Studies of the optical model for elastic scattering.

Optical model studies of medium energy alpha particles and high energy pions using the microscopic model, are carried out to investigate the nuclear matter distribution. For medium energy alpha particles, the optical potentials are obtained by folding an effective alpha-nucleon interaction into the nuclear matter distributions which are constructed from single particle wave functions, and elastic scattering of alpha particles at 42 MeV is calculated. It is shown that the nuclear matter distributions obtained as above can explain reasonably well experimental data, if a suitable form for the effective interaction is chosen. Further, the ability of the microscopic model to reproduce the observed behaviour of the strong absorption radii, is examined and it is found that the strong absorption radii obtained, show systematic A-dependence. But it is noted that the small uncertainties in the range parameter of the effective interaction become significant when one is concerned with the precise behaviour of these radii. The same uncertainties also limit the accurate determination of the nuclear matter distribution. For high energy pions, the optical potentials are obtained by folding the free pion-nucleon interaction in momentum space into the nucleon form factors which are calculated using neutron and proton distributions obtained as before. Using these pion optical potentials, the Klein-Gordon equation is solved numerically and the absorption and differential cross-sections at energies in the region 0.585-1.057 GeV are calculated. These calculations are carried out using the complete expression for the pion-nucleon interaction as well as the large A approximation. It is shown that the absorption and differential cross-sections for light and medium mass nuclei are quite sensitive to the variations in the parameters of the pion optical potential and in particular, at the minima in the differential cross-sections, significant changes are produced. From a comparison of our results for the absorption cross-sections for such nuclei with some available experimental data, it is indicated that the use of the large A approximation may significantly alter the conclusions reached before about the nuclear matter distributions. It also appears that even for heavy nuclei, the use of this approximation is probably suspect, especially when one is concerned with the analysis of accurate experimental data

Assessing polymeric nanocomposites and advanced cooling techniques for thermal management of next-generation power electronics

The field of power electronics devices has seen two significant trends in recent years: rapid miniaturization of devices and the replacement of silicon-based devices with wide bandgap semiconductor materials-based devices (Silicon Carbide (SiC), Gallium Nitride (GaN)). The end result of these advancements are devices that need advanced cooling technologies to dissipate ultrahigh high and concentrated heat loads. Multiple advanced thermal management solutions such as liquid cooling, jet, and spray impingement have been proposed as potential solutions. The present dissertation quantifies the benefits of key advanced cooling techniques for thermal management of power electronics packages. An analytical modeling framework based on a thermal resistance circuit has been utilized to estimate the maximum heat flux that can be dissipated from a power electronics package, and the junction temperatures at varying levels of power dissipation. Analysis was conducted for heat sinks made of copper (k=400 W/mK) and a polymer (k=20 W/mK). The developed modeling framework takes into account heat spreading in both lateral directions while capturing the influence of material properties on the spreading angle. The model can, therefore, be considered to capture 3D effects as well. Additionally, 3D Finite Element Analysis (FEA) simulations have been carried out to compare with the findings of the analytical model. This dissertation also studies the influence of polymeric encapsulants of varying thermal conductivities on the resulting temperature distributions in the package via steady 2D coupled electro-thermal simulations. Overall, the methodology and results presented in this dissertation provide insights for selecting optimal combinations of thermal management technologies and advanced polymeric materials, based on the heat dissipation requirements of power electronics packages.Mechanical Engineerin

Fixing the NTK: From Neural Network Linearizations to Exact Convex Programs

Recently, theoretical analyses of deep neural networks have broadly focused on two directions: 1) Providing insight into neural network training by SGD in the limit of infinite hidden-layer width and infinitesimally small learning rate (also known as gradient flow) via the Neural Tangent Kernel (NTK), and 2) Globally optimizing the regularized training objective via cone-constrained convex reformulations of ReLU networks. The latter research direction also yielded an alternative formulation of the ReLU network, called a gated ReLU network, that is globally optimizable via efficient unconstrained convex programs. In this work, we interpret the convex program for this gated ReLU network as a Multiple Kernel Learning (MKL) model with a weighted data masking feature map and establish a connection to the NTK. Specifically, we show that for a particular choice of mask weights that do not depend on the learning targets, this kernel is equivalent to the NTK of the gated ReLU network on the training data. A consequence of this lack of dependence on the targets is that the NTK cannot perform better than the optimal MKL kernel on the training set. By using iterative reweighting, we improve the weights induced by the NTK to obtain the optimal MKL kernel which is equivalent to the solution of the exact convex reformulation of the gated ReLU network. We also provide several numerical simulations corroborating our theory. Additionally, we provide an analysis of the prediction error of the resulting optimal kernel via consistency results for the group lasso.Comment: Accepted to Neurips 202

