Prerequisites: phys UN2601 or phys un2802 Primarily for junior and senior physics majors; other majors must obtain the instructors permission. Each experiment is chosen by the student in consultation with the instructor. Each section meets one afternoon per week, with registration in each section limited by the laboratory capacity. Experiments (classical and modern) cover topics in electricity, magnetism, optics, atomic physics, and nuclear physics.
Prerequisites: PHYS UN3003 or PHYS UN3007 May be taken before or concurrently with this course. A sequence of experiments in solid-state electronics, with introductory lectures.
The “Quantum Simulation and Computing Lab” will give students hands-on experience in quantum optics, quantum simulation and quantum computing. The course combines lectures, tutorials, and two lab sections. In one lab section, students will do experiments with entangled photons. In the second lab section, students will program quantum computers and run algorithms on them using the IBM Qiskit platform.
The course starts with a recap of linear algebra and quantum mechanics, followed by an introduction to quantum optics and quantum information. Two-level systems, Bloch sphere, quantum gates, and elementary quantum algorithms will be discussed. Quantum teleportation and quantum key distribution will be introduced as applications of entanglement. The lecture content will be directly applied in experiments with entangled photons. In the following, state-of-the-art quantum algorithms will be discussed, related to cutting-edge research results in quantum computing. This includes quantum Fourier transform, quantum simulation of the Schroedinger equation, and the variational quantum eigensolver (VQE) algorithm. During the course students will do one experimental project with entangled photons and one quantum programming project. Students will be guided to implement a quantum algorithm of their choice and run it on a quantum computer (IBM, IonQ, QuEra).
Prerequisites: the written permission of the faculty member who agrees to act as supervisor, and the director of undergraduate studies permission. Readings in a selected field of physics under the supervision of a faculty member. Written reports and periodic conferences with the instructor.
Prerequisites: Permission of the departmental representative required. For specially selected students, the opportunity to do a research problem in contemporary physics under the supervision of a faculty member. Each year several juniors are chosen in the spring to carry out such a project beginning in the autumn term. A detailed report on the research is presented by the student when the project is complete.
Prerequisites: differential and integral calculus, differential equations, and PHYS UN3003 or the equivalent. Lagranges formulation of mechanics, calculus of variations and the Action Principle, Hamiltons formulation of mechanics, rigid body motion, Euler angles, continuum mechanics, introduction to chaotic dynamics.
Prerequisites: PHYS GU4021 and PHYS GU4023 or the equivalent. Introduction to solid-state physics: crystal structures, properties of periodic lattices, electrons in metals, band structure, transport properties, semiconductors, magnetism, and superconductivity.
Prerequisites: PHYS GU4021. Formulation of quantum mechanics in terms of state vectors and linear operators, three-dimensional spherically symmetric potentials, the theory of angular momentum and spin, time-independent and time-dependent perturbation theory, scattering theory, and identical particles. Selected phenomena from atomic physics, nuclear physics, and elementary particle physics are described and then interpreted using quantum mechanical models.
Prerequisites: PHYS UN3003 and PHYS UN3007 or the equivalent. Tensor algebra, tensor analysis, introduction to Riemann geometry. Motion of particles, fluid, and fields in curved spacetime. Einstein equation. Schwarzschild solution; test-particle orbits and light bending. Introduction to black holes, gravitational waves, and cosmological models.
This course is the second course of a two-semester sequence that provides a rigorous, master's-level foundation in quantum mechanics, uniquely structured for an interdisciplinary cohort of physicists, engineers, and computer scientists. The course pivots from isolated systems covered in the first course to the realistic, noisy environments that define modern quantum technology. Students will master the density matrix formalism, the physics of open quantum systems, the thermodynamics of decoherence, and the Lindblad master equation to understand exactly how the physical environment degrades stored quantum information. Rather than treating errors as abstract mathematical operations, modern quantum hardware platforms—including superconducting transmons, dynamically reconfigurable Rydberg atom arrays, and trapped ions—will be analyzed to study the real-world physics of quantum memory and signal transmission. We will start by asking
“What happens when two quantum systems interact?”
