## Solid-State Electronics for Integrated Circuits

Introduction to solid-state electronics including device fabrication. Topics: semiconductor crystal growth and device fabrication technology, carrier modeling, doping, generation and recombination, pn junction diodes, MOS capacitor and MOS transistor operation, and deviations from ideal behavior. Laboratory includes fabrication and testing of semiconductor devices. Students learn photolithography, the use of vacuum systems, furnaces, analytical microscopy and device-testing equipment.

## Thermodynamics

Introduction to the use of thermodynamics and statistical mechanics in physics and engineering. Entropy, temperature, and the principal laws of thermodynamics. Canonical equations of state. Applications to cycles, engines, phase and chemical equilibria. Probability and stochastic processes. Kinetic theory of perfect gases. Statistical mechanics. Applications to gases, gas degeneration, equilibrium radiation, and simple solids. Not offered 2022-23.

## Demonstration Lectures in Classical and Quantum Photonics

This course covers fundamentals of photonics with emphasis on modern applications in classical and quantum optics. Classical optical phenomena including interference, dispersion, birefringence, diffraction, laser oscillation, and the applications of these phenomena in optical systems employing multiple-beam interferometry, Fourier-transform image processing, holography, electro-optic modulation, optical detection and heterodyning will be covered. Quantum optical phenomena like single photon emission will be discussed. Examples will be selected from optical communications, radar, adaptive optical systems, nano-photonic devices and quantum communications. Prior knowledge of quantum mechanics is not required.

## Introductory Optics and Photonics Laboratory

Laboratory experiments to acquaint students with the contemporary aspects of optics and photonics research and technology. Experiments encompass many of the topics and concepts covered in APh 23.

## Physics of Electrical Engineering

This course provides an introduction to the fundamental physics of modern device technologies in electrical engineering used for sensing, communications, computing, imaging, and displays. The course overviews topics including semiconductor physics, quantum mechanics, electromagnetics, and optics with emphasis on physical operation principles of devices. Example technologies include integrated circuits, optical and wireless communications, micromechanical systems, lasers, high-resolution displays, LED lighting, and imaging.

## Laboratory in Applied Physics

Selected experiments chosen to familiarize students with laboratory equipment, procedures, and characteristic phenomena in plasmas, fluid turbulence, fiber optics, X-ray diffraction, microwaves, high-temperature superconductivity, black-body radiation, holography, and computer interfacing of experiments. Not offered 2022-23.

## Senior Thesis, Experimental

Supervised experimental research, open only to senior-class applied physics majors. Requirements will be set by individual faculty member, but must include a written report. The selection of topic must be approved by the Applied Physics Option Representative. Not offered on a pass/fail basis. Final grade based on written thesis and oral exam.

## Senior Thesis, Theoretical

Supervised theoretical research, open only to senior-class applied physics majors. Requirements will be set by individual faculty member, but must include a written report. The selection of topic must be approved by the Applied Physics Option Representative. Not offered on a pass/fail basis. Final grade based on written thesis and oral exam. This course cannot be used to satisfy the laboratory requirement in APh.

## Advanced Work in Applied Physics

Special problems relating to applied physics, arranged to meet the needs of students wishing to do advanced work. Primarily for undergraduates. Students should consult with their advisers before registering. Graded pass/fail.

## Fluid Mechanics

Fundamentals of fluid mechanics. Microscopic and macroscopic properties of liquids and gases; the continuum hypothesis; review of thermodynamics; general equations of motion; kinematics; stresses; constitutive relations; vorticity, circulation; Bernoulli's equation; potential flow; thin-airfoil theory; surface gravity waves; buoyancy-driven flows; rotating flows; viscous creeping flow; viscous boundary layers; introduction to stability and turbulence; quasi one-dimensional compressible flow; shock waves; unsteady compressible flow; and acoustics.

## Experimental Methods

Lectures on experiment design and implementation. Measurement methods, transducer fundamentals, instrumentation, optical systems, signal processing, noise theory, analog and digital electronic fundamentals, with data acquisition and processing systems. Experiments (second and third terms) in solid and fluid mechanics with emphasis on current research methods.

