Phase Transitions in Engineered Ultracold Quantum Systems

The study of quantum degenerate gases has many applications in topics such as condensed matter dynamics, precision measurements and quantum phase transitions. We built an apparatus to create 87Rb Bose-Einstein condensates (BECs) and generated, via optical and magnetic interactions, novel quantum systems in which we studied the contained phase transitions. For our first experiment we quenched multi-spin component BECs from a miscible to dynamically unstable immiscible state. The transition rapidly drives any spin fluctuations with a coherent growth process driving the formation of numerous spin polarized domains. At much longer times these domains coarsen as the system approaches equilibrium. For our second experiment we explored the magnetic phases present in a spin-1 spin-orbit coupled BEC and the contained quantum phase transitions. We observed ferromagnetic and unpolarized phases which are stabilized by the spin-orbit coupling’s explicit locking between spin and motion. These two phases are separated by a critical curve containing both first-order and second-order transitions joined at a critical point. The narrow first-order transition gives rise to long-lived metastable states. For our third experiment we prepared independent BECs in a double-well potential, with an artificial magnetic field between the BECs. We transitioned to a single BEC by lowering the barrier while expanding the region of artificial field to cover the resulting single BEC. We compared the vortex distribution nucleated via conventional dynamics to those produced by our procedure, showing our dynamical process populates vortices much more rapidly and in larger number than conventional nucleation.

Phase transitions in gene networks evolved under different selection rules

Mathematical models of gene regulation are a powerful tool for understanding the complex features of genetic control. While various modeling efforts have been successful at explaining gene expression dynamics, much less is known about how evolution shapes the structure of these networks. An important feature of gene regulatory networks is their stability in response to environmental perturbations. Regulatory systems are thought to have evolved to exist near the transition between stability and instability, in order to have the required stability to environmental fluctuations while also being able to achieve a wide variety of functions (corresponding to different dynamical patterns). We study a simplified model of gene network evolution in which links are added via different selection rules. These growth models are inspired by recent work on `explosive' percolation which shows that when network links are added through competitive rather than random processes, the connectivity phase transition can be significantly delayed, and when it is reached, it appears to be first order (discontinuous, e.g., going from no failure at all to large expected failure) instead of second order (continuous, e.g., going from no failure at all to very small expected failure). We find that by modifying the traditional framework for networks grown via competitive link addition to capture how gene networks evolve to avoid damage propagation, we also see significant delays in the transition that depend on the selection rules, but the transitions always appear continuous rather than `explosive'.

The Borel Complexity of Isomorphism for Some First Order Theories

In this work we consider several instances of the following problem: "how complicated can the isomorphism relation for countable models be?"' Using the Borel reducibility framework, we investigate this question with regard to the space of countable models of particular complete first-order theories. We also investigate to what extent this complexity is mirrored in the number of back-and-forth inequivalent models of the theory. We consider this question for two large and related classes of theories. First, we consider o-minimal theories, showing that if T is o-minimal, then the isomorphism relation is either Borel complete or Borel. Further, if it is Borel, we characterize exactly which values can occur, and when they occur. In all cases Borel completeness implies lambda-Borel completeness for all lambda. Second, we consider colored linear orders, which are (complete theories of) a linear order expanded by countably many unary predicates. We discover the same characterization as with o-minimal theories, taking the same values, with the exception that all finite values are possible except two. We characterize exactly when each possibility occurs, which is similar to the o-minimal case. Additionally, we extend Schirrman's theorem, showing that if the language is finite, then T is countably categorical or Borel complete. As before, in all cases Borel completeness implies lambda-Borel completeness for all lambda.

