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    Ultracold ²³Na⁶Li molecules in the triplet ground state Rvachov, Timur Michael This thesis describes experiments in spectroscopy and formation of triplet ²³Na⁶Li molecules from an initial mixture of ultracold ²³Na and ⁶Li. The production of quantum degenerate molecules with long-range dipolar interactions is a long-standing goal in low temperature physics. NaLi is a fermionic molecule with an electric dipole moment of 0.2 Debye and a magnetic dipole moment of 2 [mu]B in its triplet ro-vibrational ground state. The formation of an ultracold molecule with both electric and magnetic dipole moments allows for novel opportunities in control of ultracold molecular reactions and studies of quantum many-body systems with dipolar interactions. This experimental work consists of two parts. The first is a thorough spectroscopic study of the excited and ground triplet potentials of NaLi using one- and two-photon photoassociation spectroscopy. We present the spectroscopic positions and strengths of transitions to nearly all vibrational states in the excited c³[sigma]⁺ and ground ³[sigma]⁺ potentials of NaLi. This is the first spectroscopic observation of triplet potentials in NaLi and the first demonstration of photoassociation in the Na-Li system. The second part utilizes our spectroscopic results to coherently form an ultracold gas of NaLi molecules. Starting with an ultracold Na-Li mixture, we use magneto-association to form weakly bound Feshbach molecules. The Feshbach molecules are then transfered to the ro-vibrational triplet ground state using a two-photon stimulated Raman adiabatic passage (STIRAP) technique, forming 3 x 10⁴ molecules at a density of 5 x 10¹⁰ cm⁻³ and temperature of 3 [mu]K. The molecules are long-lived with a measured lifetime of 5 seconds, which highlights their fermionic nature and low universal inelastic loss rate. The utility of the molecule's magnetic moment is demonstrated by performing electron spin resonance spectroscopy to measure the hyperfine structure of the molecule. Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, 2018.; Cataloged from PDF version of thesis.; Includes bibliographical references (pages 161-173).

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    Aspects of highly-entangled quantum matter : from exotic phases, to quantum computation, and dynamics Vijay, Ksheerasagar We explore three incarnations of highly-entangled quantum matter: as descriptions of exotic, gapped phases in three spatial dimensions, as resources for fault-tolerant quantum computation, and as the by-product of the unitary evolution of a quantum state, on its approach to equilibrium. In Part 1, we study quantum information processing in platforms hosting Majorana zero modes. We demonstrate that certain highly-entangled states may be engineered in arrays of mesoscopic topological superconducting islands, and used for fault-tolerant quantum computation. We then discuss measurement-based protocols for braiding Majorana zero modes and detecting their non-Abelian statistics in on-going experiments on proximitized, semiconductor nanowires, before proposing new families of error-correcting codes for fermionic qubits, along with concrete realizations. In Part 11, we study gapped, three-dimensional phases of matter with sub-extensive topological degeneracy, and immobile point-like excitations - termed "fractons" - which cannot be moved without nucleating other excitations. We find two broad classes of fracton phases in which (i) composites of fractons form topological excitations with reduced mobility, or (ii) all topological excitations are strictly immobile. We demonstrate a duality between these phases and interacting systems with global symmetries along sub-systems, and use this to find new fracton phases, one of which may also be obtained by coupling an isotropic array of two-dimensional states with Z₂ topological order. We introduce a solvable model in which the fracton excitations are shown to carry a protected internal degeneracy, which provides a generalization of non-Abelian anyons in three spatial dimensions. In Part III, we investigate the dynamics of operator spreading and entanglement growth in quantum circuits composed of random, local unitary operators. We relate quantities averaged over realizations of the circuit, such as the purity of a sub-system and the out-of-time-ordered commutator of spatially-separated operators, to a fictitious, classical Markov process, which yields exact results for the evolution of these quantities in various spatial dimensions. Operator spreading is ballistic, with a front that broadens as a dimension-dependent power-law in time. In this setting, we also map the dynamics of entanglement growth in one dimension to the stochastic growth of an interface and to the Kardar-Parisi-Zhang equation, which leads to a description of entanglement dynamics in terms of an evolving "minimal cut" through the quantum circuit, and provides heuristics for entanglement growth in higher-dimensions. The material presented here is based on Ref. [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]. Ref. [11, 12] are not discussed in this thesis, but were completed during my time at MIT. Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, 2018.; Cataloged from PDF version of thesis.; Includes bibliographical references (pages 307-321).

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    Quantum enhanced sensing and communication Zhuang, Quntao Quantum phenomena such as entanglement and superposition enable performance beyond what classical physics can provide in tasks of computing, communication and sensing. Quantum sensing aims to enhance the measurement precision in parameter estimation or error probability in hypothesis testing. The first part of this thesis focuses on protocols for entanglement-enhanced sensing. However, various quantum sensing schemes' quantum advantage disappears in presence of decoherence from noise and loss. The quantum illumination protocol, on the other hand, has advantage over classical illumination even in presence of decoherence. This thesis provides the optimum receiver design for quantum illumination, and extends quantum illumination target detection to the realistic scenario with target fading and the Neyman-Pearson decision criterion. Quantum algorithms can solve difficult problems more efficiently than classical algorithms, which makes various classical encryption schemes vulnerable. To remedy this security issue, quantum key distribution enables sharing of secret keys with unconditional protocol security. However, the secret-key-rate of the state-of-art single-mode based quantum key distribution protocols are limited by a fundamental rate-loss trade-off. To enhance the secret-key-rate, this thesis proposes a multi-mode based quantum key distribution protocol. To prove its security, the noisy entanglement assisted classical capacity is developed to enable a security framework for two-way quantum key distribution protocols such as the one proposed here. An essential notion in the entanglement assisted capacity is additivity. This thesis constructs a channel with non-additive classical capacity assisted by limited entanglement assistance, even when the classical capacity of the channel is additive. Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, 2018.; Cataloged from PDF version of thesis.; Includes bibliographical references.

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    Classification of base geometries in F-theory Wang, Yinan, Ph. D. Massachusetts Institute of Technology F-theory is a powerful geometric framework to describe strongly coupled type JIB supcrstring theory. After we compactify F-theory on elliptically fibered Calabi-Yau manifolds of various dimensions, we produce a large number of minimal supergravity models in six or four spacetime dimensions. In this thesis, I will describe a current classification program of these elliptic Calabi-Yau manifolds. Specifically, I will be focusing on the part of classifying complex base manifolds of these elliptic fibrations. Besides the usual algebraic geometric description of these base manifolds, F-theory provides a physical language to characterize them as well. One of the most important physical feature of the bases is called the "non-Higgsable gauge groups", which is the minimal gauge group in the low energy supergravity model for any elliptic fibration on a specific base. I will present the general classification program of complex base surfaces and threefolds using algebraic geometry machinery and the language of non- Higgsable gauge groups. While the complex base surfaces can be completely classified in principle, the zoo of generic complex threefolds is not well understood. However, I will present an exploration of the subset of toric threefold bases. I will also describe examples of base manifolds with non-Higgsable U(1)s, which lead to supergravity models in four and six dimensions with a U(1) gauge group but no massless charged matter. Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, 2018.; Cataloged from PDF version of thesis.; Includes bibliographical references (pages 187-196).