Mosaicking with cosmic microwave background interferometers

Measurements of cosmic microwave background (CMB) anisotropies by interferometers offer several advantages over single-dish observations. The formalism for analyzing interferometer CMB data is well developed in the flat-sky approximation, valid for small fields of view. As the area of sky is increased to obtain finer spectral resolution, this approximation needs to be relaxed. We extend the formalism for CMB interferometry, including both temperature and polarization, to mosaics of observations covering arbitrarily large areas of the sky, with each individual pointing lying within the flat-sky approximation. We present a method for computing the correlation between visibilities with arbitrary pointing centers and baselines and illustrate the effects of sky curvature on the l-space resolution that can be obtained from a mosaic.Comment: 9 pages; submitted to Ap

Displacement- and Timing-Noise Free Gravitational-Wave Detection

Motivated by a recently-invented scheme of displacement-noise-free gravitational-wave detection, we demonstrate the existence of gravitational-wave detection schemes insusceptible to both displacement and timing (laser) noises, and are thus realizable by shot-noise-limited laser interferometry. This is possible due to two reasons: first, gravitational waves and displacement disturbances contribute to light propagation times in different manners; second, for an N-detector system, the number of signal channels is of the order O(N^2), while the total number of timing- and displacement-noise channels is of the order O(N).Comment: 4 pages, 3 figures; mistake correcte

Optimal Image Reconstruction in Radio Interferometry

We introduce a method for analyzing radio interferometry data which produces maps which are optimal in the Bayesian sense of maximum posterior probability density, given certain prior assumptions. It is similar to maximum entropy techniques, but with an exact accounting of the multiplicity instead of the usual approximation involving Stirling's formula. It also incorporates an Occam factor, automatically limiting the effective amount of detail in the map to that justified by the data. We use Gibbs sampling to determine, to any desired degree of accuracy, the multi-dimensional posterior density distribution. From this we can construct a mean posterior map and other measures of the posterior density, including confidence limits on any well-defined function of the posterior map.Comment: 41 pages, 11 figures. High resolution figures 8 and 9 available at http://www.astro.uiuc.edu/~bwandelt/SuttonWandelt200

Density matrix numerical renormalization group for non-Abelian symmetries

We generalize the spectral sum rule preserving density matrix numerical renormalization group (DM-NRG) method in such a way that it can make use of an arbitrary number of not necessarily Abelian, local symmetries present in the quantum impurity system. We illustrate the benefits of using non-Abelian symmetries by the example of calculations for the T-matrix of the two-channel Kondo model in the presence of magnetic field, for which conventional NRG methods produce large errors and/or take a long run-time.Comment: 12 pages, 6 figures, PRB forma

Parameter Estimation with Mixed-State Quantum Computation

We present a quantum algorithm to estimate parameters at the quantum metrology limit using deterministic quantum computation with one bit. When the interactions occurring in a quantum system are described by a Hamiltonian $H= \theta H_0$, we estimate $\theta$ by zooming in on previous estimations and by implementing an adaptive Bayesian procedure. The final result of the algorithm is an updated estimation of $\theta$ whose variance has been decreased in proportion to the time of evolution under H. For the problem of estimating several parameters, we implement dynamical-decoupling techniques and use the results of single parameter estimation. The cases of discrete-time evolution and reference-frame alignment are also discussed within the adaptive approach.Comment: 12 pages. Improved introduction and technical details moved to Appendi

Implications of Qudit Superselection rules for the Theory of Decoherence-free Subsystems

The use of d-state systems, or qudits, in quantum information processing is discussed. Three-state and higher dimensional quantum systems are known to have very different properties from two-state systems, i.e., qubits. In particular there exist qudit states which are not equivalent under local unitary transformations unless a selection rule is violated. This observation is shown to be an important factor in the theory of decoherence-free, or noiseless, subsystems. Experimentally observable consequences and methods for distinguishing these states are also provided, including the explicit construction of new decoherence-free or noiseless subsystems from qutrits. Implications for simulating quantum systems with quantum systems are also discussed.Comment: 13 pages, 1 figures, Version 2: Typos corrected, references fixed and new ones added, also includes referees suggested changes and a new exampl

New insights into North Sea deep crustal structure and extension from transdimensional ambient noise tomography

SUMMARY The deep crustal structure beneath the North Sea is poorly understood since it is constrained by only a few seismic reflection and refraction profiles. However, it is widely acknowledged that the mid to lower crust plays important roles in rift initiation and evolution, particularly when large-scale sutures and/or terrane boundaries are present, since these inherited features can focus strain or act as inhibitors to extensional deformation. Ancient tectonic features are known to exist beneath the iconic failed rift system of the North Sea, making it an ideal location to investigate the complex interplay between pre-existing regional heterogeneity and rifting. To this end, we produce a 3-D shear wave velocity model from transdimensional ambient seismic noise tomography to constrain crustal properties to ∼30 km depth beneath the North Sea and its surrounding landmasses. Major North Sea sedimentary basins appear as low shear wave velocity zones that are a good match to published sediment thickness maps. We constrain relatively thin crust (13–18 km) beneath the Central Graben depocentres that contrasts with crust elsewhere at least 25–30 km thick. Significant variations in crustal structure and rift symmetry are identified along the failed rift system that appears to be related to the locations of Laurentia–Avalonia–Baltica palaeoplate boundaries. We constrain first-order differences in structure between palaeoplates; with strong lateral gradients in crustal velocity related to Laurentia–Avalonia–Baltica plate juxtaposition and reduced lower crustal velocities in the vicinity of the Thor suture, possibly representing the remnants of a Caledonian accretionary complex. Our results provide fresh insight into the pivotal roles that ancient terranes can play in the formation and failure of continental rifts and may help explain the characteristics of other similar continental rifts globally.</jats:p

Detection of Signals from Cosmic Reionization using Radio Interferometric Signal Processing

Observations of the HI 21cm transition line promises to be an important probe into the cosmic dark ages and epoch of reionization. One of the challenges for the detection of this signal is the accuracy of the foreground source removal. This paper investigates the extragalactic point source contamination and how accurately the bright sources ($\gtrsim 1$ ~Jy) should be removed in order to reach the desired RMS noise and be able to detect the 21cm transition line. Here, we consider position and flux errors in the global sky-model for these bright sources as well as the frequency independent residual calibration errors. The synthesized beam is the only frequency dependent term included here. This work determines the level of accuracy for the calibration and source removal schemes and puts forward constraints for the design of the cosmic reionization data reduction scheme for the upcoming low frequency arrays like MWA,PAPER, etc. We show that in order to detect the reionization signal the bright sources need to be removed from the data-sets with a positional accuracy of $\sim 0.1$ arc-second. Our results also demonstrate that the efficient foreground source removal strategies can only tolerate a frequency independent antenna based mean residual calibration error of $\lesssim 0.2$ in amplitude or $\lesssim 0.2$ degree in phase, if they are constant over each days of observations (6 hours). In future papers we will extend this analysis to the power spectral domain and also include the frequency dependent calibration errors and direction dependent errors (ionosphere, primary beam, etc).Comment: accepted by ApJ; 12 pages, 10 figure