## States of Matter

Thermodynamics and statistical mechanics, with emphasis on gases, liquids, materials, and condensed matter. Effects of heat, pressure, and fields on states of matter are presented with both classical thermodynamics and with statistical mechanics. Conditions of equilibrium in systems with multiple degrees of freedom. Applications include ordered states of matter and phase transitions. The three terms cover, approximately, thermodynamics, statistical mechanics, and phase transitions.

## Introduction to the Micro/Nanofabrication Lab

Introduction to techniques of micro-and nanofabrication, including solid-state, optical, and microfluidic devices. Students will be trained to use fabrication and characterization equipment available in the applied physics micro- and nanofabrication lab. Topics include Schottky diodes, MOS capacitors, light-emitting diodes, microlenses, microfluidic valves and pumps, atomic force microscopy, scanning electron microscopy, and electron-beam writing.

## Topics in Applied Physics

A seminar course designed to acquaint advanced undergraduates and first-year graduate students with the various research areas represented in the option. Lecture each week given by a different member of the APh faculty, who will review their field of research. Graded pass/fail.

## Noise and Stochastic Resonance

The presence of noise in experimental systems is often regarded as a nuisance since it diminishes the signal to noise ratio thereby obfuscating weak signals or patterns. From a theoretical perspective, noise is also problematic since its influence cannot be elicited from deterministic equations but requires stochastic-based modeling which incorporates various types of noise and correlation functions. In general, extraction of embedded information requires that a threshold be overcome in order to outweigh concealment by noise. However, even below threshold, it has been demonstrated in numerous systems that external forcing coupled with noise can actually boost very weak signatures beyond threshold by a phenomenon known as stochastic resonance. Although it was originally demonstrated in nonlinear systems, more recent studies have revealed this phenomenon can occur in linear systems subject, for example, to color-based noise. Techniques for optimizing stochastic resonance are now revolutionizing modeling and measurement theory in many fields ranging from nonlinear optics and electrical systems to condensed matter physics, neurophysiology, hydrodynamics, climate research and even finance. This course will be conducted in survey and seminar style and is expected to appeal to theorists and experimentalists alike. Review of the current literature will be complimented by background readings and lectures on statistical physics and stochastic processes as needed.

## Solid-State Physics

Introductory lecture and problem course dealing with experimental and theoretical problems in solid-state physics. Topics include crystal structure, symmetries in solids, lattice vibrations, electronic states in solids, transport phenomena, semiconductors, superconductivity, magnetism, ferroelectricity, defects, and optical phenomena in solids.

## Physics of Momentum Transport in Hydrodynamic Systems

Contemporary research in many areas of physics requires some knowledge of the principles governing hydrodynamic phenomena such as nonlinear wave propagation, symmetry breaking in pattern forming systems, phase transitions in fluids, Langevin dynamics, micro- and optofluidic control, and biological transport at low Reynolds number. This course offers students of pure and applied physics a self-contained treatment of the fundamentals of momentum transport in hydrodynamic systems. Mathematical techniques will include formalized dimensional analysis and rescaling, asymptotic analysis to identify dominant force balances, similitude, self-similarity and perturbation analysis for examining unidirectional and Stokes flow, pulsatile flows, capillary phenomena, spreading films, oscillatory flows, and linearly unstable flows leading to pattern formation. Students must have working knowledge of vector calculus, ODEs, PDEs, complex variables and basic tensor analysis. Advanced solution methods will be taught in class as needed. Not offered 2022-23.

## Physics of Thermal and Mass Transport in Hydrodynamic Systems

Contemporary research in many areas of physics requires some knowledge of how momentum transport in fluids couples to diffusive phenomena driven by thermal or concentration gradients. This course will first examine processes driven purely by diffusion and progress toward description of systems governed by steady and unsteady convection-diffusion and reaction-diffusion. Topics will include Fickian dynamics, thermal transfer in Peltier devices, Lifshitz-Slyozov growth during phase separation, thermocouple measurements of oscillatory fields, reaction-diffusion phenomena in biophysical systems, buoyancy driven flows, and boundary layer formation. Students must have working knowledge of vector calculus, ODEs, PDEs, complex variables and basic tensor analysis. Advanced solution methods such as singular perturbation, Sturm-Liouville and Green's function analysis will be taught in class as needed. Not offered 2022-23.

