Quantum Algorithmic Readout in Multi-Ion Clocks

Optical clocks based on ensembles of trapped ions offer the perspective of record frequency uncertainty with good short-term stability. Most suitable atomic species lack closed transitions for fast detection such that the clock signal has to be read out indirectly through transferring the quantum state of clock ions to co-trapped logic ions by means of quantum logic operations. For ensembles of clock ions existing methods for quantum logic readout require a linear overhead in either time or the number of logic ions. Here we report a quantum algorithmic readout whose overhead scales logarithmically with the number of clock ions in both of these respects. We show that the readout algorithm can be implemented with a single application of a multi-species quantum gate, which we describe in detail for a crystal of Aluminum and Calcium ions.Comment: 4 pages + 7 pages appendix; 5 figures; v3: published versio

Experimental and theoretical investigation of a multi-mode cooling scheme using multiple EIT resonances

We introduce and demonstrate double-bright electromagnetically induced transparency (D-EIT) cooling as a novel approach to EIT cooling. By involving an additional ground state, two bright states can be shifted individually into resonance for cooling of motional modes of frequencies that may be separated by more than the width of a single EIT cooling resonance. This allows three-dimensional ground state cooling of a $^{40}$Ca$^+$ ion trapped in a linear Paul trap with a single cooling pulse. Measured cooling rates and steady-state mean motional quantum numbers for this D-EIT cooling are compared with those of standard EIT cooling as well as concatenated standard EIT cooling pulses for multi-mode cooling. Experimental results are compared to full density matrix calculations. We observe a failure of the theoretical description within the Lamb-Dicke regime that can be overcome by a time-dependent rate theory. Limitations of the different cooling techniques and possible extensions to multi-ion crystals are discussed.Comment: 18 pages, 13 figures. We have decided to merge the contents of our submission arXiv:1711.00738 with this paper into one comprehensive work. New titl

idem: An R Package for Inferences in Clinical Trials with Death and Missingness

In randomized controlled trials of seriously ill patients, death is common and often defined as the primary endpoint. Increasingly, non-mortality outcomes such as functional outcomes are co-primary or secondary endpoints. Functional outcomes are not defined for patients who die, referred to as "truncation due to death", and among survivors, functional outcomes are often unobserved due to missed clinic visits or loss to follow-up. It is well known that if the functional outcomes "truncated due to death" or missing are handled inappropriately, treatment effect estimation can be biased. In this paper, we describe the package idem that implements a procedure for comparing treatments that is based on a composite endpoint of mortality and the functional outcome among survivors. Among survivors, the procedure incorporates a missing data imputation procedure with a sensitivity analysis strategy. A web-based graphical user interface is provided in the idem package to facilitate users conducting the proposed analysis in an interactive and user-friendly manner. We demonstrate idem using data from a recent trial of sedation interruption among mechanically ventilated patients

Precision spectroscopy by photon-recoil signal amplification

Precision spectroscopy of atomic and molecular ions offers a window to new physics, but is typically limited to species with a cycling transition for laser cooling and detection. Quantum logic spectroscopy has overcome this limitation for species with long-lived excited states. Here, we extend quantum logic spectroscopy to fast, dipole-allowed transitions and apply it to perform an absolute frequency measurement. We detect the absorption of photons by the spectroscopically investigated ion through the photon recoil imparted on a co-trapped ion of a different species, on which we can perform efficient quantum logic detection techniques. This amplifies the recoil signal from a few absorbed photons to thousands of fluorescence photons. We resolve the line center of a dipole-allowed transition in 40Ca+ to 1/300 of its observed linewidth, rendering this measurement one of the most accurate of a broad transition. The simplicity and versatility of this approach enables spectroscopy of many previously inaccessible species.Comment: 25 pages, 6 figures, 1 table, updated supplementary information, fixed typo

Renormalization : A number theoretical model

We analyse the Dirichlet convolution ring of arithmetic number theoretic functions. It turns out to fail to be a Hopf algebra on the diagonal, due to the lack of complete multiplicativity of the product and coproduct. A related Hopf algebra can be established, which however overcounts the diagonal. We argue that the mechanism of renormalization in quantum field theory is modelled after the same principle. Singularities hence arise as a (now continuously indexed) overcounting on the diagonals. Renormalization is given by the map from the auxiliary Hopf algebra to the weaker multiplicative structure, called Hopf gebra, rescaling the diagonals.Comment: 15 pages, extended version of talks delivered at SLC55 Bertinoro,Sep 2005, and the Bob Delbourgo QFT Fest in Hobart, Dec 200

Three-dimensional imaging and detection efficiency performance of orthogonal coplanar CZT strip detectors

We report on recent three-dimensional imaging performance and detection efficiency measurements obtained with 5 mm thick prototype CdZnTe detectors fabricated with orthogonal coplanar anode strips. In previous work, we have shown that detectors fabricated using this design achieve both very good energy resolution and sub-millimeter spatial resolution with fewer electronic channels than are required for pixel detectors. As electron-only devices, like pixel detectors, coplanar anode strip detectors can be fabricated in the thickness required to be effective imagers for photons with energies in excess of 500 keV. Unlike conventional double-sided strip detectors, the coplanar anode strip detectors require segmented contacts and signal processing electronics on only one surface. The signals can be processed to measure the total energy deposit and the photon interaction location in three dimensions. The measurements reported here provide a quantitative assessment of the detection capabilities of orthogonal coplanar anode strip detectors