From Cavity Electromechanics to Cavity Optomechanics

We present an overview of experimental work to embed high-Q mesoscopic mechanical oscillators in microwave and optical cavities. Based upon recent progress, the prospect for a broad field of "cavity quantum mechanics" is very real. These systems introduce mesoscopic mechanical oscillators as a new quantum resource and also inherently couple their motion to photons throughout the electromagnetic spectrum.Comment: 8 pages, 6 figures, ICAP proceedings submissio

State Transfer Between a Mechanical Oscillator and Microwave Fields in the Quantum Regime

Recently, macroscopic mechanical oscillators have been coaxed into a regime of quantum behavior, by direct refrigeration [1] or a combination of refrigeration and laser-like cooling [2, 3]. This exciting result has encouraged notions that mechanical oscillators may perform useful functions in the processing of quantum information with superconducting circuits [1, 4-7], either by serving as a quantum memory for the ephemeral state of a microwave field or by providing a quantum interface between otherwise incompatible systems [8, 9]. As yet, the transfer of an itinerant state or propagating mode of a microwave field to and from a mechanical oscillator has not been demonstrated owing to the inability to agilely turn on and off the interaction between microwave electricity and mechanical motion. Here we demonstrate that the state of an itinerant microwave field can be coherently transferred into, stored in, and retrieved from a mechanical oscillator with amplitudes at the single quanta level. Crucially, the time to capture and to retrieve the microwave state is shorter than the quantum state lifetime of the mechanical oscillator. In this quantum regime, the mechanical oscillator can both store and transduce quantum information

Hydraulic-fracture propagation in layered rock: experimental studies of fracture containment

Fracture geometry is an important concern in the design of a massive hydraulic fracture treatment for improved natural gas recovery from tight gas sands. Possible prediction of vertical fracture growth and containment in layered rock requires an improved understanding of the parameters which may control fracture growth across layer interfaces. We have conducted laboratory hydraulic fracture experiments and elastic finite element studies which show that at least two distinct geologic conditions may inhibit or contain the vertical growth of hydraulic fractures in layered rock; (1) a weak interfacial shear strength of the layers and (2) a compressional increase in the minimum horizontal stress in the bounding layer. The second condition is more important and more likely to occur at depth. Variations in the horizontal stress can result from differences in elastic properties of individual layers in a layered rock sequence. A compressional increase in the minimum horizontal stress can occur in going from high shear modulus into low shear modulus layers

Scattering into Cones and Flux across Surfaces in Quantum Mechanics: a Pathwise Probabilistic Approach

We show how the scattering-into-cones and flux-across-surfaces theorems in Quantum Mechanics have very intuitive pathwise probabilistic versions based on some results by Carlen about large time behaviour of paths of Nelson diffusions. The quantum mechanical results can be then recovered by taking expectations in our pathwise statements.Comment: To appear in Journal of Mathematical Physic

Parametric coupling between macroscopic quantum resonators

Time-dependent linear coupling between macroscopic quantum resonator modes generates both a parametric amplification also known as a {}"squeezing operation" and a beam splitter operation, analogous to quantum optical systems. These operations, when applied properly, can robustly generate entanglement and squeezing for the quantum resonator modes. Here, we present such coupling schemes between a nanomechanical resonator and a superconducting electrical resonator using applied microwave voltages as well as between two superconducting lumped-element electrical resonators using a r.f. SQUID-mediated tunable coupler. By calculating the logarithmic negativity of the partially transposed density matrix, we quantitatively study the entanglement generated at finite temperatures. We also show that characterization of the nanomechanical resonator state after the quantum operations can be achieved by detecting the electrical resonator only. Thus, one of the electrical resonator modes can act as a probe to measure the entanglement of the coupled systems and the degree of squeezing for the other resonator mode.Comment: 15 pages, 4 figures, submitte

Characterization and fluid flow simulation of naturally fractured Frontier sandstone, Green River Basin, Wyoming

Significant gas reserves are present in low-permeability sandstones of the Frontier Formation in the greater Green River Basin, Wyoming. Successful exploitation of these reservoirs requires an understanding of the characteristics and fluid-flow response of the regional natural fracture system that controls reservoir productivity. Fracture characteristics were obtained from outcrop studies of Frontier sandstones at locations in the basin. The fracture data were combined with matrix permeability data to compute an anisotropic horizontal permeability tensor (magnitude and direction) corresponding to an equivalent reservoir system in the subsurface using a computational model developed by Oda (1985). This analysis shows that the maximum and minimum horizontal permeability and flow capacity are controlled by fracture intensity and decrease with increasing bed thickness. However, storage capacity is controlled by matrix porosity and increases linearly with increasing bed thickness. The relationship between bed thickness and the calculated fluid-flow properties was used in a reservoir simulation study of vertical, hydraulically-fractured and horizontal wells and horizontal wells of different lengths in analogous naturally fractured gas reservoirs. The simulation results show that flow capacity dominates early time production, while storage capacity dominates pressure support over time for vertical wells. For horizontal wells drilled perpendicular to the maximum permeability direction a high target production rate can be maintained over a longer time and have higher cumulative production than vertical wells. Longer horizontal wells are required for the same cumulative production with decreasing bed thickness

Semi- and Non-relativistic Limit of the Dirac Dynamics with External Fields

We show how to approximate Dirac dynamics for electronic initial states by semi- and non-relativistic dynamics. To leading order, these are generated by the semi- and non-relativistic Pauli hamiltonian where the kinetic energy is related to $\sqrt{m^2 + \xi^2}$ and $\xi^2 / 2m$, respectively. Higher-order corrections can in principle be computed to any order in the small parameter v/c which is the ratio of typical speeds to the speed of light. Our results imply the dynamics for electronic and positronic states decouple to any order in v/c << 1. To decide whether to get semi- or non-relativistic effective dynamics, one needs to choose a scaling for the kinetic momentum operator. Then the effective dynamics are derived using space-adiabatic perturbation theory by Panati et. al with the novel input of a magnetic pseudodifferential calculus adapted to either the semi- or non-relativistic scaling.Comment: 42 page

Single \pi^- production in np collisions for excess energies up to 90 MeV

The quasifree reaction np\to pp\pim was studied in a kinematically complete experiment by bombarding a liquid hydrogen target with a deuteron beam of momentum 1.85 GeV/c and analyzing the data along the lines of the spectator model. In addition to the three charged ejectiles the spectator proton was also detected in the large-acceptance time-of-flight spectrometer COSY-TOF. It was identified by its momentum and flight direction thus yielding access to the Fermi motion of the bound neutron and to the effective neutron 4-momentum vector $\mathbb{P}_n$ which differed from event to event. A range of almost 90 MeV excess energy above threshold was covered. Energy dependent angular distributions, invariant mass spectra as well as fully covered Dalitz plots were deduced. Sizeable $pp$ FSI effects were found as were contributions of $p$ and $d$ partial waves. The behavior of the elementary cross section $\sigma_{01}$ close to threshold is discussed in view of new cross section data. In comparison with existing literature data the results provide a sensitive test of the spectator model.Comment: 21 pages, 9 figures, 4 tables, submitted to EPJ