An Exploration of the Weak Interaction with Drew Byron
The weak interaction is the weakest of the four four fundamental forces. It is also the only force that is mediated by massive particles; the W and Z bosons. What does it mean that the weak interaction violates conservation of parity? What does it mean that the weak interaction contains both vector and axial vector components? In this course we will begin with a review of the theory of the weak interaction. Then we will look into how historic experimental efforts revealed the unintuitive nature of the weak interaction. The course can be more focused on theory or experiment based on the interest of the students.
Readings: Lecture Notes, Experimental Research Papers, and a chapter or two from Modern Particle Physics (Thomson). Readings guided by interest.
Requirements: PHYS 322 (EM 1), PHYS 325 (QM 1)
Contemporary Neutrinoless Double-Beta Decay Experiments with Nick Ruof
In the standard model of particle physics neutrinos don't have mass, however due to flavor oscillations neutrinos must have mass, an indication of physics beyond the standard model. In minimal extensions of the standard model, neutrinos have the potential of acquiring two types of mass, Dirac and Majorana. All fermion masses in the standard model are Dirac masses, however a fundamental neutral fermion has the possibility of having a Majorana mass. In this case, the neutrino would be its' own anti-particle and would be a key phenomenon to explain the generation of matter/anti-matter asymmetry in the early universe through a process called leptogenesis. As of now the only process that can be used to probe for a Majorana mass is neutrinoless double-beta decay, a lepton flavor violating process where two beta-decays occur simultaneously and neutrinos are absent from the final state. In the last decade, many experiments have been built and planned with cutting edge technology to discover such a process. We will go over research papers relating to the theoretical background and some contemporary experiments that have set limits on the half-lifes for neutrinoless double-beta decay in various isotopes.
Experiments: EXO-200, KamLAND-Zen, GERDA, Majorana Demonstrator, neXO and more
Prerequisites: PHYS 226, PHYS 324, PHYS 322
Recommended: PHYS 422
Dark Matter Direct Detection Experiments with Alexander Piers
There is a significant amount of cosmological evidence for the existence of dark matter, but the nature of the matter that comprises 84% of the universe's mass remains elusive. Dark matter detection is an exciting area of research that spans multiple disciplines of physics; this course will be focused on the detectors and experiments of cutting edge direct detection experiments. We will be reading papers covering a range of different experiments to understand the detector design, interpret results, and critically examine issues or drawbacks in the analysis or experiment.
Reading: TBD, but will be current papers on DM experiments.
Prerequisites: None
Suggested: PHYS 321-323
Data-Driven Approaches to Physical Systems with Olivia Thomas
Data-driven modeling is increasingly used to study the multi-scale structure and dynamics that characterize complex physical systems. We will start by exploring general techniques such as principal and independent components analysis, and then move on to more specialized applications (fluid flows, atmospheric science, biophysics, etc.) and methods based on the student’s interest. Studying these techniques can deepen your understanding of the physical system that interests you and also broaden your analytical skill set.
Reading: “Data-Driven Science and Engineering” by S. Brunton and J. N. Kutz (book), assorted papers TBD
Prerequisites: MATH 307 (Intro to Differential Equations), MATH 308 (Linear Algebra)
Exploration of Axion Searches with Nick Du
Axions are a hypothesized particle that emerge as a result of the Peccei-Quinn solution to the strong CP problem. It was later realized that the properties of the axion make it a leading candidate to explain all of the dark matter in the universe. In this project we will explore various methods current experiments use to search for axions.
Reading: TBD
Prerequisites: PHYS 228, PHYS324, PHYS 322
Information Processing in Living Systems with Michael Pun
Living organisms rely on environmental information to survive. Although the complexity of biological systems can appear daunting, the simplifying approach of theoretical physics offers a powerful platform to study quantitatively how organisms process information. From this platform, physicists have asked a number of questions including what are the limits to environmental sensing at the molecular level, how do cells use sensory information to differentiate, and how can an organism's traits be explained in an environmental context. We will examine a number of papers on how living systems interact with their environment ranging from the molecular scale to the evolutionary scale with a focus on how physicists approach problems and build models in a biological context.
