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## Scholarly Works (803 results)

The Herschel Space Observatory recently detected the presence of water vapor in observations of Ceres, bringing it into the crosshairs of the search for the building blocks of life in the solar system. I present a mission concept designed in collaboration with the NASA Ames Research Center for a two-probe mission to the dwarf planet Ceres, utilizing a pair of small low-cost spacecraft. The primary spacecraft will carry both a mass and an infrared spectrometer to characterize the detected vapor. Shortly after its arrival a second and largely similar spacecraft will impact Ceres to create an impact ejecta “plume” timed to enable a rendezvous and sampling by the primary spacecraft. This enables additional subsurface chemistry, volatile content and material characterization, and new science complementary to the Dawn spacecraft, the first to arrive at Ceres. Science requirements, candidate instruments, rendezvous trajectories, spacecraft design and comparison with Dawn science are detailed.

The discovery of neutrino oscillations provides the first indication of a lepton flavor violating (LFV) process, one that isn't predicted by the Standard Model. As such, NOvA is part of a rich experimental program to constrain unknown parameters in the neutrino oscillation model, described for three neutrino flavors using the PMNS unitary matrix. It is a long-baseline experiment utilizing two detectors, a Near Detector at Fermilab and a Far Detector in Ash River, Minnesota for a total baseline of $\SI{810}{km}$. It receives a predominantly $\nu_{\mu}$/$\bar{\nu}_{\mu}$ beam peaking at $\SI{1.8}{GeV}$ from the NuMI beam facility at Fermilab. There are four oscillation channels used in the analysis, $\nu_{\mu} \rightarrow \nu_{\mu}$, $\nu_{\mu} \rightarrow \nu_{e}$, $\bar{\nu}_{\mu} \rightarrow \bar{\nu}_{\mu}$ and $\bar{\nu}_{\mu}\rightarrow \bar{\nu}_{e}$. With a total exposure of $13.6\times10^{20}$ and $12.5\times10^{20}$ protons on target for the neutrino and anti-neutrino beam modes respectively, $82$ candidates are seen in the $\nu_{\mu} \rightarrow \nu_{e}$ channel for a total predicted background of $26.8$ events. Similarly, $33$ candidates are seen in the corresponding anti-neutrino channel for a total predicted background of $14.0$ events. In the $\nu_{\mu}\rightarrow\nu_{\mu}$ ($\bar{\nu}_{\mu}\rightarrow\bar{\nu}_{\mu}$) channel, $211$ ($105$) candidates are seen with an expectation of $1156.1$ ($488.1$) events at no oscillations.

Consequently, this dissertation reports a measurement for oscillation parameters based on a joint fit for the spectra in these four channels, which is given by : $\Delta m^{2}_{32} = (2.41\pm 0.07)\times10^{-3}$ eV$^{2}$, $\sin^{2}\theta_{23} = 0.57^{+0.04}_{-0.03}$ (UO) and $\delta_{CP} = 0.82\pi^{+0.27\pi}_{-0.87\pi}$.

In addition, a leading $4.2\sigma$ confidence level of evidence is seen for $\bar{\nu}_{e}$ appearance. The oscillation analysis improves upon previous updates in several areas including particle identification, event reconstruction and cosmic background rejection. A principle component analysis (PCA)-based technique is also implemented for decorrelating important flux and cross-section systematics. In addition, new improvements are proposed in areas of energy estimation as well as confidence interval building.

Topological quantum computing seeks to store and manipulate information in a protected manner using topological phases of matter. Information encoded in the degenerate state space of pairs of non-Abelian anyons or defects is robust to local perturbations, reducing its susceptiblity to environmental errors and potentially providing a scalable approach to quantum computing. However, topological quantum computing faces significant challenges, not least of which is identifying an experimentally accessible platform supporting non-Abelian topological physics. In this thesis, we critically analyze topological quantum computing with Majorana zero modes, non-Abelian defects of a topological superconductor. We identify intrinsic error sources for Majorana-based systems and propose quantum computing architectures that minimize their effects. Additionally, we consider a new approach for realizing and detecting non-Abelian topological defects in fractional Chern insulators.

