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In this thesis we theoretically investigate effects of the interaction between electron spins and nuclear spins in different nanoscopic devices, quantum dots and spin valves. A quantum dot is a tiny potential well in which one can trap single electrons. One of the proposed applications of the quantum dot is to use the spin of the trapped electrons as qubits, the computational units in a quantum computer. The main obstacle for this application is the fact that the electron spin in the dot is coupled via the hyperfine interaction to roughly one million randomly fluctuating nuclear spins (those in the host material of the quantum dot). These fluctuations manifest themselves as a small but unpredictable magnetic field, causing the spin state of the electron to be not stable enough to be useful for quantum computation. The hyperfine interaction however works both ways: Several recent experiments have showed clear evidence that the nuclear spins, in turn, are also affected by the electron spin. So, it might be possible to suppress the fluctuations of the nuclear field by a clever manipulation of the electron spin in the dot. If so, this would bring the realization of the quantum dot spin qubit one big step closer. In this thesis we investigate the coupled electron-nuclear spin dynamics in several realistic experimental situations. We consider both single and double quantum dots, and concentrate on the combination of electronic transport (current) and electron spin resonance (a magnetic microwave field). We find that in these situations the fluctuations of the nuclear field indeed can be strongly suppressed, and we support this with experimental results. Further, we investigate the effect of strong spin-orbit coupling on the transport properties of a double quantum dot, and we also consider hyperfine effects in a metallic spin valve.

The goal of this thesis is to investigate theoretically the generation and behaviour of multipartite entanglement for solid-state nanosystems, in particular electron spin quantum bits (so-called 'qubits') in quantum dots. A quantum dot is a tiny potential well where a single electron can be trapped. A quantum bit can be implemented in this system by applying a magnetic field, and thereby lifting the degeneracy of the spin states of the electron. These spins can then be used as single qubits, and engineering many of these quantum dots next to each other gives as a register of qubits. In this scheme, the so-called Loss-DiVincenzo quantum computer, the single spins can be rotated e.g. by applying a time dependent magnetic field, and two spins can interact through controlling the potential barrier between them. A qubit cannot only be in a superposition of the two computational states 0 and 1 at the same time, but an even stranger characteristic arises for multiple qubits: this phenomenon is called entanglement and refers to a strong correlation between two or more qubits, which can not be achieved within the framework of classical physics, and exponentially enlarges the possible states for a N-qubit system as compared to a classical N-bit system. In this thesis we devise algorithms how to generate multipartite entangled states in electron spin qubits in quantum dots. We compare which classes of entangled states can be generated efficiently in this system. Once the states are created, they decay due to a process called decoherence. We compare how entangled states can be generated and detected in a realistic experiment, and which classes of states are the most suitable. Furthermore, we compare which classes conserve the entanglement, and quantify the robustness of various classes of entangled states. In the last chapter, we devise a scheme of how to execute a simple quantum algorithm, the Deutsch-Jozsa algorithm, in a system containing another type of solid-state qubit, the so-called flux qubit.

Competing populations in shared spaces with nonrenewable resources do not necessarily wage a battle for dominance at the cost of extinction of the less-fit strain if there are fitness advantages to the presence of the other strain. We report on the use of nanofabricated habitat landscapes to study the population dynamics of competing wild type and a growth advantage in stationary phase (GASP) mutant strains of Escherichia coli in a sealed and heterogeneous nutrient environment. Although GASP mutants are competitors with wild-type bacteria, we find that the 2 strains cooperate to maximize fitness (long-term total productivity) via spatial segregation: despite their very close genomic kinship, wild-type populations associate with wild-type populations and GASP populations with GASP populations. Thus, wild-type and GASP strains avoid each other locally, yet fitness is enhanced for both strains globally. This computation of fitness enhancement emerges from the local interaction among cells but maximizes global densities. At present we do not understand how fluctuations in both spatial and temporal dimensions lead to the emergent computation and how multilevel aggregates produce this collective adaptation.

