Numerical Q parameter estimates for scalar and vector models in optical communication system simulations

The Q parameter scales differently with the noise power for the signal-noise and the noise-noise beating terms in scalar and vector models. Some procedures for including noise in the scalar model largely under-estimate the Q parameter. We propose a simple method for including noise within a scalar model which will allow both the noise-noise dominated limit and the signal-noise dominated limit to be treated consistently. © 2005 Elsevier B.V. All rights reserved.

THz emission from quantum dot-based THz antennas pumped by a tunable quantum-dot laser diode

The THz optoelectronics field is now maturing and semiconductor-based THz antenna devices are becoming more widely implemented as analytical tools in spectroscopy and imaging. Photoconductive (PC) THz switches/antennas are driven optically typically using either an ultrashort-pulse laser or an optical signal composed of two simultaneous longitudinal wavelengths which are beat together in the PC material at a THz difference frequency. This allows the generation of (photo)carrier pairs which are then captured over ultrashort timescales usually by defects and trapping sites throughout the active material lattice. Defect-implanted PC materials with relatively high bandgap energy are typically used and many parameters such as carrier mobility and PC gain are greatly compromised. This paper demonstrates the implementation of low bandgap energy InAs quantum dots (QDs) embedded in standard crystalline GaAs as both the PC medium and the ultrafast capture mechanism in a PC THz antenna. This semiconductor structure is grown using standard MBE methods and allows the device to be optically driven efficiently at wavelengths up to ~1.3 µm, in this case by a single tunable dual-mode QD diode laser.

Significant quantum effects in hydrogen activation

Dissociation of molecular hydrogen is an important step in a wide variety of chemical, biological, and physical processes. Due to the light mass of hydrogen, it is recognized that quantum effects are often important to its reactivity. However, understanding how quantum effects impact the reactivity of hydrogen is still in its infancy. Here, we examine this issue using a well-defined Pd/Cu(111) alloy that allows the activation of hydrogen and deuterium molecules to be examined at individual Pd atom surface sites over a wide range of temperatures. Experiments comparing the uptake of hydrogen and deuterium as a function of temperature reveal completely different behavior of the two species. The rate of hydrogen activation increases at lower sample temperature, whereas deuterium activation slows as the temperature is lowered. Density functional theory simulations in which quantum nuclear effects are accounted for reveal that tunneling through the dissociation barrier is prevalent for H2 up to ∼190 K and for D2 up to ∼140 K. Kinetic Monte Carlo simulations indicate that the effective barrier to H2 dissociation is so low that hydrogen uptake on the surface is limited merely by thermodynamics, whereas the D2 dissociation process is controlled by kinetics. These data illustrate the complexity and inherent quantum nature of this ubiquitous and seemingly simple chemical process. Examining these effects in other systems with a similar range of approaches may uncover temperature regimes where quantum effects can be harnessed, yielding greater control of bond-breaking processes at surfaces and uncovering useful chemistries such as selective bond activation or isotope separation.

Chlorine contribution to quantitative structure and activity relationship models of disinfection by -products' quantum chemical descriptors and toxicities

Quantitative Structure-Activity Relationship (QSAR) has been applied extensively in predicting toxicity of Disinfection By-Products (DBPs) in drinking water. Among many toxicological properties, acute and chronic toxicities of DBPs have been widely used in health risk assessment of DBPs. These toxicities are correlated with molecular properties, which are usually correlated with molecular descriptors. The primary goals of this thesis are: (1) to investigate the effects of molecular descriptors (e.g., chlorine number) on molecular properties such as energy of the lowest unoccupied molecular orbital (E LUMO) via QSAR modelling and analysis; (2) to validate the models by using internal and external cross-validation techniques; (3) to quantify the model uncertainties through Taylor and Monte Carlo Simulation. One of the very important ways to predict molecular properties such as ELUMO is using QSAR analysis. In this study, number of chlorine (NCl ) and number of carbon (NC) as well as energy of the highest occupied molecular orbital (EHOMO) are used as molecular descriptors. There are typically three approaches used in QSAR model development: (1) Linear or Multi-linear Regression (MLR); (2) Partial Least Squares (PLS); and (3) Principle Component Regression (PCR). In QSAR analysis, a very critical step is model validation after QSAR models are established and before applying them to toxicity prediction. The DBPs to be studied include five chemical classes: chlorinated alkanes, alkenes, and aromatics. In addition, validated QSARs are developed to describe the toxicity of selected groups (i.e., chloro-alkane and aromatic compounds with a nitro- or cyano group) of DBP chemicals to three types of organisms (e.g., Fish, T. pyriformis, and P.pyosphoreum) based on experimental toxicity data from the literature. The results show that: (1) QSAR models to predict molecular property built by MLR, PLS or PCR can be used either to select valid data points or to eliminate outliers; (2) The Leave-One-Out Cross-Validation procedure by itself is not enough to give a reliable representation of the predictive ability of the QSAR models, however, Leave-Many-Out/K-fold cross-validation and external validation can be applied together to achieve more reliable results; (3) E LUMO are shown to correlate highly with the NCl for several classes of DBPs; and (4) According to uncertainty analysis using Taylor method, the uncertainty of QSAR models is contributed mostly from NCl for all DBP classes.

