions are close to the limit of current computational feasibility. This has been done using complementary calculations based on the energy corrected sudden formalism. Agreement of these quantum predictions with experimental data is good, but the main goal of this work is to provide a benchmark relaxation matrix for testing more approximate methods which remain of a great utility for complex molecular systems at room (and higher) temperatures

Ion Imaging via Long-Range Interaction with Rydberg Atoms

We demonstrate imaging of ions in an atomic gas with ion-Rydberg atom interaction induced absorption. This is made possible by utilizing a multi-photon electromagnetically induced transparency (EIT) scheme and the extremely large electric polarizability of a Rydberg state with high orbital angular momentum. We process the acquired images to obtain the distribution of ion clouds and to spectroscopically investigate the effect of the ions on the EIT resonance. Furthermore, we show that our method can be employed to image the dynamics of ions in a time resolved way. As an example, we map out the avalanche ionization of a gas of Rydberg atoms. The minimal disruption and the flexibility offered by this imaging technique make it ideally suited for the investigation of cold hybrid ion-atom systems.Comment: 6 pages, 4 figure

Line Interference Effects Using a Refined Robert-Bonamy Formalism: the Test Case of the Isotropic Raman Spectra of Autoperturbed N2

A symmetrized version of the recently developed refined Robert-Bonamy formalism [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)] is proposed. This model takes into account line coupling effects and hence allows the calculation of the off-diagonal elements of the relaxation matrix, without neglecting the rotational structure of the perturbing molecule. The formalism is applied to the isotropic Raman spectra of autoperturbed N2 for which a benchmark quantum relaxation matrix has recently been proposed. The consequences of the classical path approximation are carefully analyzed. Methods correcting for effects of inelasticity are considered. While in the right direction, these corrections appear to be too crude to provide off diagonal elements which would yield, via the sum rule, diagonal elements in good agreement with the quantum results. In order to overcome this difficulty, a re-normalization procedure is applied, which ensures that the off-diagonal elements do lead to the exact quantum diagonal elements. The agreement between the (re-normalized) semi-classical and quantum relaxation matrices is excellent, at least for the Raman spectra of N2, opening the way to the analysis of more complex molecular systems

Efficient microwave-to-optical conversion using Rydberg atoms

We demonstrate microwave-to-optical conversion using six-wave mixing in $^{87}$Rb atoms where the microwave field couples to two atomic Rydberg states, and propagates collinearly with the converted optical field. We achieve a photon conversion efficiency of ~5% in the linear regime of the converter. In addition, we theoretically investigate all-resonant six-wave mixing and outline a realistic experimental scheme for reaching efficiencies greater than 60%

Constructing Incremental Sequences in Graphs

Given a weighted graph , we investigate the problem of constructing a sequence of subsets of vertices (called groups) with small diameters, where the diameter of a group is calculated using distances in G. The constraint on these n groups is that they must be incremental: . The cost of a sequence is the maximum ratio between the diameter of each group Mi and the diameter of a group with I vertices and minimum diameter: . This quantity captures the impact of the incremental constraint on the diameters of the groups in a sequence. We give general bounds on the value of this ratio and we prove that the problem of constructing an optimal incremental sequence cannot be solved approximately in polynomial time with an approximation ratio less than 2 unless P = NP. Finally, we give a 4-approximation algorithm and we show that the analysis of our algorithm is tight