We use fluorescence microscopy to measure the orientation and shape of microtubules—which serve as a model system for semiflexible rods—that are electrophoretically driven. Surprisingly, a bimodal orientation distribution is observed, with microtubules in either parallel or perpendicular orientations to the electric field. The occupancy of these states varies nonmonotonically with the microtubule length L and the electric field E. We also observe a surprising bending deformation of microtubules. Interestingly, all data collapse onto a universal scaling curve when the average alignment is plotted as a function of B - EL3, which reflects the ratio between the driving force and a restoring elastic force. Our results have important implications for the interpretation of electrical birefringence experiments and, more generally, for a better understanding of the electrokinetics of rods.

This thesis is a step towards development of quantitative parallel beam electron nano-diffraction (PBED). It is focused on the superstructure determination of zig-zag and zig-zig NaxCoO2 and analysis of charge distribution in the two polymorphs Nb12O29 using PBED. It has been shown that quantitative electron nano-diffraction (parallel beam) has the potential of solving superstructures as well as charge distribution by taking the dynamicity of the data to its advantage. The information contained in the electron diffraction data has never been doubted but the dynamicity of the data (arising from multiple scattering) makes the interpretation very complex. First of all the superstructure information, which is difficult to be seen in X-ray or neutron diffraction data specially when they occur in the nanometer regime, can be resolved by electron diffraction. This has been illustrated with chapters 2 and 3. Further, the charge information contained in the electron diffraction is much more than X-ray diffraction due to the fact that X-rays are scattered by electron cloud only while electron scattering is a result electrostatic potential of the system. Hence electron diffraction can be used as a tool to study precisely the charge distribution or charge ordering which by other means is not possible. Though there are many skeptics to this argument, this thesis through chapters 4 and 5, is an attempt to prove that the future lies in the electron diffraction to study the type of systems described in here.

We show that an insulated electrostatic gate can be used to strongly suppress ubiquitous background charge noise in Schottky-gated GaAs=AlGaAs devices. Via a 2D self-consistent simulation of the conduction band profile we show that this observation can be explained by reduced leakage of electrons from the Schottky gates into the semiconductor through the Schottky barrier, consistent with the effect of ‘‘bias cooling.’’ Upon noise reduction, the noise power spectrum generally changes from Lorentzian to 1/f type. By comparing wafers with different Al content, we exclude that DX centers play a dominant role in the charge noise.

Using laser fluorescence microscopy, we study the shape and dynamics of individual DNA molecules in slitlike nanochannels confined to a fraction of their bulk radius of gyration. With a confinement size spanning 2 orders of magnitude, we observe a transition from the de Gennes regime to the Odijk regime in the scaling of both the radius of gyration and the relaxation time. The radius of gyration and the relaxation time follow the predicted scaling in the de Gennes regime, while, unexpectedly, the relaxation time shows a sharp decrease in the Odijk regime. The radius of gyration remains constant in the Odijk regime. Additionally, we report the first measurements of the effect of confinement on the shape anisotropy.

The human DNA repair protein RAD51 is the crucial component of helical nucleoprotein filaments that drive homologous recombination. The molecular mechanistic details of how this structure facilitates the requisite DNA strand rearrangements are not known but must involve dynamic interactions between RAD51 and DNA. Here, we report the real-time kinetics of human RAD51 filament assembly and disassembly on individual molecules of both single- and double-stranded DNA, as measured using magnetic tweezers. The relative rates of nucleation and filament extension are such that the observed filament formation consists of multiple nucleation events that are in competition with each other. For varying concentration of RAD51, a Hill coefficient of 4.3±0.5 is obtained for both nucleation and filament extension, indicating binding to dsDNA with a binding unit consisting of multiple (≥4) RAD51 monomers. We report Monte Carlo simulations that fit the (dis)assembly data very well. The results show that, surprisingly, human RAD51 does not form long continuous filaments on DNA. Instead each nucleoprotein filament consists of a string of many small filament patches that are only a few tens of monomers long. The high flexibility and dynamic nature of this arrangement is likely to facilitate strand exchange.