## Physics of Measurement

This course explores the fundamental underpinnings of experimental measurements from the perspectives of coupling, responsivity, noise, backaction, and information. Its overarching goal is to enable students to develop intuition about, and to critically evaluate, a diversity of real measurement systems - and to provide a framework for estimating the ultimate and practical limits to information that can be extracted from them. Topics will include physical signal transduction and responsivity, fundamental noise processes, modulation, frequency conversion, synchronous detection, signal-sampling techniques, digitization, signal transforms, spectral analyses, and correlation methods. The first term will cover the essential fundamental underpinnings, while topics in second term will focus their application to high frequency, microwave, and fast time-domain measurements where distributed approaches become imperative. The second term (in alternate years) may focus on topics that include either measurements at the quantum limit, biosensing and biological interfaces, of functional brain imaging.

## Nanofabrication Techniques

This laboratory/lecture course will enable students to become proficient in micro- and nanofabrication and get trained on most of the instruments in Caltech’s Kavli Nanoscience Institute cleanroom. Students will learn the capabilities and limitations of nanofabrication equipment, followed by training on these nanofabrication instruments in the KNI cleanroom facility.

## Physical Optics

The course focuses on applying linear systems analysis to the propagation of light waves. Contents begin with a review of Electromagnetic theory of diffraction and transitions to Fourier Optics for a scalar-wave treatment of propagation, diffraction, and image formation with coherent and incoherent light. In addition to problems in imaging, the course makes connections to a selected number of topics in optics, where the mathematics of wave phenomena plays a central role. Examples include propagation of light in multilayer films and meta-surfaces, non-diffracting beams, Fabry-Perrot cavities, and angular momentum of light. Areas of application include modern imaging, display, and beam shaping technologies. Not offered 2022-23.

## Diffraction, Imaging, and Structure

Experimental methods in transmission electron microscopy of inorganic materials including diffraction, spectroscopy, conventional imaging, high resolution imaging and sample preparation. Weekly laboratory exercises to complement material in MS 132.

## Advanced Lasers and Photonics Laboratory

This course focuses on hands-on experience with advanced techniques related to lasers, optics, and photonics. Students have the opportunity to build and run several experiments and analyze data. Covered topics include laser-based microscopy, spectroscopy, nonlinear optics, quantum optics, ultrafast optics, adaptive optics, and integrated photonics. Limited enrollment.

## Electromagnetic Theory

Electromagnetic fields in vacuum: microscopic Maxwell's equations. Monochromatic fields: Rayleigh diffraction formulae, Huyghens principle, Rayleigh-Sommerfeld formula. The Fresnel-Fraunhofer approximation. Electromagnetic field in the presence of matter, spatial averages, macroscopic Maxwell equations. Helmholtz's equation. Group-velocity and group-velocity dispersion. Confined propagation, optical resonators, optical waveguides. Single mode and multimode waveguides. Nonlinear optics. Nonlinear propagation. Second harmonic generation. Parametric amplification.

## Light Interaction with Atomic Systems-Lasers

Light-matter interaction, spontaneous and induced transitions in atoms and semiconductors. Absorption, amplification, and dispersion of light in atomic media. Principles of laser oscillation, generic types of lasers including semiconductor lasers, mode-locked lasers. Frequency combs in lasers. The spectral properties and coherence of laser light. Not offered 2022-23.

## Special Topics in Photonics and Optoelectronics

Interaction of light and matter, spontaneous and stimulated emission, laser rate equations, mode-locking, Q-switching, semiconductor lasers. Optical detectors and amplifiers; noise characterization of optoelectronic devices. Propagation of light in crystals, electro-optic effects and their use in modulation of light; introduction to nonlinear optics. Optical properties of nanostructures. Not offered 2022-23.

