Long distance coupling of a quantum mechanical oscillator to the internal states of an atomic ensemble

We propose and investigate a hybrid optomechanical system consisting of a micro-mechanical oscillator coupled to the internal states of a distant ensemble of atoms. The interaction between the systems is mediated by a light field which allows the coupling of the two systems in a modular way over long distances. Coupling to internal degrees of freedom of atoms opens up the possibility to employ high-frequency mechanical resonators in the MHz to GHz regime, such as optomechanical crystal structures, and to benefit from the rich toolbox of quantum control over internal atomic states. Previous schemes involving atomic motional states are rather limited in both of these aspects. We derive a full quantum model for the effective coupling including the main sources of decoherence. As an application we show that sympathetic ground-state cooling and strong coupling between the two systems is possible.

Asymptotic scattering and duality in the one-dimensional three-state quantum Potts model on a lattice

We determine numerically the single-particle and the two-particle spectrum of the three-state quantum Potts model on a lattice by using the density matrix renormalization group method, and extract information on the asymptotic (small momentum) S-matrix of the quasiparticles. The low energy part of the finite size spectrum can be understood in terms of a simple effective model introduced in a previous work, and is consistent with an asymptotic S-matrix of an exchange form below a momentum scale p*. This scale appears to vanish faster than the Compton scale, mc, as one approaches the critical point, suggesting that a dangerously irrelevant operator may be responsible for the behaviour observed on the lattice.

Strong quantum memory at resonant Fermi edges revealed by shot noise

Studies of non-equilibrium current fluctuations enable assessing correlations involved in quantum transport through nanoscale conductors. They provide additional information to the mean current on charge statistics and the presence of coherence, dissipation, disorder, or entanglement. Shot noise, being a temporal integral of the current autocorrelation function, reveals dynamical information. In particular, it detects presence of non-Markovian dynamics, i.e., memory, within open systems, which has been subject of many current theoretical studies. We report on low-temperature shot noise measurements of electronic transport through InAs quantum dots in the Fermi-edge singularity regime and show that it exhibits strong memory effects caused by quantum correlations between the dot and fermionic reservoirs. Our work, apart from addressing noise in archetypical strongly correlated system of prime interest, discloses generic quantum dynamical mechanism occurring at interacting resonant Fermi edges.

Carbon losses in terrestrial hydrological pathways in sugarcane cropping systems of Australia

Climate change and carbon (C) sequestration are a major focus of research in the twenty-first century. Globally, soils store about 300 times the amount of C that is released per annum through the burning of fossil fuels (Schulze and Freibauer 2005). Land clearing and introduction of agricultural systems have led to rapid declines in soil C reserves. The recent introduction of conservation agricultural practices has not led to a reversing of the decline in soil C content, although it has minimized the rate of decline (Baker et al. 2007; Hulugalle and Scott 2008). Lal (2003) estimated the quantum of C pools in the atmosphere, terrestrial ecosystems, and oceans and reported a “missing C” component in the world C budget. Though not proven yet, this could be linked to C losses through runoff and soil erosion (Lal 2005) and a lack of C accounting in inland water bodies (Cole et al. 2007). Land management practices to minimize the microbial respiration and soil organic C (SOC) decline such as minimum tillage or no tillage were extensively studied in the past, and the soil erosion and runoff studies monitoring those management systems focused on other nutrients such as nitrogen (N) and phosphorus (P).

Equilibration of quantum gases

Finding equilibration times is a major unsolved problem in physics with few analytical results. Here we look at equilibration times for quantum gases of bosons and fermions in the regime of negligibly weak interactions, a setting which not only includes paradigmatic systems such as gases confined to boxes, but also Luttinger liquids and the free superfluid Hubbard model. To do this, we focus on two classes of measurements: (i) coarse-grained observables, such as the number of particles in a region of space, and (ii) few-mode measurements, such as phase correlators.Weshow that, in this setting, equilibration occurs quite generally despite the fact that the particles are not interacting. Furthermore, for coarse-grained measurements the timescale is generally at most polynomial in the number of particles N, which is much faster than previous general upper bounds, which were exponential in N. For local measurements on lattice systems, the timescale is typically linear in the number of lattice sites. In fact, for one-dimensional lattices, the scaling is generally linear in the length of the lattice, which is optimal. Additionally, we look at a few specific examples, one of which consists ofNfermions initially confined on one side of a partition in a box. The partition is removed and the fermions equilibrate extremely quickly in time O(1 N).