Chlorine Contribution to Quantitative Structure and Activity Relationship Models of Disinfection By-Products' Quantum Chemical Descriptors and Toxicities

Quantitative Structure-Activity Relationship (QSAR) has been applied extensively in predicting toxicity of Disinfection By-Products (DBPs) in drinking water. Among many toxicological properties, acute and chronic toxicities of DBPs have been widely used in health risk assessment of DBPs. These toxicities are correlated with molecular properties, which are usually correlated with molecular descriptors. The primary goals of this thesis are: 1) to investigate the effects of molecular descriptors (e.g., chlorine number) on molecular properties such as energy of the lowest unoccupied molecular orbital (ELUMO) via QSAR modelling and analysis; 2) to validate the models by using internal and external cross-validation techniques; 3) to quantify the model uncertainties through Taylor and Monte Carlo Simulation. One of the very important ways to predict molecular properties such as ELUMO is using QSAR analysis. In this study, number of chlorine (NCl) and number of carbon (NC) as well as energy of the highest occupied molecular orbital (EHOMO) are used as molecular descriptors. There are typically three approaches used in QSAR model development: 1) Linear or Multi-linear Regression (MLR); 2) Partial Least Squares (PLS); and 3) Principle Component Regression (PCR). In QSAR analysis, a very critical step is model validation after QSAR models are established and before applying them to toxicity prediction. The DBPs to be studied include five chemical classes: chlorinated alkanes, alkenes, and aromatics. In addition, validated QSARs are developed to describe the toxicity of selected groups (i.e., chloro-alkane and aromatic compounds with a nitro- or cyano group) of DBP chemicals to three types of organisms (e.g., Fish, T. pyriformis, and P.pyosphoreum) based on experimental toxicity data from the literature. The results show that: 1) QSAR models to predict molecular property built by MLR, PLS or PCR can be used either to select valid data points or to eliminate outliers; 2) The Leave-One-Out Cross-Validation procedure by itself is not enough to give a reliable representation of the predictive ability of the QSAR models, however, Leave-Many-Out/K-fold cross-validation and external validation can be applied together to achieve more reliable results; 3) ELUMO are shown to correlate highly with the NCl for several classes of DBPs; and 4) According to uncertainty analysis using Taylor method, the uncertainty of QSAR models is contributed mostly from NCl for all DBP classes.

State sum models for quantum gravity

This paper reviews the construction of quantum field theory on a 4-dimensional spacetime by combinatorial methods, and discusses the recent developments in the direction of a combinatorial construction of quantum gravity.

Decoherence models for discrete-time quantum walks and their application to neutral atom experiments

We discuss decoherence in discrete-time quantum walks in terms of a phenomenological model that distinguishes spin and spatial decoherence. We identify the dominating mechanisms that affect quantum-walk experiments realized with neutral atoms walking in an optical lattice. From the measured spatial distributions, we determine with good precision the amount of decoherence per step, which provides a quantitative indication of the quality of our quantum walks. In particular, we find that spin decoherence is the main mechanism responsible for the loss of coherence in our experiment. We also find that the sole observation of ballistic-instead of diffusive-expansion in position space is not a good indicator of the range of coherent delocalization. We provide further physical insight by distinguishing the effects of short- and long-time spin dephasing mechanisms. We introduce the concept of coherence length in the discrete-time quantum walk, which quantifies the range of spatial coherences. Unexpectedly, we find that quasi-stationary dephasing does not modify the local properties of the quantum walk, but instead affects spatial coherences. For a visual representation of decoherence phenomena in phase space, we have developed a formalism based on a discrete analogue of the Wigner function. We show that the effects of spin and spatial decoherence differ dramatically in momentum space.

