Fully quantum mechanical dynamic analysis of single-photon transport in a single-mode waveguide coupled to a traveling-wave resonator

We analyze the dynamics of single photon transport in a single-mode waveguide coupled to a micro-optical resonator using a fully quantum mechanical model. We examine the propagation of a single-photon Gaussian packet through the system under various coupling conditions. We review the theory of single photon transport phenomena as applied to the system and we develop a discussion on the numerical technique we used to solve for dynamical behavior of the quantized field. To demonstrate our method and to establish robust single photon results, we study the process of adiabatically lowering or raising the energy of a single photon trapped in an optical resonator under active tuning of the resonator. We show that our fully quantum mechanical approach reproduces the semi-classical result in the appropriate limit and that the adiabatic invariant has the same form in each case. Finally, we explore the trapping of a single photon in a system of dynamically tuned, coupled optical cavities.Comment: 24 pages, 10 figure

Generalized Stacking Fault Energy Surfaces and Dislocation Properties of Silicon: A First-Principles Theoretical Study

The generalized stacking fault (GSF) energy surfaces have received considerable attention due to their close relation to the mechanical properties of solids. We present a detailed study of the GSF energy surfaces of silicon within the framework of density functional theory. We have calculated the GSF energy surfaces for the shuffle and glide set of the (111) plane, and that of the (100) plane of silicon, paying particular attention to the effects of the relaxation of atomic coordinates. Based on the calculated GSF energy surfaces and the Peierls-Nabarro model, we obtain estimates for the dislocation profiles, core energies, Peierls energies, and the corresponding stresses for various planar dislocations of silicon.Comment: 9 figures (not included; send requests to [email protected]

Rapid state purification protocols for a Cooper pair box

We propose techniques for implementing two different rapid state purification schemes, within the constraints present in a superconducting charge qubit system. Both schemes use a continuous measurement of charge (z) measurements, and seek to minimize the time required to purify the conditional state. Our methods are designed to make the purification process relatively insensitive to rotations about the x-axis, due to the Josephson tunnelling Hamiltonian. The first proposed method, based on the scheme of Jacobs [Phys. Rev. A 67, 030301(R) (2003)] uses the measurement results to control bias (z) pulses so as to rotate the Bloch vector onto the x-axis of the Bloch sphere. The second proposed method, based on the scheme of Wiseman and Ralph [New J. Phys. 8, 90 (2006)] uses a simple feedback protocol which tightly rotates the Bloch vector about an axis almost parallel with the measurement axis. We compare the performance of these and other techniques by a number of different measures.Comment: 14 pages, 14 figures. v2: Revised version after referee comments. Accepted for publication by Physical Review

Spectroscopy of a Cooper-Pair box in the Autler-Townes configuration

A theoretical spectroscopic analysis of a microwave driven superconducting charge qubit (Cooper-pair box coupled) to an RLC oscillator model is performed. By treating the oscillator as a probe through the backreaction effect of the qubit on the oscillator circuit, we extract frequency splitting features analogous to the Autler-Townes effect from quantum optics, thereby extending the analogies between superconducting and quantum optical phenomenology. These features are found in a frequency band that avoids the need for high frequency measurement systems and therefore may be of use in qubit characterization and coupling schemes. In addition we find this frequency band can be adjusted to suit an experimental frequency regime by changing the oscillator frequency.Comment: 13 pages, 7 figures. v2: Revised version after referee comments. Accepted for publication by Physical Review

