According to classical wave theory, the energy of a pulse or wave is proportional to the square of its amplitude. When two pulses or waves of equal amplitude, A, propagate towards each other, they can exhibit constructive interference, resulting in an amplitude of 2A, or destructive interference, resulting in zero amplitude. This implies violations of energy conservation, with constructive interference seemingly doubling the energy and destructive interference seemingly annihilating it. This apparent contradiction is addressed by analyzing the velocities and energies involved in the superposition of two pulses on a string and waves in two dimensions, respectively. Through mathematical analysis, it is demonstrated that the conservation of energy remains intact even in the presence of interference.

We discuss an undergraduate capstone project involving the visualization of Monte Carlo simulations of radiation trapping in alkali metal vapors in various buffer gases and comparison to experimental data.  Radiation trapping is the confinement of light in atomic vapors by successive absorption and reemission of photons. If the vapor is sufficiently dense, the apparent lifetime of the atomic excited state, as observed in the fluorescence decay, may be significantly longer than the natural lifetime.  The calculations modeled and visualized the random walk of photons in potassium vapor with a helium buffer gas in a small, temperature-controlled cell, from initial absorption using a broadband laser source to eventual escape and detection. The calculated effect on the measured lifetime was compared to the results of an experiment having the same geometry and utilizing a Ti:sapphire pulsed laser for excitation. This project has allowed undergraduates to meaningfully integrate numerical and experimental techniques and explore various modes of data visualization.

We visualize the ideal gas using dual vector fields (differential one-forms) on a pressure-vs-volume (PV) diagram. (Think of a set of equipotentials in the neighborhood of a point.) In particular, we visualize the inexact differential forms for work W and heat Q (which result in path-dependent quantities for processes) and the exact differential form for internal energy U (which results in a path-independent quantity for processes). Our visualization describes the distinction between exact and inexact differential forms. We suggest a graphical method to compute the work, heat, and change in internal energy for an arbitrary process on a PV diagram.

The popular “spins first” approach to teaching undergraduate quantum mechanics allows the instructor to concentrate on the conceptual difficulties of quantum physics before treating it in its full technical complexity. Nevertheless, this approach still requires students to make a challenging and rather abrupt learning leap when instruction shifts from spin systems to quantum particles. We present an approximately week-long “intervention” consisting of classroom activities and assignments that we have inserted into our “spins first” quantum mechanics course at the point of transition from spins to particles. Specifically, we use discrete-space toy models to introduce important features of wave functions, while remaining solidly grounded in the intuition about quantum mechanics of discrete systems that our students have developed by this stage in the course.

Quantum-CT is a large-scale workforce development enterprise seeking to generate a pipeline of knowledgeable, skilled, and diverse individuals who can fulfill roles across a broad spectrum in the quantum industry, spanning lower and higher-level technical positions, research and development, as well as roles in non-technical adjacent fields, such as business and entrepreneurship, patent and legal, and policy making. Quantum-CT’s vision is built from collaboration and partnership, with quantum education and training resources being developed and disseminated state and region wide across multiple institutions to educate a generation of quantum literate students and professionals that will form the foundation of a future quantum workforce. Such resources will include courses and educational modules developed for audiences from K-12 to graduate level, degree and non-degree conferring certificate-level training, 2-year, 4-year, and graduate level advanced degrees. Practical training in the form of internship programs will provide a vital direct link between education hubs and industry.  Programs to support this flow of information and innovation will engage state, local and community leaders, policy makers and stakeholders. We present an overview of the Quantum-CT initiative in the state of Connecticut, along with some of the specific efforts currently underway to help bring this vision to fruition.

The active-learning opportunities afforded by physics tutorials have been shown to effectively improve students' conceptual understanding in topics both from introductory physics and upper-division physics. Many professors, however, find it hard to justify using precious class time on a tutorial, or may not have the resources to run one. We have been developing a way to transfer paper tutorials online with interactive feedback/guidance messages, and in this talk I will discuss how we did this for quantum computing-related tutorials, how others might do the same, and what are the pros and cons of online tutorials.

The University of Tennessee at Chattanooga (UTC) is establishing a program of excellence in Quantum Information Science and Engineering (QISE).  A fundamental aspect of that program is a series of innovative curriculum developments.  In Spring 2024 UTC faculty launched a four-course undergraduate certificate in QIST (i.e., Quantum Information Science and Technology).  The four courses are: (1) Introduction to QIST, PHYS/CPSC/MATH 3810, a team-taught cross-listed course; (2) Mathematical Concepts in QIST, MATH 3720; (3) Physics Concepts in QIST, PHYS 4810; and (4) Intro to Quantum Computing, CPSC 3280.  The certificate program and each of the four courses have completed the curriculum approval process.  Plans are underway to develop a similar certificate program at the graduate level.  Academic departments are considering the addition of a quantum concentration in their bachelor's and master's degrees.  UTC has an interdisciplinary PhD program in Computational Science with three concentrations: computer science, engineering, and math.  A fourth concentration, in quantum science, is in the planning stage.  We will also discuss plans for non-credit certificates to directly train the industry workforce, and pre-college outreach efforts.

Cryptography presents one of the clearest applications of quantum information science occurs, where the fundamental principles of quantum physics can be harnessed to encrypt messages in a way that is secure and can unambiguously reveal the presence of an eavesdropper.  Here we present a simplified experimental setup that demonstrates the core concepts of quantum key distribution while using minimal resources and maintaining a small footprint. The experimental design is compatible with both a multi- and single-photon implementation, and it also can demonstrate the presence of an eavesdropper that is detectable in the communication error rate. We will discuss the successful implementation of this setup at the University of Chicago, in a quantum teaching laboratory course targeted at the undergraduate level. 

Surface characterization is critical for developing novel nanostructures and understanding their chemical, physical, mechanical, and electronic properties.  It identifies the proper materials for specific applications. Surface characterization consists of a range of techniques such as microscopy which scans the surface at atomic level and spectroscopy that provides important information about the electronic structure of the surface. Here, a teaching outline of an undergraduate Material Science special topic course is described. Synthesize, characterization and applications of different nanostructures were included to the course syllabus. The students acquired hands-on experience on Scanning Tunneling Microscopy/Spectroscopy (STM/STS) and Atomic Force Microscope (AFM).

In this work, we examine connections between well-developed introductory physics labs and consider their quantum analogs. We first describe laboratory exercises developed at UConn which are primarily aimed at demonstrating the concept of geometric resonances in mechanical structures to engineers. Students measure vibrational dispersion relations in various contexts, such as waves on a string, waves on a free-standing ring, and waves on a cantilever. Next, we explore theoretically the extent to which one can define a mapping from classical mechanical resonances to quantum energy levels, by comparing specific contexts such as the spectrum of waves on a string and electronic states in a quantum well. Our analysis of quantum analogies from tangible classical structures can be used as a guide to selecting quantum analogs, acknowledging both the strengths and limitations of this kind of approach as we consider options to modernize the introductory physics course sequence to meet the needs of a new quantum information era.