## Atoms and Photons

This course will provide an introduction to the interaction of atomic systems with photons. The main emphasis is on laying the foundation for understanding current research that utilizes cold atoms and molecules as well as quantized light fields. First term: resonance phenomena, atomic/molecular structure, and the semi-classical interaction of atoms/molecules with static and oscillating electromagnetic fields. Techniques such as laser cooling/trapping, coherent manipulation and control of atomic systems. Second term: quantization of light fields, quantized light matter interaction, open system dynamics, entanglement, master equations, quantum jump formalism. Applications to cavity QED, optical lattices, and Rydberg arrays. Third term: Topics in contemporary research. Possible areas include introduction to ultracold atoms, atomic clocks, searches for fundamental symmetry violations, synthetic quantum matter, and solid state quantum optics platforms. The emphasis will be on reading primary and contemporary literature to understand ongoing experiments. Ph/Aph 137 c not offered 2022-23

## Quantum Hardware and Techniques

This class covers multiple quantum technology platforms and related theoretical techniques, and will provide students with broad knowledge in quantum science and engineering. It will be split into modules covering various topics including solid state quantum bits, topological quantum matter, trapped atoms and ions, applications of near-term quantum computers, superconducting qubits. Topics will alternate from year to year.

## Introduction to Computational Methods for Science and Engineering

A broad introduction to scientific computing using the Python language. Introduction to Python and its packages Matplotlib, Numpy and SciPy. Numerical precision and sources of error. Root-finding and optimization. Numerical differentiation and integration. Introduction to numerical methods for linear systems and eigenvalue problems. Numerical methods for ordinary differential equations. Finite-difference methods for partial differential equations. Discrete Fourier transforms. Introduction to data-driven and machine learning methods. Singular value decomposition. Deep learning with PyTorch and Keras. Students will develop numerical calculations in the homework and in a final project.

## Frontiers of Nonlinear Photonics

This course overviews recent advances in photonics with emphasis on devices and systems that utilize nonlinearities. A wide range of nonlinearities in the classical and quantum regimes is covered, including but not limited to second- and third-order nonlinear susceptibilities, Kerr, Raman, optomechanical, thermal, and multi-photon nonlinearities. A wide range of photonic platforms is also considered ranging from bulk to ultrafast and integrated photonics. The course includes an overview of the concepts as well as review and discussion of recent literature and advances in the field. Not offered 2022-23.

## Topics in Applied Physics

Content will vary from year to year, but at a level suitable for advanced undergraduate or beginning graduate students. Topics are chosen according to the interests of students and staff. Visiting faculty may present portions of this course.

## Plasma Physics

An introduction to the principles of plasma physics. A multitiered theoretical infrastructure will be developed consisting of the Hamilton-Lagrangian theory of charged particle motion in combined electric and magnetic fields, the Vlasov kinetic theory of plasma as a gas of interacting charged particles, the two-fluid model of plasma as interacting electron and ion fluids, and the magnetohydrodynamic model of plasma as an electrically conducting fluid subject to combined magnetic and hydrodynamic forces. This infrastructure will be used to examine waves, transport processes, equilibrium, stability, and topological self-organization. Examples relevant to plasmas in both laboratory (fusion, industrial) and space (magneto-sphere, solar) will be discussed.

## Quantum Electrical Circuits

The course focuses on superconducting electrical systems for quantum computing. Contents begin with reviewing required concepts in microwave engineering, quantum optics, and superconductivity and proceed with deriving quantum mechanical description of superconducting linear circuits, Josephson qubits, and parametric amplifiers. The second part of the course provides an overview of integrated nano-mechanical, piezo-electric, and electro-optic systems and their applications in transducing quantum electrical signals from superconducting qubits.

## Physical Biology of the Cell

Physical models applied to the analysis of biological structures ranging from individual proteins and DNA to entire cells. Topics include the force response of proteins and DNA, models of molecular motors, DNA packing in viruses and eukaryotes, mechanics of membranes, and membrane proteins and cell motility.

## Electronic Materials

An overview of the relationships between chemical, structural, and symmetry properties of prominent material systems with optoelectronic functionalities. Content will be presented through discussions on synthesis and fabrication approaches, core functionalities, and current research frontiers, with a focus on group IV, III-V, and II-VI semiconductors, oxides, two-dimensional materials, dielectrics and mesoscopic systems.

## Inelastic Scattering of Materials, Molecules, and Condensed Matter

Review of Patterson function and memory function for space or time correlations. Van Hove function for correlated dynamics in space and time, especially for materials with thermal energy. Dynamical structure factors for coherent scattering from solids and liquids. Measurements of energy and momentum of dispersive excitations in crystals using neutrons, x-rays, and electrons. Additional topics to be selected from the following list: incoherent inelastic scattering and the thermodynamic partition function, transport of thermal energy, fluctuation-dissipation theorem, quasielastic scattering, sideband information in coherent inelastic scattering, transition from quantum to classical scattering.

