Applied Physics
Becton Center, 203.432.2210
http://appliedphysics.yale.edu
M.S., M.Phil., Ph.D.
Chair
Sohrab Ismail-Beigi
Director of Graduate Studies
Daniel Prober (BCT 417; 203.432.4280; daniel.prober@yale.edu)
Professors Charles Ahn, Sean Barrett (Physics), Hui Cao, Michel Devoret, Paul Fleury (Emeritus), Steven Girvin (Physics), Leonid Glazman (Physics), Jack Harris (Physics), Victor Henrich (Emeritus), Sohrab Ismail-Beigi, Simon Mochrie, Corey O’Hern (Mechanical Engineering and Materials Science), Vidvuds Ozolins, Daniel Prober, Peter Rakich, Nicholas Read, Robert Schoelkopf, John Schotland, Ramamurti Shankar (Physics), A. Douglas Stone, Hong Tang (Electrical Engineering), Robert Wheeler (Emeritus), Werner Wolf (Emeritus)
Associate Professors Michael Hatridge, Owen Miller
Assistant Professors Meng Cheng, Eduardo da Silva Neto, Yongshan Ding, Yu He, Mengxia Liu, Shruti Puri, Diana Qiu, Christina Rodriguez, John Sous, Cong Su, Logan Wright
Fields of Study
Fields include areas of theoretical and experimental condensed-matter and materials physics, optical and laser physics, quantum science, quantum information, 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, quantum optics, and random lasers.
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 requirements for a Ph.D. in applied physics include passing at least nine course units. Courses such as Dissertation Research, Master’s Thesis, or seminars do not count towards the nine-course requirement, but two terms of Special Investigation courses are acceptable. Other than the Special Investigation courses, the courses counting toward the nine-course requirement must be full-credit graduate courses. Courses outside of those identified as acceptable in the departmental degree guidelines must have a clear technical, scientific, or mathematical focus that is related to applied physics in the judgement of the student’s adviser and the DGS.
Within the nine-course requirement, students must pass the three core courses, unless they are substituted or waived with approval by the DGS. The three core courses are Electromagnetic Theory I (PHYS 5020) or Theory of Electromagnetic Waves, Radiation, and Scattering (APHY 5220), Quantum Mechanics I (PHYS 5080), and Statistical Physics I (PHYS 5120).
Students must also take the Research in Applied Physics Seminar (APHY 5760) and the Responsible Conduct in Research for Physical Scientists Seminar (APHY 5900).
Students typically complete most of their course requirements in the first year, and sufficient progress toward meeting the course requirements is necessary to remain in good standing in the program. Note that the required courses are just the minimum, and students are strongly encouraged to consult with their adviser about taking additional courses that are needed to facilitate their dissertation research.
By the end of the first year, students must find a research adviser who is willing to supervise a project that is consonant with the research program of that faculty. Research advisers must have an appointment in the graduate school and be engaged in research that falls broadly within the subject of applied physics, although they do not need to be members of the department’s faculty.
After completing coursework, the next step toward a degree is admission to candidacy, indicating that the student is prepared to do original and independent research. To be admitted to candidacy, students must submit a written research prospectus and pass an area examination early in their third year. If a student has faced unusual circumstances, this deadline can be extended, with the support of the research adviser and approval of the DGS.
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 teaching fellows for two terms, typically during years two and three. Teaching duties normally involve assisting in laboratories or discussion sections and grading papers. Teaching duties are not expected to require more than ten hours per week. Students are not permitted to teach during the first year of study. Students who require additional support from the graduate school must teach for up to an additional two terms, if needed.
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
In order to remain in good standing in the program, students are expected make steady progress in meeting their course requirements and to obtain Honors grades in at least two full-term courses by the end of their fourth term of full-time study. Courses such as Master’s Thesis, seminars, or Special Investigations cannot be used to fulfill the requirement for two Honors grades. An extension may be granted on a case-by-case basis at the discretion of the DGS, in consultation with the student’s adviser. Students are also expected to maintain an average grade of High Pass during their time at Yale, following the averaging methodology determined by the graduate school.
Master’s Degrees
M.Phil. See Degree Requirements under Policies and Regulations.
M.S. Students may apply for a terminal master’s degree in applied physics. For the M.S. degree, the requirements are that the student pass eight full-credit graduate courses (not seminars), typically courses similar to those that would meet the course requirements for the Ph.D. No more than two of the courses may be Special Investigations. Students may substitute other graduate courses with a clear technical, scientific, or mathematical focus that is related to applied physics in the judgement of the student’s adviser and the DGS. An average grade of at least High Pass is required, with at least one grade of Honors. This terminal degree program is normally completed in one year. Doctoral students who withdraw from the Ph.D. program may be eligible to receive the M.S. if they have met the above requirements and have not already received the M.Phil.
Program materials are available upon e-mail request to applied.physics@yale.edu, or at http://appliedphysics.yale.edu.