Thermal activation, long-range ordering, and topological frustration of artificial spin ice

Frustrated systems, typically characterized by competing interactions that cannot all be simultaneously satisfied, are ubiquitous in nature and display many rich phenomena and novel physics. Artificial spin ices (ASIs), arrays of lithographically patterned Ising-like single-domain magnetic nanostructures, are highly tunable systems that have proven to be a novel method for studying the effects of frustration and associated properties. The strength and nature of the frustrated interactions between individual magnets are readily tuned by design and the exact microstate of the system can be determined by a variety of characterization techniques. Recently, thermal activation of ASI systems has been demonstrated, introducing the spontaneous reversal of individual magnets and allowing for new explorations of novel phase transitions and phenomena using these systems. In this work, we introduce a new, robust material with favorable magnetic properties for studying thermally active ASI and use it to investigate a variety of ASI geometries. We reproduce previously reported perfect ground-state ordering in the square geometry and present studies of the kagome lattice showing the highest yet degree of ordering observed in this fully frustrated system. We consider theoretical predictions of long-range order in ASI and use both our experimental studies and kinetic Monte Carlo simulations to evaluate these predictions. Next, we introduce controlled topological defects into our square ASI samples and observe a new, extended frustration effect of the system. When we introduce a dislocation into the lattice, we still see large domains of ground-state order, but, in every sample, a domain wall containing higher energy spin arrangements originates from the dislocation, resolving a discontinuity in the ground-state order parameter. Locally, the magnets are unfrustrated, but frustration of the lattice persists due to its topology. We demonstrate the first direct imaging of spin configurations resulting from topological frustration in any system and make predictions on how dislocations could affect properties in numerous materials systems.

MEMS SENSOR PLATFORMS FOR IN SITU CHARACTERIZATION OF LI-ION BATTERY ELECTRODES

Lithium-ion batteries provide high energy density while being compact and light-weight and are the most pervasive energy storage technology powering portable electronic devices such as smartphones, laptops, and tablet PCs. Considerable efforts have been made to develop new electrode materials with ever higher capacity, while being able to maintain long cycle life. A key challenge in those efforts has been characterizing and understanding these materials during battery operation. While it is generally accepted that the repeated strain/stress cycles play a role in long-term battery degradation, the detailed mechanisms creating these mechanical effects and the damage they create still remain unclear. Therefore, development of techniques which are capable of capturing in real time the microstructural changes and the associated stress during operation are crucial for unravelling lithium-ion battery degradation mechanisms and further improving lithium-ion battery performance. This dissertation presents the development of two microelectromechanical systems sensor platforms for in situ characterization of stress and microstructural changes in thin film lithium-ion battery electrodes, which can be leveraged as a characterization platform for advancing battery performance. First, a Fabry-Perot microelectromechanical systems sensor based in situ characterization platform is developed which allows simultaneous measurement of microstructural changes using Raman spectroscopy in parallel with qualitative stress changes via optical interferometry. Evolutions in the microstructure creating a Raman shift from 145 cm−1 to 154 cm−1 and stress in the various crystal phases in the LixV2O5 system are observed, including both reversible and irreversible phase transitions. Also, a unique way of controlling electrochemically-driven stress and stress gradient in lithium-ion battery electrodes is demonstrated using the Fabry-Perot microelectromechanical systems sensor integrated with an optical measurement setup. By stacking alternately stressed layers, the average stress in the stacked electrode is greatly reduced by 75% compared to an unmodified electrode. After 2,000 discharge-charge cycles, the stacked electrodes retain only 83% of their maximum capacity while unmodified electrodes retain 91%, illuminating the importance of the stress gradient within the electrode. Second, a buckled membrane microelectromechanical systems sensor is developed to enable in situ characterization of quantitative stress and microstructure evolutions in a V2O5 lithium-ion battery cathode by integrating atomic force microscopy and Raman spectroscopy. Using dual-mode measurements in the voltage range of the voltage range of 2.8V – 3.5V, both the induced stress (~ 40 MPa) and Raman intensity changes due to lithium cycling are observed. Upon lithium insertion, tensile stress in the V2O5 increases gradually until the α- to ε-phase and ε- to δ-phase transitions occur. The Raman intensity change at 148 cm−1 shows that the level of disorder increases during lithium insertion and progressively recovers the V2O5 lattice during lithium extraction. Results are in good agreement with the expected mechanical behavior and disorder change in V2O5, highlighting the potential of microelectromechanical systems as enabling tools for advanced scientific investigations. The work presented here will be eventually utilized for optimization of thin film battery electrode performance by achieving fundamental understanding of how stress and microstructural changes are correlated, which will also provide valuable insight into a battery performance degradation mechanism.