Precise, controllable single-molecule force spectroscopy studies of RNA and RNA-dependent processes have recently shed new light on the dynamics and pathways of RNA folding and RNAenzyme interactions. A crucial component of this research is the design and assembly of an appropriate RNA construct. Such a construct is typically subject to several criteria. First, single-molecule force spectroscopy techniques often require an RNA construct that is longer than the RNA molecules used for bulk biochemical studies. Next, the incorporation of modified nucleotides into the RNA construct is required for its surface immobilization. In addition, RNA constructs for singlemolecule studies are commonly assembled from different single-stranded RNA molecules, demanding good control of hybridization or ligation. Finally, precautions to prevent RNase- and divalent cationdependent RNA digestion must be taken. The rather limited selection of molecular biology tools adapted to the manipulation of RNA molecules, as well as the sensitivity of RNA to degradation, make RNA construct preparation a challenging task. We briefly illustrate the types of single-molecule force spectroscopy experiments that can be performed on RNA, and then present an overview of the toolkit of molecular biology techniques at one’s disposal for the assembly of such RNA constructs. Within this context, we evaluate the molecular biology protocols in terms of their effectiveness in producing long and stable RNA constructs.

Recombinase proteins assembled into helical filaments on DNA are believed to be the catalytic core of homologous recombination. The assembly, disassembly and dynamic rearrangements of this structure must drive the DNA strand exchange reactions of homologous recombination. The sensitivity of eukaryotic recombinase activity to reaction conditions in vitro suggests that the status of bound nucleotide cofactors is important for function and possibly for filament structure. We analyzed nucleoprotein filaments formed by the human recombinase Rad51 in a variety of conditions on double-stranded and singlestrandedDNAby scanningforce microscopy. Regular filaments with extended double-stranded DNA correlated with active in vitro recombination, possibly due to stabilizing the DNA products of these assays. Though filaments formed readily on single-stranded DNA, they were very rarely regular structures. The irregular structure of filaments on single-stranded DNA suggests that Rad51 monomers are dynamic in filaments and that regular filaments are transient. Indeed, single molecule force spectroscopy of Rad51 filament assembly and disassembly in magnetic tweezers revealed protein association and disassociation from many points along the DNA, with kinetics different from those of RecA. The dynamic rearrangements of proteins and DNA within Rad51 nucleoprotein filaments could be key events driving strand exchange in homologous recombination.

This thesis presents results of theoretical and experimental work on superconducting persistent-current flux quantum bits. These qubits are promising candidates for the implementation of scalable quantum information processing. This work focuses on the study of one dimensional chains of inductively coupled flux qubits and on qubits with a tunable energy gap. Chains of flux qubits can be used as models of quantum spin chains, one of the most basic systems in many-body physics that has been extensively studied theoretically. The ability to design and tune the qubit and coupling parameters enables exploration of different phase regimes during measurements, in parameter regimes that are not accessible with magnetic materials. The study of the dynamics of quantum waves in an artificial spin chain can also be used to explore novel quantum phenomena with possible applications in quantum computing. Tunability of the minimal energy splitting (the gap) enables one to rapidly bring the flux qubit in and out of resonance with other quantum systems, including a harmonic oscillator. With tunable qubits it also becomes possible to create inter-qubit couplings of different vector nature, using magnetic fluxes. This permits the design of various interaction Hamiltonians for multiple qubit systems. These operations can be performed at the degeneracy point of the qubit, where coherence properties are optimal. Therefore the tunable flux qubit provides an attractive component for the implementation of scalable quantum computation.

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After the experimental discovery of graphene -a single atomic layer of graphite- a scientific rush started to explore graphene’s electronic behaviour. Graphene is a fascinating two-dimensional electronic system, because its electrons behave as relativistic particles. Moreover, it is a promising material for future high-speed nano-electronic applications. In this thesis, several experiments are described to reveal graphene’s electronic transport properties. We have shown that we can control the bandstructure of bilayer and trilayer graphene. Simply by applying a perpendicular electric field in a graphene device, we could tune the bandgap in the bilayer and the bandoverlap in the trilayer. Furthermore, we have described transport measurements on graphene devices (length = 0.1-1 micrometer) showing that electronic transport in graphene is phase coherent at cryogenic temperatures (4 K or less). We have observed weak localization, bipolar supercurrents and the Aharonov-Bohm effect. We have also shown that in narrow graphene nanoribbons (width less than 100 nm) a transport gap appears, which can be well explained by strong localization of electronic states. Our experimental results provide a better understanding of electronic transport in graphene, and are also a first step towards the realization of graphene nano-electronic devices.

