Projections and idempotents with fixed diagonal and the homotopy problem for unit tight frames

We investigate the topological and metric structure of the set of idempotent operators and projections which have prescribed diagonal entries with respect to a fixed orthonormal basis of a Hilbert space. As an application, we settle some cases of conjectures of Larson, Dykema, and Strawn on the connectedness of the set of unit-norm tight frames.Comment: New title and introductio

Magnetization plateaux in an extended Shastry-Sutherland model

We study an extended two-dimensional Shastry-Sutherland model in a magnetic field where besides the usual Heisenberg exchanges of the Shastry-Sutherland model two additional SU(2) invariant couplings are included. Perturbative continous unitary transformations are used to determine the leading order effects of the additional couplings on the pure hopping and on the long-range interactions between the triplons which are the most relevant terms for small magnetization. We then compare the energy of various magnetization plateaux in the classical limit and we discuss the implications for the two-dimensional quantum magnet SrCu$_2$(BO$_3$)$_2$.Comment: 8 pages, Proceedings of the HFM2008 Conferenc

An apodizing phase plate coronagraph for VLT/NACO

We describe a coronagraphic optic for use with CONICA at the VLT that provides suppression of diffraction from 1.8 to 7 lambda/D at 4.05 microns, an optimal wavelength for direct imaging of cool extrasolar planets. The optic is designed to provide 10 magnitudes of contrast at 0.2 arcseconds, over a D-shaped region in the image plane, without the need for any focal plane occulting mask.Comment: 9 pages, 5 figures, to appear in Proc. SPIE Vol. 773

High resolution coherent population trapping on a single hole spin in a semiconductor

We report high resolution coherent population trapping on a single hole spin in a semiconductor quantum dot. The absorption dip signifying the formation of a dark state exhibits an atomic physics-like dip width of just 10 MHz. We observe fluctuations in the absolute frequency of the absorption dip, evidence of very slow spin dephasing. We identify this process as charge noise by, first, demonstrating that the hole spin g-factor in this configuration (in-plane magnetic field) is strongly dependent on the vertical electric field, and second, by characterizing the charge noise through its effects on the optical transition frequency. An important conclusion is that charge noise is an important hole spin dephasing process

Comment on "Localized behavior near the Zn impurity in YBa2Cu4O8 as measured by nuclear quadrupole resonance"

Williams and Kramer [Phys. Rev. B {\bf 64}, 104506 (2001)] have recently argued against the existence of staggered magnetic moments residing on several lattice sites around Zn impurities in YBCO superconductors. This claim, which is in line with an earlier publication by Williams, Tallon and Dupree [Phys. Rev. B {\bf 61}, 4319 (2000)], is however in contradiction with a large body of experimental data from different NMR groups. On the contrary, the authors argue in favor of a very localized spin and charge density on Cu sites first neighbors to Zn. We show that the conclusions of Williams and Kramer arise from erroneous interpretations of NMR and NQR data.Comment: 4 page

Spin Dynamics near the Superconductor-to-Insulator Transition in Impurity-Doped YBa2Cu4O8

We studied low-frequency spin dynamics near the impurity-induced superconductor-to-insulator transition for underdoped high-Tc superconductor YBa2(Cu1-xMx)4O8 (M=Ni, Zn) using the Cu nuclear quadrupole resonance (NQR) spin-echo technique. We observed remarkable suppression of the normal-state pseudo spin-gap and a loss of Cu NQR spectrum intensity at low temperatures around the critical impurity concentration.Comment: 6 pages, 4 figures. To be published in J. Phys. Soc. Jpn. Vol.70, No.7 (2001

Projections and Idempotents with Fixed Diagonal and the Homotopy Problem for Unit Tight Frames

We investigate the topological and metric structure of the set of idempotent operators and projections which have prescribed diagonal entries with respect to a fixed orthonormal basis of a Hilbert space. As an application, we settle some cases of conjectures of Larson, Dykema, and Strawn on the connectedness of the set of unit-norm tight frames

Pairing of Cooper Pairs in a Fully Frustrated Josephson Junction Chain

We study a one-dimensional Josephson junction chain embedded in a magnetic field. We show that when the magnetic flux per elementary loop equals half the superconducting flux quantum $\phi_0=h/2e$, a local \nbZ_2 symmetry arises. This symmetry is responsible for a nematic Luttinger liquid state associated to bound states of Cooper pairs. We analyze the phase diagram and we discuss some experimental possibilities to observe this exotic phase.Comment: 4 pages, 4 EPS figure

High-vacuum-compatible high-power Faraday isolators for gravitational-wave interferometers

Faraday isolators play a key role in the operation of large-scale gravitational-wave detectors. Second-generation gravitational-wave interferometers such as the Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) and Advanced Virgo will use high-average-power cw lasers (up to 200 W) requiring specially designed Faraday isolators that are immune to the effects resulting from the laser beam absorption–degraded isolation ratio, thermal lensing, and thermally induced beam steering. In this paper, we present a comprehensive study of Faraday isolators designed specifically for high-performance operation in high-power gravitational-wave interferometers

Entanglement entropy in collective models

We discuss the behavior of the entanglement entropy of the ground state in various collective systems. Results for general quadratic two-mode boson models are given, yielding the relation between quantum phase transitions of the system (signaled by a divergence of the entanglement entropy) and the excitation energies. Such systems naturally arise when expanding collective spin Hamiltonians at leading order via the Holstein-Primakoff mapping. In a second step, we analyze several such models (the Dicke model, the two-level BCS model, the Lieb-Mattis model and the Lipkin-Meshkov-Glick model) and investigate the properties of the entanglement entropy in the whole parameter range. We show that when the system contains gapless excitations the entanglement entropy of the ground state diverges with increasing system size. We derive and classify the scaling behaviors that can be met.Comment: 11 pages, 7 figure