On-demand microwave generator of shaped single photons

We demonstrate the full functionality of a circuit that generates single microwave photons on demand, with a wave packet that can be modulated with a near-arbitrary shape. We achieve such a high tunability by coupling a superconducting qubit near the end of a semi-infinite transmission line. A dc superconducting quantum interference device shunts the line to ground and is employed to modify the spatial dependence of the electromagnetic mode structure in the transmission line. This control allows us to couple and decouple the qubit from the line, shaping its emission rate on fast time scales. Our decoupling scheme is applicable to all types of superconducting qubits and other solid-state systems and can be generalized to multiple qubits as well as to resonators.Comment: 10 pages, 7 figures. Published versio

Microwave Quantum Optics using Giant Artificial Atoms and Parametrically Coupled Superconducting Cavities

Artificially engineered atoms, built using superconducting electrical circuits, have had a broad impact on the field of quantum information and quantum computing. Based on the Josephson effect, superconducting qubits have provided a robust platform for engineering light-matter interactions at the single-photon level. The ability to precisely control and manipulate single photons using superconducting qubits and cavities, a field now popularly known as circuit quantum electrodynamics (circuit QED), has enabled new and novel regimes in quantum physics, which previously remained inaccessible. For instance, the coupling between individual photons and artificial atoms have been shown to reach the ultrastrong and deep-strong regimes, a feat which is difficult to achieve with natural atoms. The superconducting circuit platform is now a promising contender for building large-scale quantum processors, attracting large investments from academic, industry and government players. This thesis uses superconducting circuits to engineer photon interactions in two separate studies. The first is aimed at studying the physics of ``giant" artificial-atoms. The second study explores the route towards building a quantum heat engine using two parametrically-coupled, superconducting microwave cavities. We review the theoretical ideas and concepts which motivate our work, along with discussions of the design methodology, simulations, fabrication, measurement setup and the experimental findings. In the first study, we explore a giant artificial atom, formed from a transmon qubit, which is coupled to propagating microwaves at multiple points along an open transmission line. The multipoint coupling nature of the transmon allows its radiated field to interfere with itself leading to some striking ``giant" atom effects. For instance, we observe strong frequency dependent couplings of the transmon's transition levels to its electromagnetic environment, a feature which is not observed with ordinary artificial atoms. We measure large on/off ratios, as high as $380$, for the coupling rate of the $\ket{0}-\ket{1}$ transition. Furthermore, we show that we can enhance or suppress the coupling rate of the $\ket{1}-\ket{2}$ transition relative to the $\ket{0}-\ket{1}$ transition, by more than a factor of $200$. The relative modulation of the coupling rates was exploited to engineer a metastable state in the giant transmon and demonstrate electromagnetically-induced transparency (EIT), a typical signature of a lambda system. Our results show that we can transform the ladder structure of an ordinary transmon into a more interesting lambda system using a giant transmon, thereby paving the way for exploring new possibilities to study three-level physics in a waveguide-QED setting. Extending giant atom physics to multiple giant atoms, we then explore a device with two giant artificial atoms connected in a braided configuration to a transmission line. The braided topology of the qubits, offers an interesting regime where the qubits can interact with each other in a decoherence-free environment, where the interaction is mediated by virtual photons in the transmission line. We probe the resonant behavior of the qubits at two different frequency bias points, where we observe qualitatively different scattering behavior. Furthermore, when probing for the Autler-Townes Splitting (ATS), multiple resonances are observed for both resonant and off-resonant cases instead of the familiar doublet in the ATS spectroscopy. This comes as a surprise as the frequency-level spacings in both qubits are nominally identical. We believe these features could be an indication of a novel resonant interaction between the qubits facilitated by the braided topology. An effort to understand this theoretically is underway. For our second study, we explore a system with two parametrically-coupled superconducting resonators, which implements an optomechanical-like interaction in an all-electrical network. The nonlinear nature of this interaction is mediated by a superconducting quantum interference device (SQUID), where the current in one resonator couples to the photon number in the other resonator. We propose to use this system to build a ``photonic piston" engine in the quantum regime. We motivate the feasibility of the proposal by reviewing key theoretical results which demonstrate an Otto-cycle by appropriately driving the system with noise. Our experimental findings demonstrate the crucial nonlinear coupling that is required for the engine to work. We also show that we can increase the coupling strength between the resonators depending on the chosen flux operating point

Generating Multimode Entangled Microwaves with a Superconducting Parametric Cavity

In this Letter, we demonstrate the generation of multimode entangled states of propagating microwaves. The entangled states are generated by parametrically pumping a multimode superconducting cavity. By combining different pump frequencies, applied simultaneously to the device, we can produce different entanglement structures in a programable fashion. The Gaussian output states are fully characterized by measuring the full covariance matrices of the modes. The covariance matrices are absolutely calibrated using an in situ microwave calibration source, a shot noise tunnel junction. Applying a variety of entanglement measures, we demonstrate both full inseparability and genuine tripartite entanglement of the states. Our method is easily extensible to more modes.Comment: 5 pages, 1 figures, 1 tabl