# Applied Physics

Becton Center, 203.432.2210

http://appliedphysics.yale.edu

M.S., M.Phil., Ph.D.

**Chair**

Charles Ahn

**Director of Graduate Studies**

Hui Cao (309 BCT, hui.cao@yale.edu)

**Professors** Charles Ahn, Sean Barrett (*Physics*), Hui Cao, Richard Chang (*Emeritus*), Michel Devoret, Paul Fleury (*Emeritus*), Steven Girvin (*Physics*), Leonid Glazman (*Physics*), Jack Harris (*Physics*), Victor Henrich, Sohrab Ismail-Beigi, Marshall Long (*Mechanical Engineering & Materials Science*), Tso-Ping Ma (*Electrical Engineering*), Simon Mochrie, Daniel Prober, Nicholas Read, Mark Reed (*Electrical Engineering*), Robert Schoelkopf, Ramamurti Shankar (*Physics*), Mitchell Smooke (*Mechanical Engineering &* *Materials Science*), A. Douglas Stone, Hongxing Tang (*Electrical Engineering*), Robert Wheeler (*Emeritus*), Werner Wolf (*Emeritus*)

**Associate Professor** Corey O’Hern (*Mechanical Engineering & Materials Science*)

**Assistant Professors** Michael Choma (*Biomedical Engineering*), Liang Jiang, Owen Miller, Peter Rakich

## Fields of Study

Fields include areas of theoretical and experimental condensed-matter and materials physics, optical and laser physics, quantum engineering, and nanoscale science. Specific programs include surface and interface science, first principles electronic structure methods, photonic materials and devices, complex oxides, magnetic and superconducting artificially engineered systems, quantum computing and superconducting device research, quantum transport and nanotube physics, quantum optics, and random lasers.

## Special Admissions Requirements

The prerequisites for work toward a Ph.D. degree in Applied Physics include a sound undergraduate training in physics and a good mathematical background. The GRE General Test is required, and the Subject Test in Physics is strongly recommended.

## Integrated Graduate Program in Physical and Engineering Biology (PEB)

Students applying to the Ph.D. program in Applied Physics may also apply to be part of the PEB program. See the description under Non-Degree-Granting Programs, Councils, and Research Institutes for course requirements, and http://peb.yale.edu for more information about the benefits of this program and application instructions.

## Special Requirements for the Ph.D. Degree

The student plans a course of study in consultation with faculty advisers (the student’s advisory committee). A minimum of twelve term courses is required. These courses must be full-credit graduate courses with clear technical, scientific, or mathematical focus. These twelve courses must include seven core courses. The first core course satisfies the math requirement; must be fulfilled in the first year; and is met by taking Mathematical Methods of Physics (PHYS 506) (preferred), or, with permission of the DGS, Mathematical Methods I (APHY 500). The remaining six core courses are Solid State Physics I (APHY 548) and II (APHY 549), Quantum Mechanics I (PHYS 508) and II (PHYS 608), Electromagnetic Theory I (PHYS 502), and Statistical Physics I (PHYS 512). It is expected that most of these six core courses will be taken in the first year; no more than two may be taken in the second year. No more than two of the twelve courses can be Special Investigations, and at least two must be outside the area of the dissertation.

Well-prepared students may be able to place out of the seven required core courses after demonstrating equivalent training and competence by passing an exam in the relevant subject.

Students must take Responsible Conduct in Research for Physical Scientists (APHY 590), which discusses ethics and responsible conduct in scientific research and fulfills the requirement stipulated by the National Science Foundation for all students and for all postdoctoral researchers funded by the NSF. Note that APHY 590 may not be used to fulfill the twelve-course requirement.

Each term, the faculty review the overall performance of the student and report their findings to the director of graduate studies (DGS), who determines whether the student may continue toward the Ph.D. degree. By the end of the second term, it is expected that a faculty member has agreed to accept the student as a research assistant. By December 5 of the third year, an area examination must be passed and a written prospectus submitted before dissertation research is begun. These events result in the student’s admission to candidacy. Subsequently, the student will report orally each year to the full advisory committee on progress. When the research is nearing completion, but before the thesis writing has commenced, the full advisory committee will advise the student on the thesis plan. A final oral presentation of the dissertation research is required to be given during term time.