Reading: TBD
Prerequisites: PHYS 328
Integrated Photonics with Single Photon Emitters with Christian Pederson
Solid-state systems that emit single photons (e.g. color centers, quantum dots) are an extremely useful resource in a number of quantum applications, due to their ability to entangle distant qubit systems. Integrating these emitters into photonics is not only necessary for efficient collection and routing but also allows for precise control over fundamental properties of the emitted light. In this course, we will study the theory behind single-photon emission and investigate various experimental realizations of integrated single quantum emitters.
Readings: "Quantum Optics", Scully and Zubairy, "Quantum Photonics Incorporating Color Centers in Silicon Carbide and Diamond", Radulaski and Vučković
Papers: TBD
Prerequisites: PHYS 322, PHYS 325
Intro to Density Functional Theory with Tun Sheng Tan
Density functional theory (DFT) is the favorite method for many physicists and chemists to calculate the electronic structure of materials and to model catalytic synthesis. DFT makes a many body problem tractable by using a single particle picture. In this project, we will study the theoretical background and development of DFT as well as the computational tools needed to start doing research in this field. Depending on the student's interest, we will perform numerical calculations for some material properties (phonon density of states, thermodynamic properties, magnetic properties and many more) using Quantum Espresso.
Reading: “Density Functional Theory: A Practical Introduction” by David S. Sholl Janice A. Steckel, “The ABC of DFT” by Kieron Burke and friends, Inhomogeneous Electron Gas” by Pierre Hohenberg and Walter Kohn (Phys. Rev., 136, B864-B871).
Requirements: Phys 325 (QM 2), PHYS 328 (Stat Mech)
Recommended: Phys 423 (Solid State)
Introduction to Physics Education Research: Understanding Student Thinking with Lisa Goodhew
Physics Education Research (PER) investigates a broad range of questions regarding how students think about physics and what constitutes effective physics instruction. One particularly influential strand of PER has investigated the specific ideas that students have about physics topics, informing instructors of common student ideas so that they can target these ideas in their instruction. In this reading project we will explore the different perspectives that researchers have taken toward student thinking – are students ideas obstacles to learning that must be overcome, or resources for learning? – and the relationships between common student ideas and physics principles.
Reading: 3-4 research articles on student understanding of physics, such as: Hammer, Student resources for learning introductory physics (2000); .H. G. Close and P. R. L. Heron, “Research as a guide to improving instruction: An example from momentum conservation,” Am. J. Phys. (2010); or Posner, Strike, Hewson, and Gertzog, Accommodation of a Scientific Conception: Toward a Theory of Conceptual Change (1982). The specific reading selections will be chosen to match a DRiP participant’s interests.
Requirements: PHYS 123-123, PHYS 225 (Intro Quantum). The student should also have taken at least one of the following upper-division courses: PHYS 321-323 (EM 1-3), PHYS 324-325 (QM 1-2), or PHYS 329 (Stat Mech).
Intro to Solid State with Joseph Merritt
Quantum mechanics has become a pillar of modern physics and is able to explain many surprising aspects of our world. One of the great triumphs of quantum mechanics has been in describing properties of materials we use every day, which have on the order of 10^{23} atoms and electrons, making it a highly non-trivial task to describe even their ground state. In this course, I hope to introduce the basics of solid state physics and discuss how many body quantum mechanics can be used to explain fundamental phenomena such as quasiparticles, phonons, and charge transport in many body systems.
Reading: David Tong's notes on Applications of Quantum Mechanics, especially parts 2 - 4.
