Academic literature on the topic 'Quantum double model'

We numerically investigate a total transmission probability through QDs embedded in an AB ring. The QDs are formed by delta function-like double potential barriers and a magnetic flux is penetrated in the center of the ring. In particular, we study the coupled double-QDs in series and non-coupled double-QDs in parallel in an AB ring. In each model, we show the total transmission probability as a function of QD size and electron incident energy, and present the transmission amplitude on the complex-energy plane. Of interest is the change and progression of Fano resonances and corresponding zero-pole pairs on the complex-energy plane with magnetic flux in the center of the ring.To accomplish this, we analytically solve the scattering matrix at each junction and the transfer matrix through the arms of the ring using Schrodinger equation for the delta function barriers. Then, the total transmission probability is obtained as a function of electron energy and magnetic flux by cascading these matrices. Finally, the solutions of the analytical equations and the graphical output of the transmission characteristics in the system will be obtained numerically by using Mathematica programs run on desktop computers.<br>Department of Physics and Astronomy

The top quark is the heaviest known elementary particle of the Standard Model. Thanks to its particular properties, it allows to explore unique physics domains, inaccessible otherwise. One of them is the quantum interference between singly (tW) and doubly (t ̄t)resonant top quark production in proton-proton collisions, which can lead to identical WbWb final-states when an additional b-quark is radiated during a singly-resonant production. Studying this process is very important for a better knowledge of the Standard Model, but also to investigate some Beyond the Standard Model processes: for example,the search for top squarks suffers a large background contamination fromt W and t ̄t in the interference region. In this work, the measurement of the particle-level differential cross-section of the WbWb final-state in the eμ dilepton channel is provided, in order to better investigate the interference-sensitive region of these processes. The measurement is performed using the full dataset collected by the ATLAS detector from proton-proton collisions at the LHC during Run-2 at √s= 13 TeV corresponding to an integrated luminosity of 139 fb−1. The differential cross-section has been measured as a function of two interference-sensitive variables, defined as mminimaxbl and ∆R(b1,b2). Besides the single-differential cross-sections as a function of mminimaxbl and ∆R(b1,b2), also the double-differential cross-section as a function of mminimaxbl in bins of ∆R(b1,b2) is measured. The WbWb differential cross-section has been successfully extracted and compared to different schemes: the Diagram Removal and the Diagram Subtraction. This twopredictions model in a different way the quantum interference description.

Pour les etats de vibration tres excites de certaines molecules, l'attribution en termes des nombres quantiques usuels n'est plus valable. Dans cs#2, les modes d'elongation symetrique et de pliage sont fortement couples par une resonance non lineaire de fermi. Au moins a basse energie le mode d'elongation antisymetrique reste faiblement couple par des anharmonicites. La dynamique quantique, classique et semiclassique de ce modele tres important en physique moleculaire est etudie en detail. Il est montre comment les bifurcations successives des orbites periodiques permettent de rendre compte de l'evolution de la dynamique quantique en fonction de l'energie. L'etude du vibrogramme permet egalement d'evaluer la validite du modele de fermi entre 12000 et 19000 cm##1 dans un domaine ou elle n'etait pas connue. Nous avons ensuite effectue des experiences de fluorescence resolue a plus de 19000 cm##1 au-dessus du fondamental afin de pratiquer les statistiques spectrales permettant de caracteriser le chaos quantique. Pres de 400 raies experimentales ont ete obtenues. L'analyse demontre plusieurs points importants. En premier lieu, la transition vers le chaos quantique de la molecule vers 13000 cm##1 est remise en question a cause d'une excitation impure. D'autre part, nous avons montre le role de la resolution sur les statistiques spectrales. Des spectres mal resolus peuvent presenter des correlations qui sont des artefacts. Ceci nous a conduit a remettre en question toutes les preuves experimentales existantes de l'existence de chaos quantique vibrationnel dans les molecules. Afin d'obtenir des spectres vibrationnels purs, nous avons developpe deux nouvelles experiences pour la spectroscopie de cs#2 : la double resonance i-r u-v et un jet supersonique. Si les transferts rotationnels observes en double resonance rendent difficiles l'utilisation de cette technique, le jet supersonique permet d'exciter veritablement une raie unique.