There is no foreign language requirement.

Teaching experience is regarded as an integral part of the graduate training program at Yale University, and all Applied Physics graduate students are required to serve as a Teaching Fellow for one term, typically during year two. Teaching duties normally involve assisting in laboratories or discussion sections and grading papers and are not expected to require more than ten hours per week. Students are not permitted to teach during the first year of study. Students whose advisers experience disruption in funding may require additional support from Yale. In these cases, students will be required to teach for up to an additional two terms, but would not be required to teach more than three terms over their first five years.

If a student was admitted to the program having earned a score of less than 26 on the Speaking Section of the Internet-based TOEFL, the student will be required to take an English as a Second Language (ESL) course each term at Yale until the Graduate School’s Oral English Proficiency standard has been met. This must be achieved by the end of the third year in order for the student to remain in good standing.

## Honors Requirement

Students must meet the Graduate School’s Honors requirement in at least two term courses (excluding Special Investigations) by the end of the second term of full-time study. An extension of one term may be granted at the discretion of the DGS.

## Master’s Degrees

**M.Phil.** See Degree Requirements under Policies and Regulations.

**M.S. (en route to the Ph.D.)** To qualify for the M.S., the student must pass eight term courses; no more than two may be Special Investigations. An average grade of at least High Pass is required, with at least one grade of Honors.

**Terminal Master’s Degree Program** Students may also be admitted directly to a terminal master’s degree program. The requirements are the same as for the M.S. en route to the Ph.D., although there are no core course requirements for students in this program. This program is normally completed in one year, but a part-time program may be spread over as many as four years. Some courses are available in the evening, to suit the needs of students from local industry.

Program materials are available upon request to the Director of Graduate Studies, Department of Applied Physics, Yale University, PO Box 208267, New Haven CT 06520-8267; e-mail, applied.physics@yale.edu; website, http://appliedphysics.yale.edu.

## Courses

**APHY 500b / ENAS 500b, Mathematical Methods I** Paul Van Tassel

A beginning, graduate-level introduction to ordinary and partial differential equations, vector analysis, linear algebra, and complex functions. Laplace transform, series expansion, Fourier transform, and matrix methods are given particular attention. Applications to problems frequently encountered in engineering practice are stressed throughout.

TTh 9am-10:15am

**APHY 506a, Basic Quantum Mechanics** Peter Rakich

Basic concepts and techniques of quantum mechanics essential for solid state physics and quantum electronics. Topics include the Schrödinger treatment of the harmonic oscillator, atoms and molecules and tunneling, matrix methods, and perturbation theory.

TTh 4pm-5:15pm

**APHY 548a / ENAS 850a / PHYS 548a, Solid State Physics I** Victor Henrich

A two-term sequence (with APHY 549) covering the principles underlying the electrical, thermal, magnetic, and optical properties of solids, including crystal structures, phonons, energy bands, semiconductors, Fermi surfaces, magnetic resonance, phase transitions, and superconductivity.

TTh 1pm-2:15pm

**APHY 549b / ENAS 851b / PHYS 549b, Solid State Physics II** Vidvuds Ozolins

A two-term sequence (with APHY 548) covering the principles underlying the electrical, thermal, magnetic, and optical properties of solids, including crystal structures, phonons, energy bands, semiconductors, Fermi surfaces, magnetic resonance, phase transitions, and superconductivity.

TTh 1pm-2:15pm

**APHY 588a, Mathematical Methods in Nanophotonics** Owen Miller

Linear algebra and eigensystems for Maxwell’s equations; group theory; coupled-mode theory; causality, dispersion relations, and sum rules; equivalence and reciprocity principles; perturbation theory; quasi-static EM and plasmonics; metamaterials; computational photonics: spectral, finite-difference, finite-element, and boundary-element approaches; large-scale optimization and design.