Simulation tools for the analysis of single electronic systems

Developments in theory and experiment have raised the prospect of an electronic technology based on the discrete nature of electron tunnelling through a potential barrier. This thesis deals with novel design and analysis tools developed to study such systems. Possible devices include those constructed from ultrasmall normal tunnelling junctions. These exhibit charging effects including the Coulomb blockade and correlated electron tunnelling. They allow transistor-like control of the transfer of single carriers, and present the prospect of digital systems operating at the information theoretic limit. As such, they are often referred to as single electronic devices. Single electronic devices exhibit self quantising logic and good structural tolerance. Their speed, immunity to thermal noise, and operating voltage all scale beneficially with junction capacitance. For ultrasmall junctions the possibility of room temperature operation at sub picosecond timescales seems feasible. However, they are sensitive to external charge; whether from trapping-detrapping events, externally gated potentials, or system cross-talk. Quantum effects such as charge macroscopic quantum tunnelling may degrade performance. Finally, any practical system will be complex and spatially extended (amplifying the above problems), and prone to fabrication imperfection. This summarises why new design and analysis tools are required. Simulation tools are developed, concentrating on the basic building blocks of single electronic systems; the tunnelling junction array and gated turnstile device. Three main points are considered: the best method of estimating capacitance values from physical system geometry; the mathematical model which should represent electron tunnelling based on this data; application of this model to the investigation of single electronic systems. (DXN004909)

Degenerate Gases of Strontium for Studies of Quantum Magnetism

We describe the construction and characterization of a new apparatus that can produce degenerate quantum gases of strontium. The realization of degenerate gases is an important first step toward future studies of quantum magnetism. Three of the four stable isotopes of strontium have been cooled into the degenerate regime. The experiment can make nearly pure Bose-Einstein condensates containing approximately 1x10^4 atoms, for strontium-86, and approximately 4x10^5 atoms, for strontium-84. We have also created degenerate Fermi gases of strontium-87 with a reduced temperature, T/T_F of approximately 0.2. The apparatus will be able to produce Bose-Einstein condensates of strontium-88 with straightforward modifications. We also report the first experimental and theoretical results from the strontium project. We have developed a technique to accelerate the continuous loading of strontium atoms into a magnetic trap. By applying a laser addressing the 3P1 to 3S1 transition in our magneto-optical trap, the rate at which atoms populate the magnetically-trapped 3P2 state can be increased by up to 65%. Quantum degenerate gases of atoms in the metastable 3P0 and 3P2 states are a promising platform for quantum simulation of systems with long-range interactions. We have performed an initial numerical study of a method to transfer the ground state degenerate gases that we can currently produce into one of the metastable states via a three-photon transition. Numerical simulations of the Optical Bloch equations governing the three-photon transition indicate that >90% of a ground state degenerate gas can be transferred into a metastable state.

Probing the interactions between ionic liquids and water: experimental and quantum chemical approach

For an adequate choice or design of ionic liquids, the knowledge of their interaction with other solutes and solvents is an essential feature for predicting the reactivity and selectivity of systems involving these compounds. In this work, the activity coefficient of water in several imidazolium-based ionic liquids with the common cation 1-butyl-3-methylimidazolium was measured at 298.2 K. To contribute to a deeper insight into the interaction between ionic liquids and water, COSMO-RS was used to predict the activity coefficient of water in the studied ionic liquids along with the excess enthalpies. The results showed good agreement between experimental and predicted activity coefficient of water in ionic liquids and that the interaction of water and ionic liquids was strongly influenced by the hydrogen bonding of the anion with water. Accordingly, the intensity of interaction of the anions with water can be ranked as the following: [CF3SO3](-) < [SCN](-) < [TFA](-) < Br(-) < [TOS](-) < Cl(-) < [CH3SO3](-) [DMP](-) < [Ac](-). In addition, fluorination and aromatization of anions are shown to reduce their interaction with water. The effect of temperature on the activity coefficient of water at infinite dilution was measured by inverse gas chromatography and predicted by COSMO-RS. Further analysis based on COSMO-RS provided information on the nature of hydrogen bonding between water and anion as well as the possibility of anion-water complex formation.

