Master of Science in
Physics for Technology

Quantum technology is a field of physics and engineering which exploits quantum phenomena, such as entanglement, superposition and tunneling, for advanced applications, including quantum computing, quantum key distribution, quantum metrology, and information processing. This is a fast emerging field with strong industry potential. In this course, students will be equipped with essential knowledge in the physics and technology of a wide range of quantum devices, including quantum detectors, quantum light sources, quantum number generators, quantum sensors, and quantum computers. Students will also learn skills in the characterization of these devices, including data analysis and interpretation of quantum behavior.

This third undergraduate course in quantum mechanics starts with a recap of the main contents covered by lower-level quantum mechanics courses, in particular time-independent and time-dependent perturbation theory, with more depth. Matlab is introduced to implement the discrete variable representation to solve time-independent Schrodinger equations, and the Split-Operator technique to solve time-dependent Schrodinger equations, with necessary coding from the stratch. This course also covers a number of frontiers topics, including adiabatic theorem, adiabatic control, shortcuts to adiabaticity, geometric phases, density matrix, reduced density matrix, quantum measurement models, quantum master equations, spin-boson model, decoherence, and dynamical decoupling.

Computation is playing an increasingly important role in materials discovery. This course introduces the basic concepts and provides an overview of methods in modern computational condensed matter physics. Major topics to be covered include a brief review on empirical and semi-empirical approaches in electronic structure calculation, density functional theory, methods for solving the Kohn-Sham equation, applications to different types of materials, modelling effects of external fields and transport property. The course is suitable for upper level undergraduate and graduate students who are interested in computer modelling and simulation in condensed matter physics and materials science.

This course introduces students to elements of the physics of crystalline solids. Topics covered include: energy bands of the nearly free electron model, tight binding method, Fermi surfaces and their experimental determination, plasmons, polaritons and polarons, optical processes and excitons. We will also cover superconductivity, dielectrics and ferroelectrics, diamagnetism, paramagnetism, ferromagnetism and antiferromagnetism, and magnetic resonance. This course is targeted at physics majors, and is useful for science and engineering students who already have background knowledge of solid state physics on par with PC3235 Solid State Physics I.

This course presents the fundamentals of statistical mechanics. Starting with the classical and quantum postulates, the three ensembles of Gibbs are derived. The statistical interpretation of thermodynamics then follows. The thermodynamic quantities are obtained in terms of the number of states, partition and grand partition functions. Applications to independent electron systems, with and without magnetic field, and Bose-Einstein condensation are given. The course ends with a brief introduction to phase transitions. This course is targeted at physics students with at least one year of thermal physics.

The objective of this course is to provide students with a background to the important developments in atomic physics over the last 30 years that have now become standard techniques utilized in many laboratories around the world. The lectures provide a detailed description of the interaction of atoms with electromagnetic fields and applies this analysis to a number of applications such as laser spectroscopy, laser cooling, and magnetic and optical trapping. The course will provide students with a comprehensive background to the tools of modern atomic physics

This is an introductory course on the fundamental constituents of matter and their basic interactions; important concepts and principles, recent important experiments, underlying theoretical tools and calculation techniques in elementary particles physics will be expounded. The topics covered are: basic properties of elementary particles and the standard model, relativistic kinematics; symmetries: isospin and SU(3), quark model; parity and CP violation; Feynman diagrams and rules; quantum electrodynamics; cross sections and lifetimes: deep inelastic scattering; and introductory gauge theories and unified models. This course is mainly targeted at physics majors.

This course is an introduction to the quantum description of the electromagnetic field, with a special focus on phenomena at optical frequencies; in short, “quantum optics”. It starts with two introductory chapters: a concise reminder of important facts and devices of classical optics; and a presentation of typical quantum phenomena that have been observed with light (entanglement, violation of Bell’s inequalities, teleportation…). The core of the course is the canonical quantization of the electromagnetic field and the introduction of the corresponding vector space (“Fock space”) and field operators. Then, we present the main families of states (number, thermal, coherent, squeezed) and the most typical measurement techniques (photo-detection, homodyne measurement, first- and second-order coherence, Hong-Ou-\Mandel bunching). The statistical nature of light fields is highlighted. Finally, we present the basic case studies of photon-atom interactions in the full quantum approach: cavity quantum electrodynamics (Janyes-Cummings model), spontaneous decay (Wigner-Weisskopf approach).

