First-principle calculations of Dark Matter scattering off light nuclei

We study the scattering of Dark Matter particles off various light nuclei within the framework of chiral effective field theory. We focus on scalar interactions and include one- and two-nucleon scattering processes whose form and strength are dictated by chiral symmetry. The nuclear wave functions are calculated from chiral effective field theory interactions as well and we investigate the convergence pattern of the chiral expansion in the nuclear potential and the Dark Matter-nucleus currents. This allows us to provide a systematic uncertainty estimate of our calculations. We provide results for ${}^2$H, ${}^3$H, and ${}^3$He nuclei which are theoretically interesting and the latter is a potential target for experiments. We show that two-nucleon currents can be systematically included but are generally smaller than predicted by power counting and suffer from significant theoretical uncertainties even in light nuclei. We demonstrate that accurate high-order wave functions are necessary in order to incorporate two-nucleon currents. We discuss scenarios in which one-nucleon contributions are suppressed such that higher-order currents become dominant

Measurement of the hyperfine structure of the S1/2-D5/2 transition in 43Ca+

The hyperfine structure of the S1/2-D5/2 quadrupole transition at 729 nm in 43Ca+ has been investigated by laser spectroscopy using a single trapped 43Ca+ ion. We determine the hyperfine structure constants of the metastable level as A=-3.8931(2) MHz and B=-4.241(4) MHz. The isotope shift of the transition with respect to 40Ca+ was measured to be 4134.713(5) MHz. We demonstrate the existence of transitions that become independent of the first-order Zeeman shift at non-zero low magnetic fields. These transitions might be better suited for building a frequency standard than the well-known 'clock transitions' between m=0 levels at zero magnetic field.Comment: corrected for sign errors in the hyperfine constants. No corrections to were made to the data analysi

Process tomography of ion trap quantum gates

A crucial building block for quantum information processing with trapped ions is a controlled-NOT quantum gate. In this paper, two different sequences of laser pulses implementing such a gate operation are analyzed using quantum process tomography. Fidelities of up to 92.6(6)% are achieved for single gate operations and up to 83.4(8)% for two concatenated gate operations. By process tomography we assess the performance of the gates for different experimental realizations and demonstrate the advantage of amplitude--shaped laser pulses over simple square pulses. We also investigate whether the performance of concatenated gates can be inferred from the analysis of the single gates

Robust entanglement

It is common belief among physicists that entangled states of quantum systems loose their coherence rather quickly. The reason is that any interaction with the environment which distinguishes between the entangled sub-systems collapses the quantum state. Here we investigate entangled states of two trapped Ca$^+$ ions and observe robust entanglement lasting for more than 20 seconds

Evaluating the Performance of Ultra-Low-Field MRI for In-vivo 3D Current Density Imaging of the Human Head

Magnetic fields associated with currents flowing in tissue can be measured non-invasively by means of zero-field-encoded ultra-low-field magnetic resonance imaging (ULF MRI) enabling current density imaging (CDI) and possibly conductivity mapping of human head tissues. Since currents applied to a human are limited by safety regulations and only a small fraction of the current passes through the relatively high-resistive skull, a sufficient signal-to-noise ratio (SNR) may be difficult to obtain when using this method. In this work, we study the relationship between the image SNR and the SNR of the field reconstructions from zero-field-encoded data. We evaluate these results for two existing ULF MRI scanners, one ultra-sensitive single-channel system and one whole-head multi-channel system, by simulating sequences necessary for current-density reconstruction. We also derive realistic current-density and magnetic-field estimates from finite-element-method simulations based on a three-compartment head model. We found that existing ULF-MRI systems reach sufficient SNR to detect intra-cranial current distributions with statistical uncertainty below 10%. However, they also reveal that image artifacts influence the reconstruction quality. Further, our simulations indicate that current-density reconstruction in the scalp requires a resolution less than 5 mm and demonstrate that the necessary sensitivity coverage can be accomplished by multi-channel devices.Comment: 18 pages, 8 figures. This project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 68686