## Nanotechnology

This course will explore the techniques and applications of nanofabrication and miniaturization of devices to the smallest scale. It will be focused on the understanding of the technology of miniaturization, its history and present trends towards building devices and structures on the nanometer scale. Technology and instrumentation for nanofabrication as well as future trends will be described. Examples of applications of nanotechnology in the electronics, communications, data storage, sensing and biotechnology will be analyzed. Students will understand the underlying physics and technology, as well as limitations of miniaturization.

## Physics of Semiconductors and Semiconductor Devices

Principles of semiconductor electronic structure, carrier transport properties, and optoelectronic properties relevant to semiconductor device physics. Fundamental performance aspects of basic and advanced semiconductor electronic and optoelectronic devices. Topics include energy band theory, carrier generation and recombination mechanisms, quasi-Fermi levels, carrier drift and diffusion transport, quantum transport.

## Quantum Electronics

Generation, manipulations, propagation, and applications of coherent radiation. The basic theory of the interaction of electromagnetic radiation with resonant atomic transitions. Laser oscillation, important laser media, Gaussian beam modes, the electro-optic effect, nonlinear-optics theory, second harmonic generation, parametric oscillation, stimulated Brillouin and Raman scattering. Other topics include light modulation, diffraction of light by sound, integrated optics, phase conjugate optics, and quantum noise theory. APh/EE 190 ab offered second and third terms. APh/EE 190 c not offered 2022-23.

## Applied Physics Research

Offered to graduate students in applied physics for research or reading. Students should consult their advisers before registering. Graded pass/fail.

## Statistical Mechanics

Overview of probability and statistics, and the Maxwell-Boltzmann distribution. Overview and elements of Quantum Mechanics, degenerate energy states, particles in a box, and energy-state phase space. Statistics of indistinguishable elementary particles, Fermi-Dirac and Bose-Einstein statistics, partition functions, connections with classical thermodynamics, and the Law of Equipartition. Examples from equilibrium in fluids, solid-state physics, and others. Not offered 2022-23.

## Advanced Condensed-Matter Physics

Advanced topics in condensed-matter physics, with emphasis on the effects of interactions, symmetry, and topology in many-body systems. Ph/APh 223 a covers second quantization, Hartree-Fock theory of the electron gas, Mott insulators and quantum magnetism, spin liquids, bosonization, and the integer and fractional quantum Hall effect. Ph/APh 223 b will continue with BCS theory of superconductivity, Ginzburg-Landau theory, elements of unconventional and topological superconductors, theory of superfluidity, Bose-Hubbard model and bosonic Mott insulators, and some aspects of quantum systems with randomness.

## Advanced Topics in Applied Physics

Content will vary from year to year; topics are chosen according to interests of students and staff. Visiting faculty may present portions of this course.

## Computational Solid State Physics and Materials Science

The course will cover first-principles computational methods to study electronic structure, lattice vibrations, optical properties, and charge and heat transport in materials. Topics include: Theory and practice of Density Functional Theory (DFT) and the total-energy pseudopotential method. DFT calculations of total energy, structure, defects, charge density, bandstructures, density of states, ferroelectricity and magnetism. Lattice vibrations using the finite-difference supercell and Density Functional Perturbation Theory (DFPT) methods. Electron-electron interactions, screening, and the GW method. GW bandstructure calculations. Optical properties, excitons, and the GW-Bethe Salpeter equation method. Ab initio Boltzmann transport equation (BTE) for electrons and phonons. Computations of heat and charge transport within the BTE framework. If time permits, selected advanced topics will be covered, including methods to treat vander Waals bonds, spin-orbit coupling, correlated materials, and quantum dynamics. Several laboratories will give students direct experience with running first-principles calculations. Not offered 2022-23.

## Thesis Research in Applied Physics

APh 300 is elected in place of APh 200 when the student has progressed to the point where their research leads directly toward a thesis for the degree of Doctor of Philosophy. Approval of the student's research supervisor and department adviser or registration representative must be obtained before registering. Graded pass/fail.