This course provides an introduction to the theory of general relativity. The topics covered are: general tensor analysis, the Riemann tensor, the gravitational field equation, the Schwarzschild solution, experimental tests of general relativity, black holes, and Friedmann-Robertson-Walker models of the expanding universe. While this course is mainly targeted at physics majors, it is also suitable for science students with a strong mathematical foundation.

Starting with an introduction to the nuclear physics of stars and the processes of nucleosynthesis, following a brief introduction to nuclear physics. nucleosynthesis via quiescent burning, and the processes that lead to the production of heavy (A>60) elements are covered. The endstages (brown dwarfs, white dwarfs, neutron stars and black holes) are discussed in detail. In the second part of the course, large structures in the universe, are discussed, including star clusters, galaxy structure, and galaxy clustering. The course ends with a discussion of the cosmological scale structure of the universe. This course is a continuation of PC3246 Astrophysics I.

The scope of the course embraces the basic principles of thin-film deposition techniques such as chemical vapor deposition and physical vapor deposition as well as their applications in the microelectronics industry. The basic principles include vacuum technology, gas kinetics, adsorption, surface diffusion and nucleation. These are the fundamental features which determine the film growth and the ultimate film properties. Common thin-film characterization methods which measure film composition and structure as well as mechanical and electrical properties are also covered. This course is for senior physics students with an interest in pursuing a career in industry.

This course provides an introduction to surface physics, its techniques and applications. The topics include: surface tension, surface crystallography, surface physical processes such as relaxation, reconstruction and defects, surface chemical properties, surface segregation, surface electronic structures including surface states, band bending, dipole layer, work function, core-level-shifts, Fermi level pining, plasmon, and surface vibrational properties. Experimental techniques, such as LEED, RHEED, XAS, SEXAFS, XPS, UPS, AES, SIMS and EELS, will be also addressed with examples and applications. This course is targeted at physics or materials science students, who have a basic knowledge of quantum mechanics and solid state physics.

Remote sensing is the acquisition of information about a target from a distance, in particular from satellites, aircrafts, and drones. This course equips students with knowledge to understand, and model, satellite orbital dynamics and global positioning, radiometry, multi-spectral and hyper-spectral imaging of atmosphere, land, and ocean. Students will also learn skills in data processing of real-life satellite images through project work, including the application of radiometric, terrain and atmospheric corrections. The course will also leverage on access to Singapore’s Centre for Remote Imaging, Sensing and Processing.

This course is a follow-up of PC3241 Solid State Devices and is designed for those intending to join the semiconductor industry. The course is intended to give the students an understanding of the physics behind selected devices and that of some of their fabrication technologies. Devices examined are: MOSC & MOSFET, CCD, majority carrier diodes, transferred electron devices, non-volatile memory devices, thyristors and heterojunction devices.

This course covers the principles of statistics in relation to biophysics and bio soft materials. It focuses on: modeling of biomacromolecular structure and statistical complexities; molecular mechanics of biomolecules; statistical models for structural transitions in biopolymers, statistical physical description of structural transitions in macromolecules, simulation of macromolecular structure, structural transitions in polypeptides and proteins; coil-helix transitions; prediction of protein secondary and tertiary structures; statistics of structural transitions in polynucleotides and DNA; modeling of non-regular structures of biomacromolecules. This course is targeted at both physics and non-physics students who already have basic knowledge in physics, thermodynamics and molecular biology.

This course introduces the techniques applied in biophysics and biomolecular electronics. It covers absorption and emission spectroscopy associated with biomolecules; infrared and Raman spectroscopy; magnetic resonance; symmetry of crystal, x-ray crystal structure analysis for macromolecular-structures; principles of light scattering, Rayleigh scattering, scattering from particles comparable to wavelength of radiation, static light scattering, dynamic light scattering, low angle X ray/neutron scattering, scanning probing microscopy; chemical, somatic, and visceral receptors, elements of integrated technologies and applications for biosensors; bio-molecular devices, protein computer. There is a lab component included in this course. This course is targeted at both physics and non-physics students who already have basic knowledge in physics, electronics and molecular biology.

This course introduces advanced mathematical methods that are essential in many areas of theoretical physics. The topics covered are: differentiable manifolds, curved manifolds, tangent and dual spaces, calculus of differential forms, Stokes’ theorem, and applications to electromagnetic theory; symmetries of manifolds, Lie derivatives, Lie groups and algebras, their representations and physical applications. The course is targeted at students who wish to study theoretical physics.

This course is an introduction to advanced topics in quantum theory. Topics include applications in many-body systems; Scattering theory; Approximation methods and their applications. General description of relativistic equations and their solutions; Interaction with electromagnetic fields; Path integral formulation of quantum mechanics. This course is targeted at all students undertaking graduate studies.