Prerequisites: Phys 324 (Quantum 1)
Introduction to Topological Insulators with Qianni Jiang
The concept of topological order represents a new paradigm in condensed matter physics. Topological insulators are insulating in their bulk but conductive in their surface/edge states, which are topologically protected. Knowledge about topological insulators will help you understand many other cutting-edge topological phases, such as Dirac semimetals, Weyl semimetals, topological superconductors, and quantum anomalous Hall phases. In this project we will start with the basic band theory of solids and the concept of topology in condensed matter physics. Then we will have a historical review on the theoretical and experimental progress in realizing 2D and 3D topological insulators. Finally, we will introduce other related topological phases based on student interest.
Reading: Ashcroft and Mermin, Solid State Physics, Chapter 4,5, 8, 9.
M. Z. Hasan and C. L. Kane Rev. Mod. Phys. 82, 3045 (2010).
Requirements: PHYS 325, PHYS 322, PHYS 328
Recommended: PHYS 423
Lasers and nonlinear optics with Shervin Sahba
Let’s talk lasers, covering the theory as well as surveying historical context (i.e. Nobel Prizes) and applications. Then we’ll dive into nonlinear optics: frequency mixing, mode-locking, the optical Kerr effect, and byproducts like supercontinuum generation. We’ll read a broad selection of review papers in non-linear and perhaps quantum optics, before branching into a subtopic, likely frequency comb generation and optical solitons.
Reading: “Ultrafast Optics” by Andrew Weiner
Requirements: PHYS 322 (EM 2). Familiarity with Maxwell’s Equations necessary. PHYS 328 (Statistical Physics) recommended. QM 1-2 needed if we get into quantum optics.
Linear Response Theory with Michael Smith
Many interesting problems in physics start with taking a well known system and applying a symmetry breaking perturbation (such as an electric or magnetic field). But how do we calculate the response of materials in the presence of (sufficiently small) symmetry breaking fields? In this project we will explore linear response theory via Green’s functions, starting with the definitions of various Green’s functions, their relationship to physical observables, and their equations of motion in the presence of interactions and impurities. The second half of the course will focus on using these Green’s functions to calculate linear response coefficients such as the electrical conductivity via the Kubo formula
Reading: Landau and Lifshitz Volume 9, Various papers
Requirements: PHYS 228 (Math Methods 2), PHYS 324 (QM 2), PHYS 322 (EM 2), Phys 329 (Stat Mech)
Strongly Recommended: PHYS 423 (Condensed Matter)
Machine Learning in Biophysics with Daniela Koch
Machine learning is all around us - from movie recommendations to facial recognition, we interact with machine learning algorithms on a daily basis. But how do these algorithms actually work? And can we leverage their computational power to gain new insight into physical systems? To answer these questions, we will cover the basics of machine learning and its applications in biophysics. We will further explore how machine learning is used in areas such as image segmentation, classification, or genetic sequencing. Throughout the quarter, our focus will be on understanding the limitations of these methods, as well as their strengths when compared to more traditional computational methods. Depending on the student’s programming and math experience, this course can incorporate building basic machine learning algorithms or center around a more theoretical approach. No previous experience in biology or biophysics is required.
Reading: TBD
Requirements: PHYS 228 (Math Methods 2), PHYS 329 (Stat Mech)
Strongly recommended: Some experience with Python and/or MATLAB
Mathematical Foundations of Quantum Mechanics with Kade Cicchella
The modern mathematical foundation of quantum mechanics involves mathematical structures which are not typically presented in a physics curriculum. In particular, topics within functional analysis such as operator theory and spectral theory are of great importance. In this reading course, we will explore the use of functional analysis in quantum mechanics with a focus on mathematical rigor. More abstractly, we will consider how the kinds of mathematical structures that are used in a physical theory are determined by the kinds of statements that theory needs to make and the results of relevant experiments. Topics that might be covered include: Operator Theory, Spectral Theory, Stone-von Neumann Theorem, Wigner Theorem, Representation Theory, C*-algebras, Quantization
Reading:
Requirements: PHYS 325 (QM 2), some proof-based math course
Recommended: PHYS 329 (Classical Mechanics), MATH 340 (Linear Algebra)
Maxwell’s Equations as a Classical Yang-Mills Theory with Michael Clancy
The standard model of particle physics is a quantum Yang-Mills theory with a particular gauge symmetry. The conceptual and mathematical foundations of quantum Yang-Mills theories remain some of the most difficult open problems in modern mathematics and physics. Fortunately, their classical counterparts are comparatively much simpler to understand. Yang-Mills theories aim to generalize gauge theories like electromagnetism, which turns out to be the simplest example of a Yang-Mills theory. In this project, we will spend the first half of the quarter developing some of the prerequisite language of manifolds, vector bundles, and Lie groups, and the second half specializing our mathematical tools to realize the four Maxwell equations as two Yang-Mills equations.