Multiple sulfur isotope fractionations in inorganic aqueous systems

New constraints on isotope fractionation factors in inorganic aqueous sulfur systems based on theoretical and experimental techniques relevant to studies of the sulfur cycle in modern environments and the geologic rock record are presented in this dissertation. These include theoretical estimations of equilibrium isotope fractionation factors utilizing quantum mechanical software and a water cluster model approach for aqueous sulfur compounds that span the entire range of oxidation state for sulfur. These theoretical calculations generally reproduce the available experimental determinations from the literature and provide new constraints where no others are available. These theoretical calculations illustrate in detail the relationship between sulfur bonding environment and the mass dependence associated with equilibrium isotope exchange reactions involving all four isotopes of sulfur. I additionally highlight the effect of isomers of protonated compounds (compounds with the same chemical formula but different structure, where protons are bound to either sulfur or oxygen atoms) on isotope partitioning in the sulfite (S4+) and sulfoxylate (S2+) systems, both of which are key intermediates in oxidation-reduction processes in the sulfur cycle. I demonstrate that isomers containing the highest degree of coordination around sulfur (where protonation occurs on the sulfur atom) have a strong influence on isotopic fractionation factors, and argue that isomerization phenomenon should be considered in models of the sulfur cycle. Additionally, experimental results of the reaction rates and isotope fractionations associated with the chemical oxidation of aqueous sulfide are presented. Sulfide oxidation is a major process in the global sulfur cycle due largely to the sulfide-producing activity of anaerobic microorganisms in organic-rich marine sediments. These experiments reveal relationships between isotope fractionations and reaction rate as a function of both temperature and trace metal (ferrous iron) catalysis that I interpret in the context of the complex mechanism of sulfide oxidation. I also demonstrate that sulfide oxidation is a process associated with a mass dependence that can be described as not conforming to the mass dependence typically associated with equilibrium isotope exchange. This observation has implications for the inclusion of oxidative processes in environmental- and global-scale models of the sulfur cycle based on the mass balance of all four isotopes of sulfur. The contents of this dissertation provide key reference information on isotopic fractionation factors in aqueous sulfur systems that will have far-reaching applicability to studies of the sulfur cycle in a wide variety of natural settings.

Why can't I measure the external quantum efficiency of the Ge subcell of my multijunction solar cell?

The measurement of the external quantum efficiency (EQE) of low bandgap subcells in a multijunction solar cell can be sometimes problematic. In particular, this paper describes a set of cases where the EQE of a Ge subcell in a conventional GaInP/GaInAs/Ge triple-junction solar cell cannot be fully measured. We describe the way to identify each case by tracing the I-V curve under the same light-bias conditions applied for the EQE measurement, together with the strategies that could be implemented to attain the best possible measurement of the EQE of the Ge subcell.

Quantum of Vision

Visual inputs to artificial and biological visual systems are often quantized: cameras accumulate photons from the visual world, and the brain receives action potentials from visual sensory neurons. Collecting more information quanta leads to a longer acquisition time and better performance. In many visual tasks, collecting a small number of quanta is sufficient to solve the task well. The ability to determine the right number of quanta is pivotal in situations where visual information is costly to obtain, such as photon-starved or time-critical environments. In these situations, conventional vision systems that always collect a fixed and large amount of information are infeasible. I develop a framework that judiciously determines the number of information quanta to observe based on the cost of observation and the requirement for accuracy. The framework implements the optimal speed versus accuracy tradeoff when two assumptions are met, namely that the task is fully specified probabilistically and constant over time. I also extend the framework to address scenarios that violate the assumptions. I deploy the framework to three recognition tasks: visual search (where both assumptions are satisfied), scotopic visual recognition (where the model is not specified), and visual discrimination with unknown stimulus onset (where the model is dynamic over time). Scotopic classification experiments suggest that the framework leads to dramatic improvement in photon-efficiency compared to conventional computer vision algorithms. Human psychophysics experiments confirmed that the framework provides a parsimonious and versatile explanation for human behavior under time pressure in both static and dynamic environments.

