Browsing by Author "Maunu, Tyler"

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    Detecting Helium Vapor Pulses in Low Temperature Transmission Experiments
    (2010-09-13) Maunu, Tyler
    Bose-Einstein condensation, originally predicted in 1924 by S. Bose and A. Einstein, refers to a quantum configuration at low temperatures in which a large portion (the condensate fraction) of particles collapse into the ground state. Figure 1 shows the phenomena in Rb-87, a less complicated system that superfluid 4He, but the first experimental evidence of BEC . A superfluid is described as a phase of matter with zero viscosity, infinite conductivity, quantized vortices, and zero entropy. It is also characterized by the Cooper pairing of atoms and not electrons. It is generally accepted that superfluidity exhibited in Helium-4 is a consequence of composite boson exhibiting behavior that is associated with Bose-Einstein condensation. It has been proposed that experiments observing the transmission characteristics of a slab of Helium-4 superfluid that is subjected to a pulse of Helium-4 vapor. Figure 3 shows the set-up of our experimental cell. In the current experiment, we use a fiber optic cable to heat a slab of Helium-4 superfluid, which results in a pulse of vapor. This pulse of vapor is then allowed to impinge on the bottom of a slab of suspended Helium-4 atoms. The resultant atomic flux is then observed on a series of superconducting bolometers, which allow us to see the energy levels of transmitted Helium-4 atoms. Bolometers are essential for the detection system in this experiment because they are designed to function at the low temperatures needed to carry out this experiment, and allow for detection speeds on the order of 1 μs. Our experiment aims at pinning down Helium-4 superfluid as a Bose-Einstein condensate by observing the transmission characteristics of a Helium-4 superfluid slab. The purpose of my research was to understand and test the detection system being used to measure these transmission characteristics.
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    Fiber Optic Feedthrough Design For Use In Cryogenic Dilution Refrigeration Systems
    (2012-04-18) Maunu, Tyler
    Bose-Einstein condensation is a fundamental state of dilute gases of bosons. It was originally predicted in 1924 by S. Bose and A. Einstein, and it refers to a quantum configuration at low temperatures in which a large portion (the condensate fraction) of particles collapse into the ground state. As can be seen in Figure 1, Rb-87 has been shown to exhibit the properties of Bose-Einstein condensation at low temperatures. Our experiment focuses on studying superfluid Helium-4. A superfluid is a phase of matter with zero viscosity, infinite conductivity, and other unusual properties. It is generally accepted that the superfluid properties of supercooled Helium-4 is caused by the composite boson exhibiting behavior associated with Bose-Einstein condensation, but it has not yet been conclusively proven. The goal of our experiment is to analyze the transmission characteristics of a slab of Helium-4 superfluid. These transmission characteristics could hopefully be used to offer some evidence of Bose-Einstein condensation in superfluid Helium-4. To accomplish this task, we used a dilution refrigeration system to cool our experimental cell down to extremely low temperatures. Inside the cell, we use a laser pulse in a fiber optic cable to produce a pulse of atoms at the bottom of the slab of Helium-4. These atoms are then transmitted through the slab and shot out the other side. The transmitted atoms are then detected on a series of superconducting bolometers. With bolometers, we are able to accurately and quickly determine energy levels of the transmitted atoms when they strike the surface of each bolometer. The purpose of my research focused on the design of our internal vacuum can and cell. The aspect of the design that needed modifying was the optical fiber feed through, which can be seen in Figure 3. These feedthroughs are essential in transferring laser pulses from an external source into the experimental cell. The feedthroughs must be leak proof in order to allow the dilution refrigeration system to run smoothly as well as to maintain accuracy within the experimental cell.
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    A Framework for Nonconvex Robust Subspace Recovery
    (2018-07) Maunu, Tyler
    This thesis consists of three works from my Ph.D.~research. The first part is an overview of the problem of Robust Subspace Recovery. Then, the next parts present two algorithms for solving this problem along with supporting mathematical analysis. Robust subspace recovery involves finding an underlying low-dimensional subspace in a dataset that is possibly corrupted with outliers. While this problem is easy to state, it has been difficult to develop optimal algorithms due to its underlying nonconvexity. We give a comprehensive review of the algorithms developed for RSR in the first chapter of this thesis. After this, we will discuss our proposed solutions to this problem. The first proposed algorithm, which we refer to as Fast Median Subspace (FMS), is designed to robustly determine the underlying subspace of such datasets, while having lower computational complexity than existing accurate methods. We prove convergence of the FMS iterates to a stationary point. Further, under two special models of data, FMS converges to a point that is near to the global minimum with overwhelming probability. Under these models, we show that the iteration complexity is globally sublinear and locally r-linear. For one of the models, these results hold for any fixed fraction of outliers (less than 1). Numerical experiments on synthetic and real data demonstrate its competitive speed and accuracy. Our second proposed algorithm involves geodesic gradient descent on the Grassmannian manifold. In the accompanying mathematical analysis, we prove that an underlying subspace is the only stationary point and local minimizer in a specified neighborhood if a deterministic condition holds for a dataset. We further show that if the deterministic condition is satisfied, the geodesic gradient descent method over the Grassmannian manifold can exactly recover the underlying subspace with proper initialization. Proper initialization by principal component analysis is guaranteed with a similar stability condition. Under slightly stronger assumptions, the gradient descent method with an adaptive step size scheme achieves linear convergence. The practicality of the deterministic condition is demonstrated on some statistical models of data, and the method achieves almost state-of-the-art recovery guarantees on the Haystack Model. We show that our gradient method can exactly recover the underlying subspace for any fixed fraction of outliers (less than 1) provided that the sample size is large enough.