A simplified model of a double quantum dot is presented and analyzed, with applications to spin-qubit quantum computation. The ability to trap single electrons in semiconductor nanostructures has led to the proposal of quantum computers with spin-based qubits coupled by the exchange interaction. Current theory predicts an exchange interaction with a -1 power-law dependence on the detuning ϵ, the energy offset between the two dots. However, experiment has shown a -3/2 power-law dependence on ϵ. Using WKB analysis, this thesis explores one possible source of the modified dependence, namely an ϵ-dependent tunnel coupling between the two wells. WKB quantization is used to find expressions for the tunnel coupling of a one-dimensional double-well, and these results are compared to the exact, numerical solutions, as determined by the finite difference method and the transfer matrix method. Small ϵ-dependent corrections to the tunnel coupling are observed. In typical cases, WKB correctly predicts a constant tunnel coupling at leading-order. WKB also predicts small ϵ-dependent corrections for typical cases and strongly ϵ-dependent tunnel couplings for certain exceptional cases. However, numerical simulations suggest that WKB is not accurate enough to analyze the small corrections, and is not valid in the exceptional cases. Deviations from the conventional form of the low-energy Hamiltonian for a double-well are also observed and discussed.

<p>The results of this thesis concern the real-world realization of quantum computers, specifically how to build their "hard drives" or quantum memories. These are many-body quantum systems, and their building blocks are qubits, the same way bits are the building blocks of classical computers.</p> <p>Quantum memories need to be robust against thermal noise, noise that would otherwise destroy the encoded information, similar to how strong magnetic field corrupts data classically stored in magnetic many-body systems (e.g., in hard drives). In this work I focus on a subset of many-body models, called quantum doubles, which, in addition to storing the information, could be used to perform the steps of the quantum computation, i.e., work as a "quantum processor".</p> <p>In the first part of my thesis, I investigate how long a subset of quantum doubles (qudit surface codes) can retain the quantum information stored in them, referred to as their memory time. I prove an upper bound for this memory time, restricting the maximum possible performance of qudit surface codes.</p> <p>Then, I analyze the structure of quantum doubles, and find two interesting properties. First, that the high-level description of doubles, utilizing only their quasi-particles to describe their states, disregards key components of their microscopic properties. In short, quasi-particles (anyons) of quantum doubles are not in a one-to-one correspondence with the energy eigenstates of their Hamiltonian. Second, by investigating phase transitions of a simple quantum double, D(S₃), I map its phase diagram, and interpret the physical processes the theory undergoes through terms borrowed from the Landau theory of phase transitions.</p>

Two graphene layers placed in close proximity offer a unique system to investigate interacting electron physics as well as to test novel electronic device concepts. In this system, the interlayer spacing can be reduced to value much smaller than that achievable in semiconductor heterostructures, and the zero energy band-gap allows the realization of coupled hole-hole, electron-hole, and electron-electron two-dimensional systems in the same sample. Leveraging the fabrication technique and electron transport study in dual-gated graphene field-effect transistors, we realize independently contacted graphene double layers separated by an ultra-thin dielectric. We probe the resistance and density of each layer, and quantitatively explain their dependence on the backgate and interlayer bias. We experimentally measure the Coulomb drag between the two graphene layers for the first time, by flowing current in one layer and measuring the voltage drop in the opposite layer. The drag resistivity gauges the momentum transfer between the two layers, which, in turn, probes the interlayer electron-electron scattering rate. The temperature dependence of the Coulomb drag above temperatures of 50 K reveals that the ground state in each layer is a Fermi liquid. Below 50 K we observe mesoscopic fluctuations of the drag resistivity, as a result of the interplay between coherent intralayer transport and interlayer interaction. In addition, we develop a technique to directly measure the Fermi energy in an electron system as a function of carrier density using double layer structure. We demonstrate this method in the double layer graphene structure and probe the Fermi energy in graphene both at zero and in high magnetic fields. Last, we realize dual-gated bilayer graphene devices, where we investigate quantum Hall effects at zero energy as a function of transverse electric field and perpendicular magnetic field. Here we observe a development of v = 0 quantum Hall state at large electric fields and in high magnetic fields, which is explained by broken spin and valley spin symmetry in the zero energy Landau levels.<br>text