A pointwise constrained version of the Liapunov convexity theorem for vectorial linear first-order control systems

We generalize the Liapunov convexity theorem's version for vectorial control systems driven by linear ODEs of first-order p = 1 , in any dimension d ∈ N , by including a pointwise state-constraint. More precisely, given a x ‾ ( ⋅ ) ∈ W p , 1 ( [ a , b ] , R d ) solving the convexified p-th order differential inclusion L p x ‾ ( t ) ∈ co { u 0 ( t ) , u 1 ( t ) , … , u m ( t ) } a.e., consider the general problem consisting in finding bang-bang solutions (i.e. L p x ˆ ( t ) ∈ { u 0 ( t ) , u 1 ( t ) , … , u m ( t ) } a.e.) under the same boundary-data, x ˆ ( k ) ( a ) = x ‾ ( k ) ( a ) & x ˆ ( k ) ( b ) = x ‾ ( k ) ( b ) ( k = 0 , 1 , … , p − 1 ); but restricted, moreover, by a pointwise state constraint of the type 〈 x ˆ ( t ) , ω 〉 ≤ 〈 x ‾ ( t ) , ω 〉 ∀ t ∈ [ a , b ] (e.g. ω = ( 1 , 0 , … , 0 ) yielding x ˆ 1 ( t ) ≤ x ‾ 1 ( t ) ). Previous results in the scalar d = 1 case were the pioneering Amar & Cellina paper (dealing with L p x ( ⋅ ) = x ′ ( ⋅ ) ), followed by Cerf & Mariconda results, who solved the general case of linear differential operators L p of order p ≥ 2 with C 0 ( [ a , b ] ) -coefficients. This paper is dedicated to: focus on the missing case p = 1 , i.e. using L p x ( ⋅ ) = x ′ ( ⋅ ) + A ( ⋅ ) x ( ⋅ ) ; generalize the dimension of x ( ⋅ ) , from the scalar case d = 1 to the vectorial d ∈ N case; weaken the coefficients, from continuous to integrable, so that A ( ⋅ ) now becomes a d × d -integrable matrix; and allow the directional vector ω to become a moving AC function ω ( ⋅ ) . Previous vectorial results had constant ω, no matrix (i.e. A ( ⋅ ) ≡ 0 ) and considered: constant control-vertices (Amar & Mariconda) and, more recently, integrable control-vertices (ourselves).

Semiclassical analysis of systems of Schrödinger equations

The scalar Schrödinger equation models the probability density distribution for a particle to be found in a point x given a certain potential V(x) forming a well with respect to a fixed energy level E_0. Formally two real inversion points a,b exist such that V(a)=V(b)=E_0, V(x)<0 in (a,b) and V(x)>0 for xb. Following the work made by D.Yafaev and performing a WKB approximation we obtain solutions defined on specific intervals. The aim of the first part of the thesis is to find a condition on E, which belongs to a neighbourhood of E_0, such that it is an eigenvalue of the Schrödinger operator, obtaining in this way global and linear dependent solutions in L2. In quantum mechanics this condition is known as Bohr-Sommerfeld quantization. In the second part we define a Schrödinger operator referred to two potential wells and we study the quantization conditions on E in order to have a global solution in L2xL2 with respect to the mutual position of the potentials. In particular their wells can be disjoint,can have an intersection, can be included one into the other and can have a single point intersection. For these cases we refer to the works of A.Martinez, S. Fujiié, T. Watanabe, S. Ashida.