AP 50A is the first half of a year-long, team- and project-based introduction to physics focusing on the application of physics to real-world problems. The AP 50A and B sequence, designed for engineering and physics concentrators, is equivalent in content and rigor to a standard calculus-based introductory physics course sequence. Lectures and exams are replaced by interactive, hands-on, and collaborative learning activities that will not only help you master physics concepts and hone your scientific reasoning and problem-solving skills, but also grow your capacity for self-directed learning and develop your collaborative skills.

Course Content: Kinematics, mechanics, waves

AP 50B is the second half of a year-long, team- and project-based introduction to physics focusing on the application of physics to real-world problems. The AP 50A and B sequence, designed for engineering and physics concentrators, is equivalent in content and rigor to a standard calculus-based introductory physics course sequence. Lectures and exams are replaced by interactive, hands-on, and collaborative learning activities that will not only help you master physics concepts and hone your scientific reasoning and problem-solving skills, but also grow your capacity for self-directed learning and develop your collaborative skills.

Course Content: Electromagnetism and optics

The physics of crystalline solids and their electric, magnetic, optical, and thermal properties. Designed as a first course in solid-state physics. Topics: free electron model; Drude model; the physics of crystal binding; crystal structure and vibration (phonons); x-ray diffraction; electrons in solids (Bloch theorem) and electronic band structures; metals and insulators; semiconductors (and their applications in pn junctions and transistors); magnetism; superconductivity.

This course provides an introduction to quantum materials and devices, including low-dimensional materials, single and double quantum dots, Josephson junctions, and graphene. Their behavior is explained using quantum and semiclassical transport, the Coulomb blockade, and superconductivity. Quantum devices offer new approaches for electronics and photonics.

The first half of the course will cover the interaction of quantized atoms with electromagnetic fields, introducing a number of basic concepts such as coherent Rabi transitions vs. rate-equation dynamics, stimulated & spontaneous transitions, and energy & phase relaxations. These will be then used to study a range of applications of atom-field interactions, such as nuclear magnetic resonance, molecular beam and paramagnetic masers, passive and active atomic clocks, dynamic nuclear polarization, pulse sequence techniques to coherently manipulate atomic quantum states, and laser oscillators with applications. We will also touch upon the interaction of quantized atoms with quantized fields, discussing the atom + photon (Jaynes-Cummings) Hamiltonian, dressed states, and cavity quantum electrodynamics. The second half will cover the classical interaction of electromagnetic fields with matter, with special attentions to collective electrodynamics in particular, magnetohydrodynamics and plasma physics with applications in astrophysics, space physics, and Bloch electrons in crystalline solids.

Foundational concepts of E&M, optics, imaging, and interaction of electromagnetic fields with matter. Topics include electromagnetic wave propagation, optical properties of materials from a microscopic viewpoint, propagation of electromagnetic fields in inhomogeneous media: Ray optics and effective forces on optical rays and ray bending. Fourier Optics and advanced imaging based on full E-M wave theory. The lens as a Fourier transformer, Fourier synthesis and phase contrast imaging. Light matter interactions in the semiclassical limit and quantization of the electromagnetic radiation field. We will illustrate the material with applications in AMO physics and in biological as well as astrophysical imaging. The class has two weekly lectures and, in parallel, a series of workshops with a project-based approach that will illustrate and support the material covered in the lectures and motivate the homework problems. 

This course covers the electrical, optical and magnetic properties of technologically important materials. It provides a quantitative description of structure-property relation by introducing tensor property, crystal symmetry, Neumann's principle and Curie principle. A variety of properties of materials are then introduced, including pyroelectricity, dielectricity, piezoelectricity, ferroelectricity; pyromagnetism, magnetoelectricity, piezomagnetism, ferromagnetism; defect chemistry, transport properties and applications in semiconducting, dielectric and energy storage materials; crystal optics including birefringence, Pockels effect, Kerr effect, photoelastic effect and optical activity. In addition, special topics will cover ferroelectric and ferromagnetic phase transitions and electrical, optical and magnetic properties of energy storage materials.

This course will present a survey of soft matter physics, providing an overview of the richness and breadth of the field. The emphasis will be on the physics of the systems, rather than on the formalism. It will cover most of the fields of interest within soft matter physics, both current and through the history of the field. The course is intended to be of value to both experimentalists and theorists.

Select topics in materials chemistry, focusing on chemical bonds, crystal chemistry, organic and polymeric materials, hybrid materials, surfaces and interfaces, self-assembly, electrochemistry, biomaterials, and bio-inspired materials synthesis.

Single-molecule biophysics is a vibrant research field that has grown substantially over the past ~30 years. The impact of single-molecule biophysics has been significant in terms of not only the experimental and theoretical methods that have been developed, but also the scientific insights in biological and soft matter science that these tools have enabled. This course covers the motivation behind single-molecule measurements in biology and, for the majority of the time, focuses on discussing state-of-the-art single-molecule imaging techniques as well as the key biological discoveries that they have enabled.

This course covers theoretical background and practical hands-on applications of modern computational atomistic methods used to understand and design properties of advanced functional materials. Topics include classical interatomic potentials and machine learning methods, quantum first-principles electronic structure models based on wave functions and density functional theory, Monte Carlo sampling and molecular dynamics simulations of phase transitions and free energies, fluctuations and transport properties. Applications include atomistic and electronic effects in materials for energy conversion and storage, catalysis, alloys, polymers, and low-dimensional materials.