MW 11:35am-12:50pm

**APHY 590b / PHYS 590b, Responsible Conduct in Research for Physical Scientists** Staff

Required seminar for all first-year students.

HTBA

**APHY 610b / PHYS 610b, Quantum Many-Body Theory** Yoram Alhassid

Identical particles and second quantization. Electron tunneling and spectral function. General linear response theory. Approximate methods of quantum many-body theory. Dielectric response, screening of long-range interactions, electric conductance, collective modes, and photon absorption spectra. Fermi liquid; Cooper and Stoner instabilities; notions of superconductivity and magnetism. BCS theory, Josephson effect, and Majorana fermions in condensed matter; superconducting qubits. Bose-Einstein condensation; Bogoliubov quasiparticles and solitons.

TTh 11:35am-12:50pm

**APHY 628a / PHYS 628a, Statistical Physics II** Meng Cheng

An advanced course in statistical mechanics. Topics may include mean field theory of and fluctuations at continuous phase transitions; critical phenomena, scaling, and introduction to the renormalization group ideas; topological phase transitions; dynamic correlation functions and linear response theory; quantum phase transitions; superfluid and superconducting phase transitions; cooperative phenomena in low-dimensional systems.

TTh 2:30pm-3:45pm

**APHY 633b / PHYS 633b, Introduction to Superconductivity** Daniel Prober

The fundamentals of superconductivity, including both theoretical understandings of basic mechanism and description of major applications. Topics include historical overview, Ginzburg-Landau (mean field) theory, critical currents and fields of type II superconductors, BCS theory, Josephson junctions and microelectronic and quantum-bit devices, and high-Tc oxide superconductors.

MW 11:35am-12:50pm

**APHY 634a / PHYS 634a, Mesoscopic Physics I** Michel Devoret

Introduction to the physics of nanoscale solid state systems, which are large and disordered enough to be described in terms of simple macroscopic parameters like resistance, capacitance, and inductance, but small and cold enough that effects usually associated with microscopic particles, like quantum-mechanical coherence and/or charge quantization, dominate. Emphasis is placed on transport and noise phenomena in the normal and superconducting regimes.

MW 9am-10:15am

**APHY 675a / PHYS 675a, Principles of Optics with Applications** Hui Cao

Introduction to the principles of optics and electromagnetic wave phenomena with applications to microscopy, optical fibers, laser spectroscopy, nanophotonics, plasmonics, and metamaterials. Topics include propagation of light, reflection and refraction, guiding light, polarization, interference, diffraction, scattering, Fourier optics, and optical coherence.

TTh 11:35am-12:50pm

**APHY 725b / ENAS 725b, Advanced Synchrotron Techniques and Electron Spectroscopy of Materials** Charles Ahn

This course provides descriptions of advanced concepts in synchrotron X-ray and electron-based methodologies for studies of a wide range of materials at atomic and nano-scales. Topics include X-ray and electron interactions with matter, X-ray scattering and diffraction, X-ray spectroscopy and inelastic methods, time-resolved applications, X-ray imaging and microscopy, photo-electron spectroscopy, electron microscopy and spectroscopy, among others. Emphasis is on applying the fundamental knowledge of these advanced methodologies to real-world materials studies in a variety of scientific disciplines.

Th 1:30pm-3:20pm

**APHY 816a / PHYS 816a, Techniques Microwave Measurement** Robert Schoelkopf

An advanced course covering the concepts and techniques of radio-frequency design and their application in making microwave measurements. The course begins with a review of lumped element and transmission line circuits, network analysis, and design of passive elements, including filters and impedance transformers. We continue with a treatment of passive and active components such as couplers, circulators, amplifiers, and modulators. Finally, we employ this understanding for the design of microwave measurement systems and techniques for modulation and signal recovery, to analyze the performance of heterodyne/homodyne receivers and radiometers.

TTh 2:30pm-3:45pm

**APHY 990a or b, Special Investigations** Staff

Faculty-supervised individual projects with emphasis on research, laboratory, or theory. Students must define the scope of the proposed project with the faculty member who has agreed to act as supervisor, and submit a brief abstract to the director of graduate studies for approval.

HTBA