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.

MULTI-BAND BOSE HUBBARD MODELS AND EFFECTIVE THREE-BODY INTERACTIONS

Experiments with ultracold atoms in optical lattice have become a versatile testing ground to study diverse quantum many-body Hamiltonians. A single-band Bose-Hubbard (BH) Hamiltonian was first proposed to describe these systems in 1998 and its associated quantum phase-transition was subsequently observed in 2002. Over the years, there has been a rapid progress in experimental realizations of more complex lattice geometries, leading to more exotic BH Hamiltonians with contributions from excited bands, and modified tunneling and interaction energies. There has also been interesting theoretical insights and experimental studies on “un- conventional” Bose-Einstein condensates in optical lattices and predictions of rich orbital physics in higher bands. In this thesis, I present our results on several multi- band BH models and emergent quantum phenomena. In particular, I study optical lattices with two local minima per unit cell and show that the low energy states of a multi-band BH Hamiltonian with only pairwise interactions is equivalent to an effec- tive single-band Hamiltonian with strong three-body interactions. I also propose a second method to create three-body interactions in ultracold gases of bosonic atoms in a optical lattice. In this case, this is achieved by a careful cancellation of two contributions in the pair-wise interaction between the atoms, one proportional to the zero-energy scattering length and a second proportional to the effective range. I subsequently study the physics of Bose-Einstein condensation in the second band of a double-well 2D lattice and show that the collision aided decay rate of the con- densate to the ground band is smaller than the tunneling rate between neighboring unit cells. Finally, I propose a numerical method using the discrete variable repre- sentation for constructing real-valued Wannier functions localized in a unit cell for optical lattices. The developed numerical method is general and can be applied to a wide array of optical lattice geometries in one, two or three dimensions.

Engineering a Quantum Many-body Hamiltonian with Trapped Ions

While fault-tolerant quantum computation might still be years away, analog quantum simulators offer a way to leverage current quantum technologies to study classically intractable quantum systems. Cutting edge quantum simulators such as those utilizing ultracold atoms are beginning to study physics which surpass what is classically tractable. As the system sizes of these quantum simulators increase, there are also concurrent gains in the complexity and types of Hamiltonians which can be simulated. In this work, I describe advances toward the realization of an adaptable, tunable quantum simulator capable of surpassing classical computation. We simulate long-ranged Ising and XY spin models which can have global arbitrary transverse and longitudinal fields in addition to individual transverse fields using a linear chain of up to 24 Yb+ 171 ions confined in a linear rf Paul trap. Each qubit is encoded in the ground state hyperfine levels of an ion. Spin-spin interactions are engineered by the application of spin-dependent forces from laser fields, coupling spin to motion. Each spin can be read independently using state-dependent fluorescence. The results here add yet more tools to an ever growing quantum simulation toolbox. One of many challenges has been the coherent manipulation of individual qubits. By using a surprisingly large fourth-order Stark shifts in a clock-state qubit, we demonstrate an ability to individually manipulate spins and apply independent Hamiltonian terms, greatly increasing the range of quantum simulations which can be implemented. As quantum systems grow beyond the capability of classical numerics, a constant question is how to verify a quantum simulation. Here, I present measurements which may provide useful metrics for large system sizes and demonstrate them in a system of up to 24 ions during a classically intractable simulation. The observed values are consistent with extremely large entangled states, as much as ~95% of the system entangled. Finally, we use many of these techniques in order to generate a spin Hamiltonian which fails to thermalize during experimental time scales due to a meta-stable state which is often called prethermal. The observed prethermal state is a new form of prethermalization which arises due to long-range interactions and open boundary conditions, even in the thermodynamic limit. This prethermalization is observed in a system of up to 22 spins. We expect that system sizes can be extended up to 30 spins with only minor upgrades to the current apparatus. These results emphasize that as the technology improves, the techniques and tools developed here can potentially be used to perform simulations which will surpass the capability of even the most sophisticated classical techniques, enabling the study of a whole new regime of quantum many-body physics.