The course introduces various aspects of quantum science, including quantum computing, quantum simulation, quantum communication and quantum metrology. It will particularly focus on the presentation of different experimental platforms currently used in the field and include superconducting qubits, trapped ions, neutral atoms, defects in solids, photons, among others. The course will cover an introduction of the general goals and essential prerequisites for these platforms; it will elucidate their operational principles and highlight some of their most significant and recent achievements, as well as the main challenges in their development.

Bonding, crystallography, diffraction, phase diagrams, microstructure, point defects, dislocations, and grain boundaries.

Basic principles of statistical physics with applications including: the equilibrium properties of classical and quantum gases; phase diagrams, phase transitions and critical points, as illustrated by the gas-liquid transition and simple magnetic models; Bose-Einstein condensation.

Lectures and laboratory instruction on transmission electron microscopy (TEM) and Cs corrected, aberration-correction microscopy and microanalysis. Lab classes include; diffraction, dark field imaging, X-ray spectroscopy, electron energy-loss spectroscopy, atomic imaging, materials sample preparation, polymers, and biological samples.

Kinetic principles underlying atomic motions, transformations, and other atomic transport processes in condensed matter. Application to atomic diffusion, continuous phase transformations, nucleation, growth, coarsening and mechanisms of plastic deformation.

Lattices and symmetries. Electronic Structure of Crystals. Semiclassical Transport Theory. Semiconductors. Localization. Integer Quantum Hall effect. Topological Insulators. Phonons. Additional topics from the theory of interacting electrons, including introduction to magnetism and superconductivity.

A course on the application of the principles of many-particle quantum mechanics to the properties of solids. The objective is to make students familiar with the tools of second quantization and diagrammatic perturbation theory, while describing the theory of the electron liquid, the BCS theory of superconductivity, and theory of magnetism in metals and insulators. Modern topics on correlated electron systems will occupy the latter part of the course.

Concepts of condensed matter physics are applied to the science and technology of beyond-CMOS devices, in particular, mesoscale, low-dimensional, and superconducting devices. Topics include: quantum dots/wires/wells and two-dimensional (2D) materials; optoelectronics with confined electrons; conductance quantization, Landauer-Buttiker formalism, and resonant tunneling; magneto oscillation; integer and fractional quantum Hall effects; Berry phase and topology in condensed matter physics; various Hall effects (anomalous, spin, valley, etc.); Weyl semimetal; topological insulator; spintronic devices and circuits; collective electron behaviors in low dimensions and applications; Cooper-pair boxes and superconducting quantum circuits.

Supervision of experimental or theoretical research on acceptable problems in applied physics and supervision of reading on topics not covered by regular courses of instruction.

Supervision of experimental or theoretical research on acceptable problems in applied physics and supervision of reading on topics not covered by regular courses of instruction.

Supervision of experimental or theoretical research on acceptable problems in applied physics and supervision of reading on topics not covered by regular courses of instruction.

Supervision of experimental or theoretical research on acceptable problems in applied physics and supervision of reading on topics not covered by regular courses of instruction.

This course is an introduction to the foundations of quantum mechanics, with specific focus on the basic principles involved in the control of quantum systems. Experimental foundations of quantum mechanics. Superposition principle, Schrödinger’s equation, eigenvalue and time dependent problems, wave packets, coherent states; uncertainty principle. One dimensional problems: double well potentials, tunneling, resonant tunneling, harmonic oscillator. WKB approximation. Hermitian operators and expectation values; time evolution and Hamiltonian, commutation rules, transfer matrix methods. Schrödinger, Heisenberg and interaction representations. Perturbation theory. Variational methods. Angular momentum, spin, Pauli matrices. Coherent interaction of light with two-level systems. Quantization of the EM field, absorption, spontaneous and stimulated emission. Density matrix and applications. Elements of quantum information (qubits, entanglement, teleportation, etc.). Taking this course meets the quantum mechanics core course requirement for the Applied Physics model programs.

The focus is on the foundations of optics/photonics and on some of its most important modern developments and applications. Powerful and widely used computational tools will be developed in the sections. Topics to be covered: Maxwell's equations, Free space optics. Reflection, refraction, polarization (Jones Calculus and Stokes parameters); interference and diffraction. Light-matter interaction, dispersion and absorption. Guided wave optics (including optical fibers). Perturbation and couple mode theory, transfer matrix methods; numerical methods. Optical resonators.  Photonic crystals. Near-field optics. Metal optics and Plasmonics. Metamaterials and Metasurfaces.

This course is an introduction to the foundations of quantum mechanics, with specific focus on the basic principles involved in the control of quantum systems. Experimental foundations of quantum mechanics. Superposition principle, Schrödinger’s equation, eigenvalue and time dependent problems, wave packets, coherent states; uncertainty principle. One dimensional problems: double well potentials, tunneling and resonant tunneling; WKB approximation. Hermitian operators and expectation values; time evolution and Hamiltonian, commutation rules, transfer matrix methods. Crystals, Bloch theorem, superlattices. Angular momentum, spin, Pauli matrices. Coherent interaction of light with two-level systems. Quantization of the EM field, spontaneous and stimulated emission; qubits, entanglement, teleportation.

Taking this course meets the quantum mechanics core course requirement for the Applied Physics model programs.