Entanglement in Quantum Spin Chains, Symmetry Classes of Random Matrices, and Conformal Field Theory

We compute the entropy of entanglement between the first $N$ spins and the rest of the system in the ground states of a general class of quantum spin-chains. We show that under certain conditions the entropy can be expressed in terms of averages over ensembles of random matrices. These averages can be evaluated, allowing us to prove that at critical points the entropy grows like $\kappa\log_2 N + {\tilde \kappa}$ as $N\to\infty$, where $\kappa$ and ${\tilde \kappa}$ are determined explicitly. In an important class of systems, $\kappa$ is equal to one-third of the central charge of an associated Virasoro algebra. Our expression for $\kappa$ therefore provides an explicit formula for the central charge.Comment: 4 page

First Energy and Angle differential Measurements of e^+e^- -pairs emitted by Internal Pair Conversion of excited Heavy Nuclei

We present the first energy and angle resolved measurements of e+e- pairs emitted from heavy nuclei (Z>=40) at rest by internal pair conversion (IPC) of transitions with energies of less than 2MeV as well as recent theoretical results using the DWBA method, which takes full account of relativistic effects, magnetic substates and finite size of the nucleus. The 1.76MeV E0 transition in Zr90 (Sr source) and the 1.77MeV M1 transition in Pb207 (Bi source) have been investigated experimentally using the essentially improved set-up at the double-ORANGE beta-spectrometer of GSI. The measurements prove the capability of the setup to cleanly identify the IPC pairs in the presence of five orders of magnitude higher beta- and gamma background from the same source and to yield essentially background-free sum spectra despite the large background. Using the ability of the ORANGE setup to directly determine the opening angle of the e+e- pairs, the angular correlation of the emitted pairs was measured. In the Zr90 case the correlation could be deduced for a wide range of energy differences of the pairs. The Zr90 results are in good agreement with recent theory. The angular correlation deduced for the M1 transition in Pb207 is in strong disagreement with theoretical predictions derived within the Born approximation and shows almost isotropic character. This is again in agreement with the new theoretical results.Comment: LaTeX, 28 pages incl. 10 PS figures; Accepted by Z.Phys.

Asymptotics of skew orthogonal polynomials

Exact integral expressions of the skew orthogonal polynomials involved in Orthogonal (beta=1) and Symplectic (beta=4) random matrix ensembles are obtained: the (even rank) skew orthogonal polynomials are average characteristic polynomials of random matrices. From there, asymptotics of the skew orthogonal polynomials are derived.Comment: 17 pages, Late

Quantum test of the Universality of Free Fall using rubidium and potassium

We report on an improved test of the Universality of Free Fall using a rubidium-potassium dual-species matter wave interferometer. We describe our apparatus and detail challenges and solutions relevant when operating a potassium interferometer, as well as systematic effects affecting our measurement. Our determination of the E\"otv\"os ratio yields $\eta_{\,\text{Rb,K}}=-1.9\times10^{-7}$ with a combined standard uncertainty of $\sigma_\eta=3.2\times10^{-7}$

Phase Estimation from Atom Position Measurements

We study the measurement of the position of atoms as a means to estimate the relative phase between two Bose-Einstein condensates. First, we consider $N$ atoms released from a double-well trap, forming an interference pattern, and show that a simple least-squares fit to the density gives a shot-noise limited sensitivity. The shot-noise limit can instead be overcome by using correlation functions of order $\sqrt{N}$ or larger. The measurement of the $N\mathrm{th}$-order correlation function allows to estimate the relative phase at the Heisenberg limit. Phase estimation through the measurement of the center-of-mass of the interference pattern can also provide sub-shot-noise sensitivity. Finally, we study the effect of the overlap between the two clouds on the phase estimation, when Mach-Zehnder interferometry is performed in a double-well.Comment: 20 pages, 6 figure

Positron spectra from internal pair conversion observed in {238}U + {181}Ta collisions

We present new results from measurements and simulations of positron spectra, originating from 238U + 181Ta collisions at beam energies close to the Coulomb barrier. The measurements were performed using an improved experimental setup at the double-Orange spectrometer of GSI. Particular emphasis is put on the signature of positrons from Internal-Pair-Conversion (IPC) processes in the measured e+ energy spectra, following the de-excitation of electromagnetic transitions in the moving Ta-like nucleus. It is shown by Monte Carlo simulations that, for the chosen current sweeping procedure used in the present experiments, positron emission from discrete IPC transitions can lead to rather narrow line structures in the measured energy spectra. The measured positron spectra do not show evidence for line structures within the statistical accuracy achieved, although expected from the intensities of the observed $\gamma$ transitions (E$_{\gamma}~1250-1600$ keV) and theoretical conversion coefficients. This is due to the reduced detection efficiency for IPC positrons, caused by the limited spatial and momentum acceptance of the spectrometer. A comparison with previous results, in which lines have been observed, is presented and the implications are discussed.Comment: LaTeX, 20 pages including 5 EPS figures; Accepted by Eur. Phys.Jour.

Magnetotransport Mechanisms in Strongly Underdoped YBa_2Cu_3O_x Single Crystals

We report magnetoresistivity measurements on strongly underdoped YBa_2Cu_3O_x (x=6.25, 6.36) single crystals in applied magnetic fields H || c-axis. We identify two different contributions to both in-plane and out-of-plane magnetoresistivities. The first contribution has the same sign as the temperature coefficient of the resistivity \partial ln(\rho_i)/\partial T (i={c,ab}). This contribution reflects the incoherent nature of the out-of-plane transport. The second contribution is positive, quadratic in field, with an onset temperature that correlates to the antiferromagnetic ordering.Comment: 4 pages, 3 figure

Transverse emittance measurement in 2D and 4D performed on a Low Energy Beam Transport line: benchmarking and data analysis

2D and 4D transverse phase-space of a low-energy ion-beam is measured with two of the most common emittance scanners. The article covers the description of the installation, the setup, the settings, the experiment and the benchmark of the two emittance meters. We compare the results from three series of measurements and present the advantages and drawbacks of the two systems. Coupling between phase-space planes, correlations and mitigation of deleterious effects are discussed. The influence of background noise and aberrations of trace-space figures on emittance measurements and RMS calculations is highlighted, especially for low density beams and halos. A new data analysis method using noise reduction, filtering, and reconstruction of the emittance figure is described. Finally, some basic concepts of phase-space theory and application to beam transport are recalled

Exponential behavior of the interlayer exchange coupling across non-magnetic metallic superlattices

It is shown that the coupling between magnetic layers separated by non-magnetic metallic superlattices can decay exponentially as a function of the spacer thickness $N$, as opposed to the usual $N^{-2}$ decay. This effect is due to the lack of constructive contributions to the coupling from extended states across the spacer. The exponential behavior is obtained by properly choosing the distinct metals and the superlattice unit cell composition.Comment: To appear in Phys. Rev.