Topological quantum computing is predicated on the idea that braiding non-Abelian anyons adiabatically can implement quantum gates fault tolerantly. However, any braiding experiment will necessarily depart from the strict adiabatic limit. We begin by analyzing the nature of diabatic errors for anyon braiding, paying particular attention to how such errors scale with braiding time. We find that diabatic errors are unfavorably large and worryingly sensitive to details of the time evolution. We present a measurement-based correction protocol for such errors, and illustrate its application in a particular Majorana-based qubit design.

We next propose designs for Majorana-based qubits operated entirely by a measurement-based protocol, thereby avoiding the diabatic errors discussed above. Our designs can be scaled into large two dimensional arrays amenable to long-term quantum computing goals, whose core components are testable in near-term devices. These qubits are robust to quasiparticle poisoning, anticipated to be one of the dominant error sources coupling to Majorana zero modes. We demonstrate that our designs support topologically protected Clifford operations and can be augmented to a universal gate set without requiring additional control parameters.

While topological protection greatly suppresses errors, residual coupling to noise limits the lifetimes of our proposed Majorana-based qubits. We analyze the dephasing times for our quasiparticle-poisoning-protected qubits by calculating their charge distribution using a particle number-conserving formalism. We find that fluctuations in the electromagnetic environment couple to an exponentially suppressed topological dipole moment. We estimate dephasing times due to $1/f$ noise, thermal quasiparticle excitations, and phonons for different qubit sizes.

The residual errors discussed above will necessarily require error correction for a sufficiently long quantum computation. We develop physically motivated noise models for Majorana-based qubits that can be used to analyze the performance of a quantum error correcting code. We apply this noise model to estimate pseudo-thresholds for a small subsystem code, identifying the relative importance of difference error processes from a fault tolerance perspective. Our results emphasize the necessity of suppressing long-lived quasiparticle excitations that can spread across the code.

Finally, we turn our attention to a different platform that could host non-Abelian topological defects: fractional Chern insulators in graphene. We study the edge states of fractional Chern insulators using the field theory of fractional quantum Hall edges supplemented with a symmetry action. We find that lattice symmetries impose a quantized momentum difference for edge electrons in a fractional state of a $C=2$ Chern band. This momentum difference can be used to selectively contact the different edge states, thereby allowing detection of topological defects in the bulk with a standard four terminal measurement. Our proposal could be implemented in graphene subject to an artificially patterned lattice.

We investigate the edge properties of Abelian topological phases in two spatial dimensions. We discover that many of them support multiple fully chiral edge phases, with surprising and measurable experimental consequences. Using the machinery of conformal field theory and integral quadratic forms we establish that distinct chiral edge phases correspond to genera of positive-definite integral lattices. This completes the notion of bulk-boundary correspondence for topological phases. We establish that by tuning inter-channel interactions the system can be made to transition between the different edge phases without closing the bulk gap.

Separately we construct a family of one-dimensional models, called Perfect Metals, with no relevant mass-generating operators. These theories describe stable quantum critical phases of interacting fermions, bosons or spins in a quantum nanowire. These models rigorously answer a long-standing question about the existence of stable metallic phases in one and two spatial dimensions in the presence of generic disorder. Separately, they are the first example of a stable phase of an infinite parallel array of coupled Luttinger liquids.

We perform a detailed study of the transport properties of Perfect Metals and show that in addition to violating the Wiedemann-Franz law, they naturally exhibit low power-law dependence of electric and thermal conductivities on temperature all the way to zero temperature. We dub this phenomenological set of properties a hyperconductor because in some sense, hyperconductors are better conductors that superconductors, which may have thermal conductivities that are exponentially small in temperature.