Reconstruction of SU(1,1) States

We show how group symmetries can be used to reconstruct quantum states. In our scheme for SU(1,1) states, the input field passes through a non-degenerate parametric amplifier and one measures the probability of finding the output state with a certain number (usually zero) of photons in each mode. The density matrix in the Fock basis is retrieved from the measured data by least squares method after singular value decomposition of the design matrix. Several illustrative examples involving the reconstruction of a pair coherent state, a Perelomov coherent state, and a coherent superposition of pair coherent states are considered.Comment: 8 pages, 5 figures, submitted to PR

Heavily reddened type 1 quasars at z > 2 I: Evidence for significant obscured black-hole growth at the highest quasar luminosities

We present a new population of z>2 dust-reddened, Type 1 quasars with 0.5<E(B-V)<1.5, selected using near infra-red (NIR) imaging data from the UKIDSS-LAS, ESO-VHS and WISE surveys. NIR spectra obtained using the Very Large Telescope (VLT) for 24 new objects bring our total sample of spectroscopically confirmed hyperluminous (>10^{13}L_0), high-redshift dusty quasars to 38. There is no evidence for reddened quasars having significantly different H$\alpha$ equivalent widths relative to unobscured quasars. The average black-hole masses (~10^9-10^10 M_0) and bolometric luminosities (~10^{47} erg/s) are comparable to the most luminous unobscured quasars at the same redshift, but with a tail extending to very high luminosities of ~10^{48} erg/s. Sixty-six per cent of the reddened quasars are detected at $>3\sigma$ at 22um by WISE. The average 6um rest-frame luminosity is log10(L6um/erg/s)=47.1+/-0.4, making the objects among the mid-infrared brightest AGN currently known. The extinction-corrected space-density estimate now extends over three magnitudes (-30 < M_i < -27) and demonstrates that the reddened quasar luminosity function is significantly flatter than that of the unobscured quasar population at z=2-3. At the brightest magnitudes, M_i < -29, the space density of our dust-reddened population exceeds that of unobscured quasars. A model where the probability that a quasar becomes dust-reddened increases at high luminosity is consistent with the observations and such a dependence could be explained by an increase in luminosity and extinction during AGN-fuelling phases. The properties of our obscured Type 1 quasars are distinct from the heavily obscured, Compton-thick AGN that have been identified at much fainter luminosities and we conclude that they likely correspond to a brief evolutionary phase in massive galaxy formation.Comment: 16 pages, 9 figures (+ 2 appendices), Accepted for publication in MNRA

Entanglement by linear SU(2) transformations: generation and evolution of quantum vortex states

We consider the evolution of a two-mode system of bosons under the action of a Hamiltonian that generates linear SU(2) transformations. The Hamiltonian is generic in that it represents a host of entanglement mechanisms, which can thus be treated in a unified way. We start by solving the quantum dynamics analytically when the system is initially in a Fock state. We show how the two modes get entangled by evolution to produce a coherent superposition of vortex states in general, and a single vortex state under certain conditions. The degree of entanglement between the modes is measured by finding the explicit analytical dependence of the Von Neumann entropy on the system parameters. The reduced state of each mode is analyzed by means of its correlation function and spatial coherence function. Remarkably, our analysis is shown to be equally as valid for a variety of initial states that can be prepared from a two-mode Fock state via a unitary transformation and for which the results can be obtained by mere inspection of the corresponding results for an initial Fock state. As an example, we consider a quantum vortex as the initial state and also find conditions for its revival and charge conjugation. While studying the evolution of the initial vortex state, we have encountered and explained an interesting situation in which the entropy of the system does not evolve whereas its wave function does. Although the modal concept has been used throughout the paper, it is important to note that the theory is equally applicable for a two-particle system in which each particle is represented by its bosonic creation and annihilation operators.Comment: 6 figure

Surface casing estimator site, 2018-2019

The Surface Casing Estimator Site (SCES), hosted at the Bureau of Economic Geology (Bureau), is an interactive website that provides depth and elevation estimates for select subsurface water-quality zones chosen by Groundwater Advisory Unit staff at the Railroad Commission of Texas (RRC). These depths enable users to estimate surface casing needs for possible future drilling activity prior to obtaining a surface casing determination from the RRC. Work during fiscal year 2019 (September 2018 to August 2019) for the SCES involved: 1. Scanning geophysical logs from the Q-log library for 12 counties. 2. Constructing digital datasets composed of geologic information related to estimating surface casing requirements and groundwater depths for 5 counties in the Texas Panhandle and 3 counties on the Texas Gulf Coastal Plain. 3. Adding the newly interpreted counties to existing SCES data. 4. Adding selected geophysical logs to the SCES. 5. Updating and revising the SCES as requested. For the Panhandle counties, the SCES provides elevation and depth estimates for the base of usable-quality water (BUQW) and the base of underground sources of drinking water (USDW). For the coastal counties, the SCES provides depth and elevation estimates for the base of fresh water, the BUQW, and the base of USDW. Critical water-bearing stratigraphic units, aquifer names, geophysical logs, and well locations are also displayed. All depths and elevations are estimated based on horizon picks provided by the RRC and on select supplemental geophysical well-log determinations. Approximately 280 geophysical logs across 8 Texas counties were added to the SCES web portal during the FY2019 project year.Bureau of Economic Geolog

Off Resonant Pumping for Transition from Continuous to Discrete Spectrum and Quantum Revivals in Systems in Coherent States

We show that in parametrically driven systems and, more generally, in systems in coherent states, off-resonant pumping can cause a transition from a continuum energy spectrum of the system to a discrete one, and result in quantum revivals of the initial state. The mechanism responsible for quantum revivals in the present case is different from that in the non-linear wavepacket dynamics of systems such as Rydberg atoms. We interpret the reported phenomena as an optical analog of Bloch oscillations realized in Fock space and propose a feasible scheme for inducing Bloch oscillations in trapped ions.Comment: 5 pages, 4 figures, submitted to Jnl. of Optics

Superrevivals in the quantum dynamics of a particle confined in a finite square well potential

We examine the revival features in wave packet dynamics of a particle confined in a finite square well potential. The possibility of tunneling modifies the revival pattern as compared to an infinite square well potential. We study the dependence of the revival times on the depth of the square well and predict the existence of superrevivals. The nature of these superrevivals is compared with similar features seen in the dynamics of wavepackets in an anharmonic oscillator potential.Comment: 8 pages in Latex two-column format with 5 figures (eps). To appear in Physical Review