This course presents an introduction to phase transitions and fluctuations. For phase transitions, the course starts with the treatment of Landau and mean field. Exact Ising model results are then discussed. Critical exponents are introduced and their relations obtained using the scaling hypothesis and Kadanoff’s scheme. Real space renormalization is then used to show how the critical exponents can be calculated. For fluctuations, Langevin, Fokker-Planck equations will be used. Time dependence and fluctuation dissipation theorem then follow. Brownian motion will be used as an example. This course is targeted at physics graduate students with at least one year of statistical mechanics.

This course aims to give graduate students additional training in the foundations of solid state physics and is intended to prepare them for research work and other graduate coursework courses. Topics to be covered include: translational symmetry and Bloch’s theorem, rotational symmetry and group representation, electron-electron interaction and Hartree-Fock method, pseudopotential and LCAO schemes of energy band calculations, Boltzmann equation and thermoelectric phenomena, optical properties of semiconductors, insulators and metals, origin of ferromagnetism, models of Heisenberg, Stoner and Hubbard, Kondo effect. Berry phase and topological insulators. Students are expected to read from a range of recommended and reference texts, and will be given an opportunity to present their reading as part of the regular lessons.

This course presents special selected topics of current interest. The is flexible and the topic chosen shall be timely and represent the latest trend. For example, for this academic year, the course aims to introduce novel magnetic phenomena in solids with emphasis on physics and applications of spin based electronics or spintronics. The topics covered include general introduction to magnetism, exchange interactions in magnetic solids, band structure, half metals, dilute magnetic semiconductors, spin dependent electrical transport, spin polarization & detection, magneto transport in multilayers, oxides & magnetic semiconductors, magnetic nanostructures and spin injection across various interfaces. Other spin dependent phenomena such as magneto caloric, magneto elastic, magneto impedance and magnetic resonance effects will also be discussed. Application of spintronics in novel devices including GMR read heads, MRAM, spinFET, spin transistor, magnetic sensors for strain & bio-molecule detection will be illustrated. This course is targeted at postgraduate students of physics, engineering and materials science who have basic knowledge in magnetism and solid state physics/devices.

This course covers advanced mathematical methods for obtaining approximate analytical solutions to physical problems. It is designed to help graduate students build the skills necessary to analyse equations, integrals, and series that they encounter in their research. Topics include local analysis of differential equations, asymptotic expansion of integrals, and summation of series.

This course provides an introduction to surface physics for graduate and year-4 undergraduate students major in physics, chemistry and materials science and engineering. It covers the properties of solid surfaces, experimental techniques and applications. The topics include the importance of surfaces in science & technology, surface crystallography and topography, surface energy and stress, surface electronic properties (surface states, work function, band bending and Fermi level pining at semiconductor surface/interface, magnetism), surface phonon and plasmon, adsorption, desorption and reaction on surfaces. The applications of basic surface science knowledge in semiconductor technology, materials growth and processing, heterogeneous catalysis, nanoscience and thin film technology will be demonstrated. Experimental techniques, such as XPS, UPS, AES, LEED, STM, AFM, SIMS, EELS, TPD and vacuum technology, will be addressed with examples and applications. To take this course, students should have a basic knowledge of quantum physics, thermodynamics and solid state physics.

This is an advanced course for students of theoretical physics. The topics covered are: Second quantization and path integral formulation of quantum field theory, Feynman rules for scalar, spinor, and vector fields, renormalization and symmetry, renormalization group, and connection with condensed matter physics.

This course gives an in-depth introduction to the field of Ion Beam Analysis (IBA). IBA methods allow the composition of unknown material systems to be quantitatively determined through the use of ion beams that are produced by small particle accelerators. Theoretical fundamentals will be covered in detail, e.g. Thomas-Fermi statistical model, screened inter-atomic potentials, scattering cross sections, stopping powers etc. Accelerators, detectors and basic pulse processing instrumentation will be discussed. A range of analytical techniques will be discussed in detail: Rutherford Backscattering (RBS), Proton Induced X-ray Emission (PIXE), Elastic Recoil Detection Analysis (ERDA), Nuclear Reaction Analysis NRA, and Accelerator Mass Spectrometry (AMS). Apart from academic content, students will be required to engage in group discussions and work on group research projects that involve performing literature review, producing a conference poster as well as giving an individual oral presentation. Through these discussions and projects, students will gain experience in real-world skills of teamwork, online literature search, academic writing, design of conference posters and giving academic oral presentations.