Interacting damage models mapped onto Ising and percolation models

We introduce a class of damage models on regular lattices with isotropic interactions, as e.g. quasistatic fiber bundles. The system starts intact with a surface-energy threshold required to break any cell sampled from an uncorrelated quenched-disorder distribution. The evolution of this heterogeneous system is ruled by Griffith's principle which states that a cell breaks when the release in elastic energy in the system exceeds the surface-energy barrier necessary to break the cell. By direct integration over all possible realizations of the quenched disorder, we obtain the probability distribution of each damage configuration at any level of the imposed external deformation. We demonstrate an isomorphism between the distributions so obtained and standard generalized Ising models, in which the coupling constants and effective temperature in the Ising model are functions of the nature of the quenched-disorder distribution and the extent of accumulated damage. In particular, we show that damage models with global load sharing are isomorphic to standard percolation theory, that damage models with local load sharing rule are isomorphic to the standard Ising model, and draw consequences thereof for the universality class and behavior of the autocorrelation length of the breakdown transitions corresponding to these models. We also treat damage models having more general power-law interactions, and classify the breakdown process as a function of the power-law interaction exponent. Last, we also show that the probability distribution over configurations is a maximum of Shannon's entropy under some specific constraints related to the energetic balance of the fracture process, which firmly relates this type of quenched-disorder based damage model to standard statistical mechanics.Comment: 16 pages, 3 figure

Scattering in an environment

The cross section of elastic electron-proton scattering taking place in an electron gas is calculated within the Closed Time Path method. It is found to be the sum of two terms, one being the expression in the vacuum except that it involves dressing due to the electron gas. The other term is due to the scattering particles-electron gas entanglement. This term dominates the usual one when the exchange energy is in the vicinity of the Fermi energy. Furthermore it makes the trajectories of the colliding particles more consistent and the collision more irreversible, rendering the scattering more classical in this regime.Comment: final version to appear in Phys. Rev.

Experimental Evidence for Different Strain Regimes of Crack Populations in a Clay Model

We report results from clay extension experiments used as a model for the evolution of fault populations due to stress interactions. At yielding cracks begin to appear and the brittle strain due to them quickly reaches a rate matching the applied stretching rate. The crack density (number of cracks per unit area) initially increases apace, then reaches a maximum at a critical strain, decreasing thereafter. At low strains, where the crack population is dilute, a power law length distribution is observed, which at high strain, gradually transitions to an exponential. This agrees with fault populations data observed in low and high strain settings. These results indicate that fault populations ranging from power law to exponential size-frequency distributions reflect the population evolution with increased strain

The effects of entry on incumbent innovation and productivity

How does firm entry affect innovation incentives in incumbent firms? Microdata suggest that there is heterogeneity across industries. Specifically, incumbent productivity growth and patenting is positively correlated with lagged greenfield foreign firm entry in technologically advanced industries, but not in laggard industries. In this paper we provide evidence that these correlations arise from a causal effect predicted by Schumpeterian growth theory—the threat of technologically advanced entry spurs innovation incentives in sectors close to the technology frontier, where successful innovation allows incumbents to survive the threat, but discourages innovation in laggard sectors, where the threat reduces incumbents' expected rents from innovating. We find that the empirical patterns hold using rich micro panel data for the United Kingdom. We control for the endogeneity of entry by exploiting major European and U.K. policy reforms, and allow for endogeneity of additional factors. We complement the analysis for foreign entry with evidence for domestic entry and entry through imports

Microscopic origin of diagonal stripe phases in doped nickelates

We investigate the electron density distribution and the stability of stripe phases in the realistic two-band model with hopping elements between e_g orbitals at Ni sites on the square lattice, and compare these results with those obtained for the doubly degenerate Hubbard model with two equivalent orbitals and diagonal hopping. For both models we determine the stability regions of filled and half-filled stripe phases for increasing hole doping x=2-n in the range of x<0.4, using Hartree-Fock approximation for large clusters. In the parameter range relevant to the nickelates, we obtain the most stable diagonal stripe structures with filling of nearly one hole per atom, as observed experimentally. In contrast, for the doubly degenerate Hubbard model the most stable stripes are somewhat reminiscent of the cuprates, with half-filled atoms at the domain wall sites. This difference elucidates the crucial role of the off-diagonal e_g hopping terms for the stripe formation in La_2-xSr_xNiO_4. The influence of crystal field is discussed as well.Comment: 15 pages, 12 figure