We experimentally investigate Quantum Dots, formed in Carbon Nanotubes. The first part of this thesis deals with charge sensing on such quantum dots. The charge sensor is a metallic Single-electron-transistor, sensitive to the charge of a single electron on the quantum dot. We use this technique for real-time charge readout and precise tuning of the tunnel barriers of the quantum dot. The second part of this thesis describes the realization of exceptionally clean Carbon Nanotube quantum dots. We create few-electon single, double and triple quantum dots. In a few electron double quantum dot, we observe an effect which is analogous to Klein tunneling in relativistic quantum mechanics.

For small magnetic memories, the ultimate limit is a single magnetic particle, a single electron spin. A lot of research is put in developing devices that can utilize such a single spin memory. At the same time, there is also interest from a more fundamental point of view: on these small scales, Quantum Mechanics starts to play a role. Devices of this size have unique possibilities that have no parallel in the classical world around us. In this work we study a single electron spin that is captured in a small box, a quantum dot. This is all made inside a semiconducting nanowire. By measuring the current we can determine how the spin orients in a magnetic field. We can also see interactions of the spin with its environment. We study how the semiconductor crystal influences the spin, via spin-orbit interaction and via its nuclei. We also determine how this affects the interaction between two such spins.

Graphene is an exceptionally thin semiconductor that consists of only one atomic layer of carbon atoms. The electrons in graphene live in a strictly two-dimensional (2D) world. In addition to this remarkable 2Dness, it is also peculiar that the behavior of the electrons in graphene is governed by the Dirac equation rather than the well known Schrödinger’s equation, leading to the discovery of several new physics phenomena. Such unusual properties of graphene have stirred up great excitements since it was first isolated in the lab about five years ago. In this thesis, we investigate the low temperature transport properties of the electrons and holes in several graphene based nano-devices. Overall, two topics are explored in this thesis. First we engineer an energy gap in graphene, which is naturally a zero-gap semiconductor, and further form quantum dot devices on the gapped graphene. The low temperature electronic transport properties of the confined electrons are then studied experimentally in such graphene dots. In a second project,we fabricated Josephson junction devices on graphene using a high critical field superconductor as leads. Here the goal is to research on the interactions between the electrons from graphene and the Cooper pairs from the superconductor in the quantum Hall regime.

This thesis is concerned with two distinct fundamental research questions that are both investigated using the E. coli lac system. In the first chapters we investigate what the shape of biological fitness landscapes look like. Chapter 2 reviews recent progress in measurement of empirical fitness landscapes, and introduces the open questions in evolution that they may answer, such as why particular evolutionary paths are taken. In this chapter, we also introduce the concept of epistasis as a useful description of the local shape of fitness landscapes. In chapter 3 we describe existing in vivo measurements on lac repressor and operator mutants and show how these can be used to construct a fitness landscape of lac regulation. Using computer simulations we simulate mutational pathways and reveal that new regulatory interactions can easily evolve. Chapter 4 deals with the local structure of the lac landscape. We determine that the landscape is multi-peaked and, consistent with earlier predictions, show the presence of reciprocal sign epistasis. We conclude our analysis of the lac landscape in chapter 5 with a more global analysis of its structure, focusing on which landscape features are important for evolution. This study reveals that the essential features of the lac landscape can be sufficiently captured by modeling the presence or absence of additivity between functional residues. In chapter 6 we turn to another fundamental research question: how do random molecular fluctuations in the number proteins in a single cell propagate to its growth? Again, we use the E. coli lac system to investigate this question. But whereas the first part of this thesis consists of theoretical simulations of lac regulation, here we perform laboratory experiments on E. coli cells that require use of their lac enzymes for growth. By means of automated and highly sensitive fluorescence microscopy, we measure both fluctuations in lac level and in growth rate in individual growing cells. These experiments show that fluctuations in the growth rate of single cells can be linked to protein fluctuations, but also reveal a intricate dynamic interdependency between these two properties.