The course aims to understand Lagrangian mechanics, Hamiltonian mechanics, and basic ideas of nonlinear dynamics and chaos. Topics discussed are: variational principle and Lagrangian mechanics, Hamiltonian mechanics, the Hamiltonian formulation of relativistic mechanics, symplectic approach to canonical transformation, Poisson brackets and other canonical invariants, Liouville theorem, the Hamilton-Jacobi equation, Hamilton’s characteristic function, action-angle variables, integrable systems, transition from a discrete to continuous system, relativistic field theory, Noether’s theorem, Lie groups and group actions, Poisson manifolds, Hamiltonian vector fields, properties of the Hamiltonian fields, conservative chaos, the Poincare surface of section, KAM theorem, Poincare-Birkhoff theorem, Lyapunov exponents, global chaos, effects of double dissipation and fractals.

This advanced course presents the fundamentals of classical electrodynamics in much depth. It covers the following topics: Maxwell’s equations to define conservations laws for energy and momentum, properties of electromagnetic waves, light scattering from interfaces, the concept of optical dispersion, and investigate how waves propagate in bounded structures such as waveguides and transmission lines. In depth investigations of radiation by moving charges, special relativity from Maxwell’s equations such as relativistic length contraction, and covariant formulation of E&M. An understand of applications ranging satellites to fiber optics to transmon qubit would be related to E&M. A good mathematical foundation is required.

This course provides an introduction to the physics of nanostructures. Students taking this course will be introduced methods of fabrication and characterization of nanostructured materials and nanodevices, common types of nanostructures, their properties and applications. More importantly, the underlying physics of the intricate properties and functions of nanostructures will be discussed. The course starts with a brief review of relevant topics of quantum mechanics and solid state physics in reduced dimensions. Common techniques for nanostructure fabrication and characterization are introduced next. Transport in low-dimensional systems, optoelectronics of nanostructures, nanotubes and nanowires, clusters and nanocrystallites are discussed. Finally, magnetic nanostructures, and molecular electronics (optional), will be covered. This course is designed for postgraduate students who are interested in nanoscience and nanotechnology research and applications. Understanding the physics of nanostructures will allow the students to better appreciate the interesting properties and their tunability of nanostructures, understand the operating principles of nanodevices, and to design and optimize nanostructures for different applications.

This course discusses the molecules in cells and the physics behind their functions. At the core is the understanding of biomolecular conformations, structural stability and interactions under physical constraints such as force, geometry and temperature, by theory and state-of-art experimental technologies. Besides homework and quiz, projects are an important component of assignments. Multiple projects are provided for students to choose, which may involve numerical/Monte Carlo simulation of biomolecular conformations, analysis of experimental data, or investigation of the DNA micromechanics by analyzing DNA conformations. This course is targeted at students who have a basic knowledge in general physics and thermodynamics.

Covers computational techniques for the solution of problems arising in physics and engineering, with an emphasis on molecular simulation and modelling. Topics will be from the text, “Numerical Recipes”, Press et al, supplemented with examples in materials and condensed matter physics. This course insures that graduate students intending to do research in computational physics will have sufficient background in computational methods and programming experience.

This course introduces from an experimentalists point of view to the modern world of ultracold quantum gases that so much changed atomic physics in the past two decades. The lectures present the basic experimental methods of laser cooling, magnetic and optical trapping, and evaporative cooling that produce matter near absolute zero temperature. We then discuss basic effects like Bose-Einstein condensation and Pauli pressure. Further, selected research examples are presented that give insight to some of the many close relations between quantum matter designed in many labs worldwide and other physical systems found in the range of quantum information science, condensed matter physics, metrology, nuclear physics, and astronomy. Solid background in quantum mechanics, atomic physics, and statistical mechanics is desired.

This course will introduce a phenomenological description of superconducting materials and their applications to modern technologies. For this, the course will cover bulk and thin-film superconducting materials and introduce the Josephson junction, which is the basis of many superconducting devices. From this, we will introduce the main parameters that are relevant to the design of modern superconducting devices, namely resonators, qubits, SQUIDs and photodetectors. Finally, we will cover how the choice of materials and geometry influences the functioning of these devices.

This course will introduce modern theoretical concepts and methods of quantum many-body physics. It will cover tensor networks, a graphical framework for manipulating and classifying quantum many-body states based on quantum entanglement. It will discuss bounds on quantum information propagation, and how they constrain the behavior of correlation functions of phases of matter. It will also introduce quantum circuit models as testbeds to probe collective dynamical phenomena like thermalization and emergence of random matrix theory. This course is relevant for understanding and describing the novel physical regimes realized by emerging quantum simulator and quantum computational technologies.