There is a compelling need to explore different material options as well as device structures to facilitate smooth transistor scaling for higher speed, higher density and lower power. The enormous potential of nanoelectronics, and nanotechnology in general, offers us the possibility of designing devices with added functionality. However, at the same time, the new materials come with their own challenges that need to be overcome. In this work, we have addressed some of these challenges in the context of quasi-2D Silicon, III-V semiconductor and graphene. Bulk Si is the most widely used semiconductor with an indirect bandgap of about 1.1 eV. However, when Si is thinned down to sub-10nm regime, the quasi-2D nature of the system changes the electronic properties of the material significantly due to the strong geometrical confinement. Using a tight-binding study, we show that in addition to the increase in bandgap due to quantization, it is possible to transform the original in direct bandgap to a direct one. The effective masses at different valleys are also shown to vary uniquely in an anisotropic way. This ultra-thin Si, when used as a channel in a double gate MOSFET structure, creates so called “volume in version” which is extensively investigated in this work. It has been found that the both the quantum confinement as well as the gating effect play a significant role in determining the spatial distribution of the charge, which in turn has an important role in the characteristics of transistor. Compound III-V semiconductors, like Inx Ga1-xAs, provide low effective mass and low density of states. This, when coupled with strong confinement in a nanowire channel transistor, leads to the “Ultimate Quantum Capacitance Limit” (UQCL) regime of operation, where only the lowest subband is occupied. In this regime, the channel capacitance is much smaller than the oxide capacitance and hence dominates in the total gate capacitance. It is found that the gate capacitance change qualitatively in the UQCL regime, allowing multi-peak, non-monotonic capacitance-voltage characteristics. It is also shown that in an ideal condition, UQCL provides improved current saturation, on-off ratio and energy-delay product, but a degraded intrinsic gate delay. UQCL shows better immunity towards series resistance effect due to increased channel resistance, but is more prone to interfacial traps. A careful design can provide a better on-off ratio at a given gate delay in UQCL compared to conventional MOSFET scenario. To achieve the full advantages of both FinFET and HEMT in III-V domain, a hybrid structure, called “HFinFET” is proposed which provides excellent on performance like HEMT with good gate control like FinFET. During on state, the carriers in the channel are provided using a delta-doped layer(like HEMT) from the top of a fin-like non-planar channel, and during off state, the gates along the side of the fin(like FinFET) help to pull-off the carriers from the channel. Using an effective mass based coupled Poisson-Schrodinger simulation, the proposed structure is found to outperform the state of the art planar and non-planar MOSFETs. By careful optimization of the gate to source-drain underlap, it is shown that the design window of the device can be increased to meet ITRS projections at similar gate length. In addition, the performance degradation of HFinFET in presence of interface traps has been found to be significantly mitigated by tuning the underlap parameter. Graphene is a popular 2D hexagonal carbon crystal with extraordinary electronic, mechani-cal and chemical properties. However, the zero band gap of grapheme has limited its application in digital electronics. One could create a bandgap in grapheme by making quasi-1D strips, called nanoribbon. However, the bandgap of these nanoribbons depends on the the type of the edge, depending on which, one can obtain either semiconducting or metallic nanoribbon. It has been shown that by the application of an external transverse field along the sides of a nanoribbon, one could not only modulate the magnitude of the bandgap, but also change it from direct to indirect. This could open up interesting possibilities for novel electronic and optoelectronic applications. The asymmetric potential distribution inside the nanoribbon is found to result in such direct to indirect bandgap transition. The corresponding carrier masses are also found to be modulated by the external field, following a transition from a“slow”electron to a“fast” electron and vice-versa. Experimentally, it is difficult to control the bandgap in nanoribbons as precise edge control at nanometer scale is nontrivial. One could also open a bandgap in a bilayer graphene, by the application of vertical electric field, which has raised a lot of interest for digital applications. Using a self-consistent tight binding theory, it is found that, inspite of this bandgap opening, the intrinsic bias dependent electronic structure and the screening effect limit the subthreshold slope of a metal source drain bilayer grapheme transistor at a relatively higher value-much above the Boltzmann limit. This in turn reduces the on-off ratio of the transistor significantly. To overcome this poor on-off ratio problem, a semiconductor source-drain structure has been proposed, where the minority carrier injection from the drain is largely switched off due to the bandgap of the drain. Using a self-consistent Non-Equilibrium Green’s Function(NEGF) approach, the proposed device is found to be extremely promising providing unipolar grapheme devices with large on-off ratio, improved subthreshold slope and better current saturation. At high drain bias, the transport properties of grapheme is extremely intriguing with a number of nontrivial effects. Optical phonons in monolayer grapheme couple with carriers in a much stronger way as compared to a bilayer due to selection rules. However, it is difficult to experimentally probe this through transport measurements in substrate supported grapheme as the surface polar phonons with typical low activation energy dominates the total scattering. However, at large drain field, the carriers obtain sufficient energy to interact with the optical phonons, and create so called ‘hot phonons’ which we have experimentally found to result in a negative differential conductance(NDC). The magnitude of this NDC is found to be much stronger in monolayer than in bilayer, which agrees with theoretical calculations. This NDC has also been shown to be compensated by extra minority carrier injection from drain at large bias resulting in an excellent current saturation through a fundamentally different mechanism as compared to velocity saturation. A transport model has been proposed based on the theory, and the experimental observations are found to be in agreement with the model.