Quasiparticle spin susceptibility in heavy-fermion superconductors : An NMR study compared with specific heat results

Quasi-particle spin susceptibility ($\chi^{qp}$) for various heavy-fermion (HF) superconductors are discussed on the basis of the experimental results of electronic specific heat ($\gamma_{el}$), NMR Knight shift ($K$) and NMR relaxation rate ($1/T_1$) within the framework of the Fermi liquid model for a Kramers doublet crystal electric field (CEF) ground state. $\chi^{qp}_{\gamma}$ is calculated from the enhanced Sommerfeld coefficient $\gamma_{el}$ and $\chi^{qp}_{T_1}$ from the quasi-particle Korringa relation $T_1T(K^{qp}_{T_1})^2=const.$ via the relation of $\chi^{qp}_{T_1}=(N_A\mu_B/A_{hf})K^{qp}_{T_1}$ where $A_{hf}$ is the hyperfine coupling constant, $N_A$ the Abogadoro's number and $\mu_B$ the Bohr magneton. For the even-parity (spin-singlet) superconductors CeCu$_2$Si$_2$, CeCoIn$_5$ and UPd$_2$Al$_3$, the fractional decrease in the Knight shift, $\delta K^{obs}$, below the superconducting transition temperature ($T_c$) is due to the decrease of the spin susceptibility of heavy quasi-particle estimated consistently from $\chi^{qp}_{\gamma}$ and $\chi^{qp}_{T_1}$. This result allows us to conclude that the heavy quasi-particles form the spin-singlet Cooper pairs in CeCu$_2$Si$_2$, CeCoIn$_5$ and UPd$_2$Al$_3$. On the other hand, no reduction in the Knight shift is observed in UPt$_3$ and UNi$_2$Al$_3$, nevertheless the estimated values of $\chi^{qp}_{\gamma}$ and $\chi^{qp}_{T_1}$ are large enough to be probed experimentally. The odd-parity superconductivity is therefore concluded in these compounds. The NMR result provides a convincing way to classify the HF superconductors into either even- or odd- parity paring together with the identification for the gap structure, as long as the system has Kramers degeneracy.Comment: 11 pages, 3 tables, 5 figures, RevTex4(LaTex2e

Scale setting the M\"obius Domain Wall Fermion on gradient-flowed HISQ action using the omega baryon mass and the gradient-flow scales t0t_0 and w0w_0

We report on a sub-percent scale determination using the omega baryon mass and gradient-flow methods. The calculations are performed on 22 ensembles of $N_f=2+1+1$ highly improved, rooted staggered sea-quark configurations generated by the MILC and CalLat Collaborations. The valence quark action used is M\"obius Domain-Wall fermions solved on these configurations after a gradient-flow smearing is applied with a flowtime of $t_{\rm gf}=1$ in lattice units. The ensembles span four lattice spacings in the range $0.06 \lesssim a \lesssim 0.15$ fm, six pion masses in the range $130 \lesssim m_\pi \lesssim 400$ MeV and multiple lattice volumes. On each ensemble, the gradient-flow scales $t_0/a^2$ and $w_0/a$ and the omega baryon mass $a m_\Omega$ are computed. The dimensionless product of these quantities is then extrapolated to the continuum and infinite volume limits and interpolated to the physical light, strange and charm quark mass point in the isospin limit, resulting in the determination of $\sqrt{t_0}=0.1422(14)$ fm and $w_0 = 0.1709(11)$ fm with all sources of statistical and systematic uncertainty accounted for. The dominant uncertainty in this result is the stochastic uncertainty, providing a clear path for a few-per-mille uncertainty, as recently obtained by the Budapest-Marseille-Wuppertal Collaboration.Comment: v3: Published version; v2: Added determination of t_0 as well as w_0; v1: 13 pages plus appendices. The correlation function data, mass results and analysis code accompanying this publication can be found at this github repository: https://github.com/callat-qcd/project_scale_setting_mdwf_his