Optical Signatures of Non-Markovian Behaviour in Open Quantum Systems

We derive an extension to the quantum regression theorem which facilitates the calculation of two-time correlation functions and emission spectra for systems undergoing non-Markovian evolution. The derivation exploits projection operator techniques, with which we obtain explicit equations of motion for the correlation functions, making only a second order expansion in the system--environment coupling strength, and invoking the Born approximation at a fixed initial time. The results are used to investigate a driven semiconductor quantum dot coupled to an acoustic phonon bath, where we find the non-Markovian nature of the dynamics has observable signatures in the form of phonon sidebands in the resonance fluorescence emission spectrum. Furthermore, we use recently developed non-Markovianity measures to demonstrate an associated flow of information from the phonon bath back into the quantum dot exciton system.Comment: Comments welcom

Does Abnormal Sleep Impair Memory Consolidation in Schizophrenia?

Although disturbed sleep is a prominent feature of schizophrenia, its relation to the pathophysiology, signs, and symptoms of schizophrenia remains poorly understood. Sleep disturbances are well known to impair cognition in healthy individuals. Yet, in spite of its ubiquity in schizophrenia, abnormal sleep has generally been overlooked as a potential contributor to cognitive deficits. Amelioration of cognitive deficits is a current priority of the schizophrenia research community, but most efforts to define, characterize, and quantify cognitive deficits focus on cross-sectional measures. While this approach provides a valid snapshot of function, there is now overwhelming evidence that critical aspects of learning and memory consolidation happen offline, both over time and with sleep. Initial memory encoding is followed by a prolonged period of consolidation, integration, and reorganization, that continues over days or even years. Much of this evolution of memories is mediated by sleep. This article briefly reviews (i) what is known about abnormal sleep in schizophrenia, (ii) sleep-dependent memory consolidation in healthy individuals, (iii) recent findings of impaired sleep-dependent memory consolidation in schizophrenia, and (iv) implications of impaired sleep-dependent memory consolidation in schizophrenia. This literature suggests that abnormal sleep in schizophrenia disrupts attention and impairs sleep-dependent memory consolidation and task automation. We conclude that these sleep-dependent impairments may contribute substantially to generalized cognitive deficits in schizophrenia. Understanding this contribution may open new avenues to ameliorating cognitive dysfunction and thereby improve outcome in schizophrenia

Modelling exciton-phonon interactions in optically driven quantum dots

We provide a self-contained review of master equation approaches to modelling phonon effects in optically driven self-assembled quantum dots. Coupling of the (quasi) two-level excitonic system to phonons leads to dissipation and dephasing, the rates of which depend on the excitation conditions, intrinsic properties of the QD sample, and its temperature. We describe several techniques, which include weak-coupling master equations that are perturbative in the exciton-phonon coupling, as well as those based on the polaron transformation that can remain valid for strong phonon interactions. We additionally consider the role of phonons in altering the optical emission characteristics of quantum dot devices, outlining how we must modify standard quantum optics treatments to account for the presence of the solid-state environment.Comment: Invited Topical Review, 26 pages, 7 figures. V2 - close to published version, 28 pages, 9 figures. Minor changes to text, added a few new references and two new figure

The implementation and validation of improved landsurface hydrology in an atmospheric general circulation model

Landsurface hydrological parameterizations are implemented in the NASA Goddard Institute for Space Studies (GISS) General Circulation Model (GCM). These parameterizations are: (1) runoff and evapotranspiration functions that include the effects of subgrid scale spatial variability and use physically based equations of hydrologic flux at the soil surface, and (2) a realistic soil moisture diffusion scheme for the movement of water in the soil column. A one dimensional climate model with a complete hydrologic cycle is used to screen the basic sensitivities of the hydrological parameterizations before implementation into the full three dimensional GCM. Results of the final simulation with the GISS GCM and the new landsurface hydrology indicate that the runoff rate, especially in the tropics is significantly improved. As a result, the remaining components of the heat and moisture balance show comparable improvements when compared to observations. The validation of model results is carried from the large global (ocean and landsurface) scale, to the zonal, continental, and finally the finer river basin scales

Atmospheric water vapor transport: Estimation of continental precipitation recycling and parameterization of a simple climate model

The advective transport of atmospheric water vapor and its role in global hydrology and the water balance of continental regions are discussed and explored. The data set consists of ten years of global wind and humidity observations interpolated onto a regular grid by objective analysis. Atmospheric water vapor fluxes across the boundaries of selected continental regions are displayed graphically. The water vapor flux data are used to investigate the sources of continental precipitation. The total amount of water that precipitates on large continental regions is supplied by two mechanisms: (1) advection from surrounding areas external to the region; and (2) evaporation and transpiration from the land surface recycling of precipitation over the continental area. The degree to which regional precipitation is supplied by recycled moisture is a potentially significant climate feedback mechanism and land surface-atmosphere interaction, which may contribute to the persistence and intensification of droughts. A simplified model of the atmospheric moisture over continents and simultaneous estimates of regional precipitation are employed to estimate, for several large continental regions, the fraction of precipitation that is locally derived. In a separate, but related, study estimates of ocean to land water vapor transport are used to parameterize an existing simple climate model, containing both land and ocean surfaces, that is intended to mimic the dynamics of continental climates