Courses
APHY 5060a, Basic Quantum Mechanics John Sous
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 2:30pm-3:45pm
APHY 5220b, Theory of Electromagnetic Waves, Radiation, and Scattering A Douglas Stone
This is a graduate-level course on electromagnetic theory, focusing on electromagnetic wave phenomena in a variety of contexts. Electrostatics and magnetostatics are reviewed briefly and then the full time-dependent Maxwell equations are studied to derive the fundamentals of wave propagation, the wave equation, plane waves, polarization, energy and momentum flow in EM waves, conservation laws, gauge transformation, and Green functions for the wave equations. Dielectric media and Fresnel reflection and refraction, total internal reflection, group velocity, wave packets and dispersion. Beam propagation and gaussian optics, optical birefringence. Waves in confined structures, waveguides, optical fibers, resonant cavities. Radiating sources, electric and magnetic dipolar radiation, multipolar radiation, near and far-field solutions, radiating antennas. Scattering theory, scalar and vector diffraction, Rayleigh scattering, scattering matrix and temporal coupled mode theory, scattering resonances, multiple scattering, systems with gain and lasing. Time permitting: relativistic kinematics, covariance of Maxwell's equations, Lorentz transformation of electric and magnetic fields, relativistic mechanics of charged particles. Prerequisites: an undergraduate course on electricity and magnetism and graduate-level vector calculus and differential equations.
TTh 1pm-2:15pm
APHY 5260a, Explorations in Physics and Computation Logan Wright
Computation has taken on an important, often central, role in both the practice and conception of physical science and engineering physics. This relationship is intricate and multifaceted, including computation for physics, computation with physics, and computation as a lens through which to understand physical processes. This course takes a more or less random walk within this space, surveying ideas and technologies that either apply computation to physics, that understand physical phenomena through the lens of computation, or that use physics to perform computation. Given the extent to which machine learning methods are currently revolutionizing this space of ideas, we focus somewhat more on topics related to modern machine learning, as opposed to other sorts of algorithms and computation. Since it is covered more deeply in other courses, we do not extensively cover error-corrected/fault tolerant quantum information processing, but we do frequently consider quantum physics. The course does not provide a systematic overview of any one topic, but rather a sampling of ideas and concepts relevant to modern research challenges. It is therefore intended for graduate students in early years of their program or research-inclined senior undergraduate students contemplating a research career. As a result, in addition to the scientific topics at hand, key learning goals include the basics of literature review, presentation, collegial criticism (peer review), and synthesizing new research ideas. Evaluation is primarily through two projects, one a lecture reviewing a topic area of interest and one a tutorial notebook providing worked numerical examples/code meant to develop or introduce a concept. Prior experience with Python is ideal, but can be learned as part of the coursework. Students should ideally be familiar with quantum mechanics, including density matrices and some phase-space methods, but this applies to only small fraction of the course. The course is primarily a survey-level overview of many topics, not a deep dive into any one topic. As a result, students who have extensive background on many of the topics described in the syllabus are welcome to participate but should speak with the instructor beforehand so we can determine if their learning goals can be met.
MW 11:35am-12:50pm
APHY 5480a / PHYS 5480a, Solid State Physics I Yu He
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.
HTBA
APHY 5490b / ENAS 851 / PHYS 5490b, 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.
HTBA
APHY 5750b, Physics of AI John Sous
A introduction to current research in AI from a physics perspective, i.e. one that emphasizes the mechanisms through which various AI architectures learn. Topics include, linear regression, neural nets, transformers, diffusion, etc. Prerequisites: linear algebra, calculus.
M 1:30pm-3:20pm
APHY 5760a, Topics in Applied Physics Research Peter Rakich
The course introduces the fundamentals of applied physics research to graduate students in the Department of Applied Physics in order to introduce them to resources and opportunities for research activities. The content of the class includes overview presentations from faculty and other senior members of the department and related departments about their research and their career trajectories. The class also includes presentations from campus experts who offer important services that support Applied Physics graduate students in their successful degree completion.
F 1:30pm-3:20pm
APHY 5900b / PHYS 5900b, Responsible Conduct in Research for Physical Scientists Staff
A review and discussion of best practices of conduct in research including scientific integrity and misconduct; mentorship; data management; and diversity, equity, and inclusion in science.
F 10am-11:15am
APHY 6070b, Modern Topics in Optics and Quantum Electronics Peter Rakich
This course provides a survey of modern topics involving integrated photonics, optomechanics, nonlinear optics, and laser physics for students interested in contemporary experimental optics research. Subjects include nonlinear wave phenomena, optomechanical interactions, phonon physics, light scattering, light emission and detection, cavities, systems of cavities, traveling-wave devices and interactions, perturbation theory, reciprocal and nonreciprocal systems, parametric interactions, laser oscillators and related technologies. Students are encouraged to explore these and related research topics through independent study and classroom presentations.
