Twisted equivariant K-theory, groupoids and proper actions

In this paper we define twisted equivariant K-theory for actions of Lie groupoids. For a Bredon-compatible Lie groupoid, this defines a periodic cohomology theory on the category of finite CW-complexes with equivariant stable projective bundles. A classification of these bundles is shown. We also obtain a completion theorem and apply these results to proper actions of groups.Comment: 26 page

Double wells, scalar fields and quantum phase transitions in ions traps

Since Hund's work on the ammonia molecule, the double well potential has formed a key paradigm in physics. Its importance is further underlined by the central role it plays in the Landau theory of phase transitions. Recently, the study of entanglement properties of many-body systems has added a new angle to the study of quantum phase transitions of discrete and continuous degrees of freedom, i.e., spin and harmonic chains. Here we show that control of the radial degree of freedom of trapped ion chains allows for the simulation of linear and non-linear Klein-Gordon fields on a lattice, in which the parameters of the lattice, the non-linearity and mass can be controlled at will. The system may be driven through a phase transition creating a double well potential between different configurations of the ion crystal. The dynamics of the system are controllable, local properties are measurable and tunnelling in the double well potential would be observable.Comment: 6 pages, 5 figure

Doppler-free laser spectroscopy of buffer gas cooled molecular radicals

We demonstrate Doppler-free saturated absorption spectroscopy of cold molecular radicals formed by laser ablation inside a cryogenic buffer gas cell. By lowering the temperature, congested regions of the spectrum can be simplified, and by using different temperatures for different regions of the spectrum a wide range of rotational states can be studied optimally. We use the technique to study the optical spectrum of YbF radicals with a resolution of 30 MHz, measuring the magnetic hyperfine parameters of the electronic ground state. The method is suitable for high resolution spectroscopy of a great variety of molecules at controlled temperature and pressure, and is particularly well-suited to those that are difficult to produce in the gas phase.Comment: 11 pages, 4 figure

Hammerhead, an ultrahigh resolution ePix camera for wavelength-dispersive spectrometers

Wavelength-dispersive spectrometers (WDS) are often used in synchrotron and FEL applications where high energy resolution (in the order of eV) is important. Increasing WDS energy resolution requires increasing spatial resolution of the detectors in the dispersion direction. The common approaches with strip detectors or small pixel detectors are not ideal. We present a novel approach, with a sensor using rectangular pixels with a high aspect ratio (between strips and pixels, further called "strixels"), and strixel redistribution to match the square pixel arrays of typical ASICs while avoiding the considerable effort of redesigning ASICs. This results in a sensor area of 17.4 mm x 77 mm, with a fine pitch of 25 $\mu$m in the horizontal direction resulting in 3072 columns and 176 rows. The sensors use ePix100 readout ASICs, leveraging their low noise (43 e$^-$, or 180 eV rms). We present results obtained with a Hammerhead ePix100 camera, showing that the small pitch (25 $\mu$m) in the dispersion direction maximizes performance for both high and low photon occupancies, resulting in optimal WDS energy resolution. The low noise level at high photon occupancy allows precise photon counting, while at low occupancy, both the energy and the subpixel position can be reconstructed for every photon, allowing an ultrahigh resolution (in the order of 1 $\mu$m) in the dispersion direction and rejection of scattered beam and harmonics. Using strixel sensors with redistribution and flip-chip bonding to standard ePix readout ASICs results in ultrahigh position resolution ($\sim$1 $\mu$m) and low noise in WDS applications, leveraging the advantages of hybrid pixel detectors (high production yield, good availability, relatively inexpensive) while minimizing development complexity through sharing the ASIC, hardware, software and DAQ development with existing versions of ePix cameras.Comment: 8 pages, 6 figure

QED in external fields from the spin representation

Systematic use of the infinite-dimensional spin representation simplifies and rigorizes several questions in Quantum Field Theory. This representation permutes ``Gaussian'' elements in the fermion Fock space, and is necessarily projective: we compute its cocycle at the group level, and obtain Schwinger terms and anomalies from infinitesimal versions of this cocycle. Quantization, in this framework, depends on the choice of the ``right'' complex structure on the space of solutions of the Dirac equation. We show how the spin representation allows one to compute exactly the S-matrix for fermions in an external field; the cocycle yields a causality condition needed to determine the phase.Comment: 32 pages, Plain TeX, UCR-FM-01-9

Rigorous Dynamics and Radiation Theory for a Pauli-Fierz Model in the Ultraviolet Limit

The present paper is devoted to the detailed study of quantization and evolution of the point limit of the Pauli-Fierz model for a charged oscillator interacting with the electromagnetic field in dipole approximation. In particular, a well defined dynamics is constructed for the classical model, which is subsequently quantized according to the Segal scheme. To this end, the classical model in the point limit is reformulated as a second order abstract wave equation, and a consistent quantum evolution is given. This allows a study of the behaviour of the survival and transition amplitudes for the process of decay of the excited states of the charged particle, and the emission of photons in the decay process. In particular, for the survival amplitude the exact time behaviour is found. This is completely determined by the resonances of the systems plus a tail term prevailing in the asymptotic, long time regime. Moreover, the survival amplitude exhibites in a fairly clear way the Lamb shift correction to the unperturbed frequencies of the oscillator.Comment: Shortened version. To appear in J. Math. Phy

The Anti-Coincidence Detector for the GLAST Large Area Telescope

This paper describes the design, fabrication and testing of the Anti-Coincidence Detector (ACD) for the Gamma-ray Large Area Space Telescope (GLAST) Large Area Telescope (LAT). The ACD is LAT first-level defense against the charged cosmic ray background that outnumbers the gamma rays by 3-5 orders of magnitude. The ACD covers the top and 4 sides of the LAT tracking detector, requiring a total active area of ~8.3 square meters. The ACD detector utilizes plastic scintillator tiles with wave-length shifting fiber readout. In order to suppress self-veto by shower particles at high gamma-ray energies, the ACD is segmented into 89 tiles of different sizes. The overall ACD efficiency for detection of singly charged relativistic particles entering the tracking detector from the top or sides of the LAT exceeds the required 0.9997.Comment: 33 pages, 19 figure

Laser cooling in the Penning trap: an analytical model for cooling rates in the presence of an axializing field

Ions stored in Penning traps may have useful applications in the field of quantum information processing. There are, however, difficulties associated with the laser cooling of one of the radial motions of ions in these traps, namely the magnetron motion. The application of a small radio-frequency quadrupolar electric potential resonant with the sum of the two radial motional frequencies has been shown to couple these motions and to lead to more efficient laser cooling. We present an analytical model that enables us to determine laser cooling rates in the presence of such an 'axializing' field. It is found that this field leads to an averaging of the laser cooling rates for the two motions and hence improves the overall laser cooling efficiency. The model also predicts shifts in the motional frequencies due to the axializing field that are in qualitative agreement with those measured in recent experiments. It is possible to determine laser cooling rates experimentally by studying the phase response of the cooled ions to a near resonant excitation field. Using the model developed in this paper, we study the expected phase response when an axializing field is present.Comment: 22 pages, 7 figure