Smallest disentangling state spaces for general entangled bipartite quantum states

Entangled quantum states can be given a separable decomposition if we relax the restriction that the local operators be quantum states. Motivated by the construction of classical simulations and local hidden variable models, we construct `smallest' local sets of operators that achieve this. In other words, given an arbitrary bipartite quantum state we construct convex sets of local operators that allow for a separable decomposition, but that cannot be made smaller while continuing to do so. We then consider two further variants of the problem where the local state spaces are required to contain the local quantum states, and obtain solutions for a variety of cases including a region of pure states around the maximally entangled state. The methods involve calculating certain forms of cross norm. Two of the variants of the problem have a strong relationship to theorems on ensemble decompositions of positive operators, and our results thereby give those theorems an added interpretation. The results generalise those obtained in our previous work on this topic [New J. Phys. 17, 093047 (2015)].

Understanding Co-translational Protein Targeting and Lithium Dendrite Formation through Free Energy Simulations and Coarse-Grained Models

We describe the application of alchemical free energy methods and coarse-grained models to study two key problems: (i) co-translational protein targeting and insertion to direct membrane proteins to the endoplasmic reticulum for proper localization and folding, (ii) lithium dendrite formation during recharging of lithium metal batteries. We show that conformational changes in the signal recognition particle, a central component of the protein targeting machinery, confer additional specificity during the the recognition of signal sequences. We then develop a three-dimensional coarse-grained model to study the long-timescale dynamics of membrane protein integration at the translocon and a framework for the calculation of binding free energies between the ribosome and translocon. Finally, we develop a coarse-grained model to capture the dynamics of lithium deposition and dissolution at the electrode interface with time-dependent voltages to show that pulse plating and reverse pulse plating methods can mitigate dendrite growth.

Disorder driven transitions in non-equilibrium quantum systems

This thesis presents studies of the role of disorder in non-equilibrium quantum systems. The quantum states relevant to dynamics in these systems are very different from the ground state of the Hamiltonian. Two distinct systems are studied, (i) periodically driven Hamiltonians in two dimensions, and (ii) electrons in a one-dimensional lattice with power-law decaying hopping amplitudes. In the first system, the novel phases that are induced from the interplay of periodic driving, topology and disorder are studied. In the second system, the Anderson transition in all the eigenstates of the Hamiltonian are studied, as a function of the power-law exponent of the hopping amplitude.

In periodically driven systems the study focuses on the effect of disorder in the nature of the topology of the steady states. First, we investigate the robustness to disorder of Floquet topological insulators (FTIs) occurring in semiconductor quantum wells. Such FTIs are generated by resonantly driving a transition between the valence and conduction band. We show that when disorder is added, the topological nature of such FTIs persists as long as there is a gap at the resonant quasienergy. For strong enough disorder, this gap closes and all the states become localized as the system undergoes a transition to a trivial insulator.

Interestingly, the effects of disorder are not necessarily adverse, disorder can also induce a transition from a trivial to a topological system, thereby establishing a Floquet Topological Anderson Insulator (FTAI). Such a state would be a dynamical realization of the topological Anderson insulator. We identify the conditions on the driving field necessary for observing such a transition. We realize such a disorder induced topological Floquet spectrum in the driven honeycomb lattice and quantum well models.

Finally, we show that two-dimensional periodically driven quantum systems with spatial disorder admit a unique topological phase, which we call the anomalous Floquet-Anderson insulator (AFAI). The AFAI is characterized by a quasienergy spectrum featuring chiral edge modes coexisting with a fully localized bulk. Such a spectrum is impossible for a time-independent, local Hamiltonian. These unique characteristics of the AFAI give rise to a new topologically protected nonequilibrium transport phenomenon: quantized, yet nonadiabatic, charge pumping. We identify the topological invariants that distinguish the AFAI from a trivial, fully localized phase, and show that the two phases are separated by a phase transition.

The thesis also present the study of disordered systems using Wegner's Flow equations. The Flow Equation Method was proposed as a technique for studying excited states in an interacting system in one dimension. We apply this method to a one-dimensional tight binding problem with power-law decaying hoppings. This model presents a transition as a function of the exponent of the decay. It is shown that the the entire phase diagram, i.e. the delocalized, critical and localized phases in these systems can be studied using this technique. Based on this technique, we develop a strong-bond renormalization group that procedure where we solve the Flow Equations iteratively. This renormalization group approach provides a new framework to study the transition in this system.