MW 4pm-5:15pm
APHY 6100a / PHYS 6100a, 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 6280a / PHYS 6120a, Statistical Physics II Nicholas Read
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 6330b / PHYS 6330b, Introduction to Superconductivity Yu He
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 6600a / PHYS 6010a, Quantum Information and Computation Shruti Puri
This course focuses on the theory of quantum information and computation. We cover the following tentative list of topics: overview of postulates of quantum mechanics and measurements, quantum circuits, physical implementation of quantum operations, introduction to computational complexity, quantum algorithms (DJ, Shor’s, Grover’s, and others as time permits), decoherence and noisy quantum channels, quantum error-correction and fault-tolerance, stabilizer formalism, error-correcting codes (Shor, Steane, surface-code, and others as time permits), quantum key distribution, quantum Shannon theory, entropy, and data compression.
TTh 11:35am-12:50pm
APHY 6610b, Fault Tolerance and Quantum Error Correction Aleksander Kubica
This course focuses on the theory of fault tolerance and quantum error correction. We cover the following tentative list of topics: criteria for quantum error correction, classical linear codes and quantum CSS codes, stabilizer codes, existence of good codes, concatenated codes, threshold theorems, topological codes, decoding algorithms, statistical-mechanical mappings, logical gates and fault-tolerant quantum computing, resource overheads, limitations and no-go theorems, quantum LDPC codes, approximate quantum error correction, experimental realizations of quantum error correction, and open research problems. Prerequisite: APHY 660 or CPSC 547 (or equivalent).
W 3:30pm-5:20pm
APHY 6700a, Statistical Methods with Applications in Science and Finance Sohrab Ismail-Beigi
Introduction to key methods in statistical physics with examples drawn principally from the sciences (physics, chemistry, astronomy, statistics, biology) as well as added examples from finance. Students learn the fundamentals of Monte Carlo, stochastic random walks, and analysis of covariance analytically as well as via numerical exercises. Prerequisites: ENAS 1940, MATH 2220, ENAS 1300 or equivalents.
HTBA
APHY 6750a / PHYS 6750a, 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.
HTBA
APHY 6760a / PHYS 6760a, Introduction to Light-Matter Interactions Peter Rakich
Optical properties of materials and a variety of coherent light-matter interactions are explored through the classical and quantum treatments. The role of electronic, phononic, and plasmonic interactions in shaping the optical properties of materials is examined using generalized quantum and classical coupled-mode theories. The dynamic response of media to strain, magnetic, and electric fields is also treated. Modern topics are explored, including optical forces, photonic crystals, and metamaterials; multi-photon absorption; and parametric processes resulting from electronic, optomechanical, and Raman interactions.
MW 4pm-5:15pm
APHY 6790b / PHYS 6790b, Nonlinear Optics and Lasers Logan Wright
Properties and origins of the nonlinear susceptibility; Sum-freq, diff-freq and 2nd-harmonic generation; Intensity-dependent refractive index; Optical phase conjugation; Self-focusing, self-phase modulation, solitons; Stimulated light scattering; Fixed points, bifurcations; Amplification; Rate equations; Relaxation oscillations, frequency pulling; Hole burning; Q-switching; Semiconductor and DFB lasers; Mode-locking; Injection-locking; Intense-field NLO and QM laser theory (time permitting)
MW 1pm-2:15pm
APHY 7260a, Advanced Thin Film Synthesis and Characterization Charles Ahn
This course covers principles of thin film growth and characterization for advanced electronic and quantum materials applications. Topics include physical vapor deposition and related techniques for achieving state-of-the-art thin films and heterostructures, along with atomic-scale and spectroscopic characterization of thin film structures, including scanning probe microscopies, electron microscopies, diffraction techniques, and photon-based spectroscopies.
MW 1pm-2:15pm
APHY 7270b, Circuit Quantum Electrodynamics Michael Hatridge and Robert Schoelkopf
Circuit quantum electrodynamics, or circuit QED, is the field of quantum optics with microwave photons, and is the basis of most solid-state quantum computing technologies. In the microwave domain, we can engineer the properties of “artificial atoms” constructed from circuits containing Josephson junctions and couple them strongly to stationary photons trapped in a cavity or resonant circuit and to traveling photons in a waveguide or transmission line. With this approach, one can access regions of strong coupling between “light” and “matter” that are not accessible in atomic physics. This course is an introduction to the concepts and techniques of circuit QED, aimed for the beginning graduate student or advanced undergraduate with a solid background in classical electricity and magnetism and also basic quantum mechanics. The course is intended to provide an important base of knowledge that can prepare the student for research in quantum information processing with superconducting circuits. Topics to be covered include the basics of superconducting qubits, the Jaynes-Cummings model and the strong dispersive regime, and the use of light-matter interactions for measurement, control, and quantum computing with quantum circuits. Extra work for graduate students: The last homework set is optional for undergrads and required for grads. Prerequisites: one semester QM and one semester E&M at advanced undergrad or higher.
TTh 2:30pm-3:45pm