There is a compelling need to explore different material options as well as device structures to facilitate smooth transistor scaling for higher speed, higher density and lower power. The enormous potential of nanoelectronics, and nanotechnology in general, offers us the possibility of designing devices with added functionality. However, at the same time, the new materials come with their own challenges that need to be overcome. In this work, we have addressed some of these challenges in the context of quasi-2D Silicon, III-V semiconductor and graphene. Bulk Si is the most widely used semiconductor with an indirect bandgap of about 1.1 eV. However, when Si is thinned down to sub-10nm regime, the quasi-2D nature of the system changes the electronic properties of the material significantly due to the strong geometrical confinement. Using a tight-binding study, we show that in addition to the increase in bandgap due to quantization, it is possible to transform the original in direct bandgap to a direct one. The effective masses at different valleys are also shown to vary uniquely in an anisotropic way. This ultra-thin Si, when used as a channel in a double gate MOSFET structure, creates so called “volume in version” which is extensively investigated in this work. It has been found that the both the quantum confinement as well as the gating effect play a significant role in determining the spatial distribution of the charge, which in turn has an important role in the characteristics of transistor. Compound III-V semiconductors, like Inx Ga1-xAs, provide low effective mass and low density of states. This, when coupled with strong confinement in a nanowire channel transistor, leads to the “Ultimate Quantum Capacitance Limit” (UQCL) regime of operation, where only the lowest subband is occupied. In this regime, the channel capacitance is much smaller than the oxide capacitance and hence dominates in the total gate capacitance. It is found that the gate capacitance change qualitatively in the UQCL regime, allowing multi-peak, non-monotonic capacitance-voltage characteristics. It is also shown that in an ideal condition, UQCL provides improved current saturation, on-off ratio and energy-delay product, but a degraded intrinsic gate delay. UQCL shows better immunity towards series resistance effect due to increased channel resistance, but is more prone to interfacial traps. A careful design can provide a better on-off ratio at a given gate delay in UQCL compared to conventional MOSFET scenario. To achieve the full advantages of both FinFET and HEMT in III-V domain, a hybrid structure, called “HFinFET” is proposed which provides excellent on performance like HEMT with good gate control like FinFET. During on state, the carriers in the channel are provided using a delta-doped layer(like HEMT) from the top of a fin-like non-planar channel, and during off state, the gates along the side of the fin(like FinFET) help to pull-off the carriers from the channel. Using an effective mass based coupled Poisson-Schrodinger simulation, the proposed structure is found to outperform the state of the art planar and non-planar MOSFETs. By careful optimization of the gate to source-drain underlap, it is shown that the design window of the device can be increased to meet ITRS projections at similar gate length. In addition, the performance degradation of HFinFET in presence of interface traps has been found to be significantly mitigated by tuning the underlap parameter. Graphene is a popular 2D hexagonal carbon crystal with extraordinary electronic, mechani-cal and chemical properties. However, the zero band gap of grapheme has limited its application in digital electronics. One could create a bandgap in grapheme by making quasi-1D strips, called nanoribbon. However, the bandgap of these nanoribbons depends on the the type of the edge, depending on which, one can obtain either semiconducting or metallic nanoribbon. It has been shown that by the application of an external transverse field along the sides of a nanoribbon, one could not only modulate the magnitude of the bandgap, but also change it from direct to indirect. This could open up interesting possibilities for novel electronic and optoelectronic applications. The asymmetric potential distribution inside the nanoribbon is found to result in such direct to indirect bandgap transition. The corresponding carrier masses are also found to be modulated by the external field, following a transition from a“slow”electron to a“fast” electron and vice-versa. Experimentally, it is difficult to control the bandgap in nanoribbons as precise edge control at nanometer scale is nontrivial. One could also open a bandgap in a bilayer graphene, by the application of vertical electric field, which has raised a lot of interest for digital applications. Using a self-consistent tight binding theory, it is found that, inspite of this bandgap opening, the intrinsic bias dependent electronic structure and the screening effect limit the subthreshold slope of a metal source drain bilayer grapheme transistor at a relatively higher value-much above the Boltzmann limit. This in turn reduces the on-off ratio of the transistor significantly. To overcome this poor on-off ratio problem, a semiconductor source-drain structure has been proposed, where the minority carrier injection from the drain is largely switched off due to the bandgap of the drain. Using a self-consistent Non-Equilibrium Green’s Function(NEGF) approach, the proposed device is found to be extremely promising providing unipolar grapheme devices with large on-off ratio, improved subthreshold slope and better current saturation. At high drain bias, the transport properties of grapheme is extremely intriguing with a number of nontrivial effects. Optical phonons in monolayer grapheme couple with carriers in a much stronger way as compared to a bilayer due to selection rules. However, it is difficult to experimentally probe this through transport measurements in substrate supported grapheme as the surface polar phonons with typical low activation energy dominates the total scattering. However, at large drain field, the carriers obtain sufficient energy to interact with the optical phonons, and create so called ‘hot phonons’ which we have experimentally found to result in a negative differential conductance(NDC). The magnitude of this NDC is found to be much stronger in monolayer than in bilayer, which agrees with theoretical calculations. This NDC has also been shown to be compensated by extra minority carrier injection from drain at large bias resulting in an excellent current saturation through a fundamentally different mechanism as compared to velocity saturation. A transport model has been proposed based on the theory, and the experimental observations are found to be in agreement with the model.