(entanglement). Then we will ask,
“What happens if we can only look at one of them?”
(density matrix and partial trace). Finally, we will ask,
“What happens if the second system is the entire rest of the universe?”
(open systems, decoherence, and the Lindblad equation). Ultimately, this sequence equips students with the conceptual maturity required to engage with state-of-the-art quantum hardware, experimental device physics, and condensed matter research.
The “Quantum Simulation and Computing Lab” will give students in the Quantum Masters program hands-on experience in quantum optics, quantum simulation and quantum computing. The course combines lectures, tutorials, and two lab sections. In one lab section, students will do experiments with entangled photons. In the second lab section, students will program quantum computers and run algorithms on them using the IBM Qiskit platform.
The course starts with a recap of linear algebra and quantum mechanics, followed by an introduction to quantum optics and quantum information. Two-level systems, Bloch sphere, quantum gates, and elementary quantum algorithms will be discussed. Quantum teleportation and quantum key distribution will be introduced as applications of entanglement. The lecture content will be directly applied in experiments with entangled photons. In the following, state-of-the-art quantum algorithms will be discussed, related to cutting-edge research results in quantum computing. This includes quantum Fourier transform, quantum simulation of the Schroedinger equation, and the variational quantum eigensolver (VQE) algorithm. During the course students will do one experimental project with entangled photons and one quantum programming project. Students will be guided to implement a quantum algorithm of their choice and run it on a quantum computer (IBM, IonQ, QuEra).
Prerequisites: PHYS W4021-W4022, or their equivalents. Applications to atoms and molecules, including Thomas-Fermi and Hartree-Fock atoms; interaction of radiation with matter; collision theory; second quantization.
Lagrangian density formalism of Lorentz scalar, Dirac and Weyl spinor, and vector gauge fields. Action variations, symmetries, conservation laws. Canonical quantization, Fock space. Interacting local fields, temporal evolution. Wicks theorem, propagators, and vertex functions, Feynman rules and diagrams. Scattering S matrix examples with tree level amplitudes. Path quantization. 1-loop intro to renormalization.
Course Summary: the quantum many-body problem and its the conceptual formulation in terms of functional integrals, the basics of perturbative calculations at both zero and non-zero temperature, mean field theory and its interpretation as a saddle point of a functional integral, fluctuations including collective modes, the field theory of linear response and transport calculations and the new features associated with nonequilibrium physics.
Quantum optics, including: quantiziation of the electromagnetic field, open quantum systems, light-matter interaction, coherent control, collective phenomena, measurement theory and decoherence, and applications in quantum information science.
Prerequisites: PHYS E6081 or the instructors permission. Semiclassical and quantum mechanical electron dynamics and conduction; dielectric properties of insulators; semiconductors; defects; magnetism; superconductivity; low-dimensional structures; soft matter.
Prerequisites: PHYS G6092. This course will study the classical field theories used in electromagnetism, fluid dynamics, plasma physics, and elastic solid dynamics. General field theoretic concepts will be discussed, including the action, symmetries, conservation laws, and dissipation. In addition, classical field equations will be analyzed from the viewpoint of macroscopic averaging and small-parameter expansions of the fundamental microscopic dynamics. The course will also investigate the production and propagation of linear and nonlinear waves; with topics including linearized small-amplitude waves, ordinary and extraordinary waves, waves in a plasma, surface waves, nonlinear optics, wave-wave mixing, solitons, shock waves, and turbulence.
Prerequisites: Prerequisites; GR6011, another introductory astrophysics course or the instructor's permission; basic General Relativity or familiarity with tensors in flat space. A continuation of G6011. Likely topics include shocks and their application to supernovae; pulsar wind nebulae; atomic physics of astrophysical plasmas; accretion onto magnetized neutron stars and white dwarfs; thick accretion disks, non-thermal X-ray generation processes; particle acceleration and propagation; gravitational wave radiation; magnetars.
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Advanced topics at the discretion of the instructor, including string theory, supersymmetry and other aspects of beyond-standard-model physics.
Prerequisites: PHYS G6037-G6038. Basic aspects of particle physics, focusing on the Standard Model.