Reading: “An introduction to Yang-Mills theory” by Michael Nielson (.pdf on his website). (supplemental: Gauge Fields, Knots and Gravity by Baez and Muniain)
Requirements: PHYS 322 (EM 2), PHYS 228 (Math Methods 2), MATH 308 (Matrix Algebra)
Recommended: MATH 340 (Abstract Linear Algebra)
The Role of Mathematics in Physics Education Research with Charlotte Zimmerman
Quantitative reasoning, or how we make sense of the world through the application of mathematics, is essential to “thinking like a physicist” and therefore at the heart of physics. Recent work in physics education research suggests that physics and mathematics are so cognitively intertwined that they cannot be separated. Together, we will explore how mathematics manifests in undergraduate physics curricula and how education research is being conducted to better understand how physicists are using quantitative reasoning. As this topic is being explored at all levels of physics education, from introductory material to electromagnetism and quantum mechanics, our direct focus will be guided by the student’s interest.
Reading:
[1] Sherin, B. L. (2001). How Students Understand Physics Equations. Cognition and Instruction, 19(4), 479–541.
[2] Redish, E. F., & Kuo, E. (2015). Language of Physics, Language of Math: Disciplinary Culture and Dynamic Epistemology. Science and Education, 24(5–6), 561–590.
Requirements: Experience in the subject you would like to explore (i.e. if you are interested in the introductory sequence, all you need is completion of 12X. If you are interested in quantum mechanics, you’ll need to have completed or are currently taking Phys 324 and 325, etc.)
The “Quantumness” of Light with Kevin Smith
We know that light is inherently quantum, but there are surprisingly few phenomena which cannot be explained using a classical description of the electromagnetic field. However, with an eye towards quantum technology, harnessing the “quantumness” of light has become increasingly important over the past decade. We will discuss the wave-particle duality of light as well as how it differs from matter-based wave-particle duality (for example, can photons be described by wavefunctions?). Next we will focus on ways in which physicists have enhanced non-classical behavior. Depending on interest, we can dive headfirst into the math, or have more qualitative discussions. Time permitting, we can also discuss some modern work on photonics-based quantum simulation.
Reading: The intro to “Quantum Optics” by Garrison and Chiao. Various papers by Haroche, Cohen-Tannoudji, TBD.
Requirements: Phys 322 (EM 2), Phys 325 (QM 2)
Quantum Entanglement with Trapped Ions with Jennifer Lilieholm
Quantum mechanics holds many mysteries, and behaves in a manner which is counterintuitive to the macroscopic world. One of the best known examples of this is quantum entanglement, where the state of one quantum particle becomes linked (or entangled) with the state of another. This project will follow experimental progress on entanglement, from Einstein, Podolsky, and Rosen’s paper on the nature of quantum mechanics to its position today as an essential part of quantum computing, with a focus on trapped ion quantum computing.
Readings: Le Bellac’s “A Short Introduction to Quantum Information and Quantum Computation,” Papers on Molmer-Sorenson and Cirac-Zoller gates with trapped ions, Bell’s Inequality experiments
Prerequisites: PHYS 324, PHYS 325 (fine if taking concurrently)