The Dynamics of the Forest Graph Operator

In 1966, Cummins introduced the "tree graph": the tree graph $\mathbf{T}(G)$ of a graph $G$ (possibly infinite) has all its spanning trees as vertices, and distinct such trees correspond to adjacent vertices if they differ in just one edge, i.e., two spanning trees $T_1$ and $T_2$ are adjacent if $T_2 = T_1 -e +f$ for some edges $e\in T_1$ and $f\notin T_1$. The tree graph of a connected graph need not be connected. To obviate this difficulty we define the "forest graph": let $G$ be a labeled graph of order $\alpha$, finite or infinite, and let $\mathfrak{N}(G)$ be the set of all labeled maximal forests of $G$. The forest graph of $G$, denoted by $\mathbf{F}(G)$, is the graph with vertex set $\mathfrak{N}(G)$ in which two maximal forests $F_1$, $F_2$ of $G$ form an edge if and only if they differ exactly by one edge, i.e., $F_2 = F_1 -e +f$ for some edges $e\in F_1$ and $f\notin F_1$. Using the theory of cardinal numbers, Zorn's lemma, transfinite induction, the axiom of choice and the well-ordering principle, we determine the $\mathbf{F}$-convergence, $\mathbf{F}$-divergence, $\mathbf{F}$-depth and $\mathbf{F}$-stability of any graph $G$. In particular it is shown that a graph $G$ (finite or infinite) is $\mathbf{F}$-convergent if and only if $G$ has at most one cycle of length 3. The $\mathbf{F}$-stable graphs are precisely $K_3$ and $K_1$. The $\mathbf{F}$-depth of any graph $G$ different from $K_3$ and $K_1$ is finite. We also determine various parameters of $\mathbf{F}(G)$ for an infinite graph $G$, including the number, order, size, and degree of its components.Comment: 13 p

Strong non-linearity-induced correlations for counter-propagating photons scattering on a two-level emitter

We analytically treat the scattering of two counter-propagating photons on a two-level emitter embedded in an optical waveguide. We find that the non-linearity of the emitter can give rise to significant pulse-dependent directional correlations in the scattered photonic state, which could be quantified via a reduction in coincident clicks in a Hong-Ou-Mandel measurement setup, analogous to a linear beam splitter. Changes to the spectra and phase of the scattered photons, however, would lead to reduced interference with other photons when implemented in a larger optical circuit. We introduce suitable fidelity measures which account for these changes, and find that high values can still be achieved even when accounting for all properties of the scattered photonic state.Comment: 10 pages, 7 figure

Mycorrhizae in Sagebrush-Steppe Community Restoration: Mycorrhizal Dependency of Invasive and Native Grasses With Intraspecific and Interspecific Competition

Mycorrhizae have been used in restoration for decades. However, studies assessing the use of mycorrhizae in Bromus tectorum-invaded areas of the Great Basin are limited. Two greenhouse pot experiments were conducted to assess the role of mycorrhizae in sagebrush restoration. The first objective (Chapter 2) was to determine the response of Pseudoroegneria spicatum, Elymus elymoides, and B. tectorum to mycorrhizal symbiosis by altering phosphorus, density, species, presence of mycorrhizae and water levels in a 5 factor design. To assess the mycorrhizal response, a variety of morphological and physiological traits were measured, such as tissue P concentration, specific root length, specific leaf area, carbon isotope discrimination, etc. The effects of the different treatment combinations were analyzed using ANOVA. The second objective (Chapter 3) was to determine the role of different inocula in competition between the three grasses. Species, density, and inoculum type were altered in a 3 factor design. Inoculum was cultured on Allium plants. The effect of locally cultured inoculum on the species was compared to the effect of commercial inoculum. The response of each species to mycorrhizae with different species compositions and densities was assessed. Morphological measurements were used to determine each species response to the different factor combinations. The effects of the different treatment combinations were analyzed using ANOVA. This research provides land managers with information regarding the efficacy of using local versus commercial inocula and whether they should use mycorrhizae in restoring their systems

Error distributions on large entangled states with non-Markovian dynamics

We investigate the distribution of errors on a computationally useful entangled state generated via the repeated emission from an emitter undergoing strongly non-Markovian evolution. For emitter-environment coupling of pure-dephasing form, we show that the probability that a particular patten of errors occurs has a bound of Markovian form, and thus accuracy threshold theorems based on Markovian models should be just as effective. This is the case, for example, for a charged quantum dot emitter in a moderate to strong magnetic field. Beyond the pure-dephasing assumption, though complicated error structures can arise, they can still be qualitatively bounded by a Markovian error model.Comment: Close to published versio

Model of the optical emission of a driven semiconductor quantum dot: phonon-enhanced coherent scattering and off-resonant sideband narrowing

We study the crucial role played by the solid-state environment in determining the photon emission characteristics of a driven quantum dot. For resonant driving, we predict a phonon-enhancement of the coherently emitted radiation field with increasing driving strength, in stark contrast to the conventional expectation of a rapidly decreasing fraction of coherent emission with stronger driving. This surprising behaviour results from thermalisation of the dot with respect to the phonon bath, and leads to a nonstandard regime of resonance fluorescence in which significant coherent scattering and the Mollow triplet coexist. Off-resonance, we show that despite the phonon influence, narrowing of dot spectral sideband widths can occur in certain regimes, consistent with an experimental trend.Comment: Published version. 5 pages, 2 figures, plus 4 page supplement. Title changed, figure 1 revised, various edits and additions to the tex