The course provides an introduction to quantum information and quantum computation. In addition to physics majors, the course addresses students with a good background in discrete mathematics or computer science.The following topics will be covered: (1) Introduction: a brief review of basic notions of information science (Shannon entropy, channel capacity) and of basic quantum kinematics with emphasis on the description of multi-qubit systems and their discrete dynamics. (2) Quantum information: Entanglement and its numerical measures, separability of multi-partite states, quantum channels, standard protocols for quantum cryptography and entanglement purification, physical implementations. And (3) Quantum computation: single-qubit gates, two-qubit gates and their physical realization in optical networks, ion traps, quantum dots, Universality theorem, quantum networks and their design, simple quantum algorithms (Jozsa-Deutsch decision algorithm, Grover search algorithm, Shor factorization algorithm). The course is tightly integrated with IBM quantum computer hands-on experience via IBM Q Experience cloud services. Students will learn fundamentals of Qiskit, a modern and rapidly developing quantum computer programming language, by directly implementing concepts learnt in the classroom.

Functional electronic devices are an essential part of modern technology, and they are used in a wide range of applications, including communication systems, computers, medical devices, and consumer electronics. In this course, we will discuss the working principles of a variety of functional electronic devices, such as transistors, diodes, and different photodetectors. We will focus on the physical concepts behind their work and how those devices can be built and/or improved using novel artificial materials such as van der Waals heterostructures and 2D materials.

The course is intended to provide detailed treatment of the principles of lasers and working knowledge of major optical techniques used in manipulating laser spatial mode properties and their temporal and spectral characteristics. The topics being covered include laser beams, laser theory, laser survey, modulation techniques, non-linear optics, and fiber optics. This is a graduate-level course and is to prepare students for using lasers and related techniques in either academic research or industrial R&D. Students will acquire a solid understanding of laser principles, will learn characteristics and applications of various types of lasers, and will become familiar with major techniques on manipulating laser outputs based on electro-optic, acousto-optic, and non-linear effects for different kinds of applications. At the end of the course, students will be equipped with sufficient theoretical and working knowledge to effectively apply commercially available laser instruments in their research as well as build from basic optical components their own coherent light sources where lasers for particular experiments and applications may not be readily available. This course should be relevant to any student who is or will be working in R&D areas involving laser-related techniques.

This course exposes graduate students to examples of Machine Learning and Data Science that are commonly encountered in data analyses in the Physical Sciences (e.g. optics, statistical physics, condensed matter, biological physics). We will take a hands-on approach to implementing, training, and evaluating machine learning models. This course will be taught in the Python programming language. Prior experience in any programming language will be helpful.

In the age of big scientific data, Bayesian statistical methods and machine-learning techniques are becoming a vital part of the modern scientist’s toolkit. This course provides a graduate-level introduction to the two related fields, with equal emphasis on both. Key topics for the first part include: fundamentals of probability and inference, hierarchical modelling, model validation and comparison, and Monte Carlo methods; for the second part, they include: classification and regression, kernel methods, variational methods, and neural networks. The course will be largely theoretically oriented, with the occasional computational component.

Much of our real world data are manifestations or measurements of their underlying complex interactions. Hence, modelling and analysis of the underlying complex systems can reveal understandings and predictions that complement black-box machine learning tools. This course will cover the basic concepts and tools in analysing complex systems and simulation models, and more importantly why and when we need such white-box tools derived from statistical physics. Certain key concepts in complexity science will be intrudcued. It will also provide hands-on experience with system analysis and imulation modelling in Python.

This course covers the physical principles behind a wide variety of nano/micromachines and active matters involving these small energy-consuming building blocks. Specifically, the course covers molecular motors, nano/micro-robots, microswimmers, related active matters, and applications (e.g., actuation, precise control, chemistry, biotechnology, precision medicine, etc.). This course aims at a unified physical understanding, mainly based on stochastic thermodynamics, fluid dynamics at low Reynolds numbers, and active soft matter theories. The course focuses on artificial systems but also touches biological counterparts. Advanced design and fabrication methods like DNA nanotechnology will be discussed too.

In this course, the physics behind a wide spectrum of modern sensors is covered, capturing basic properties like temperature, distance, forces, pressure, magnetic fields, and light that are relevant in everyday applications, as well as more advanced sensors for acceleration and rotation that became commonplace in mobile devices for orientation and navigation. Furthermore, advanced sensing techniques used in microbalances, particle detection and advanced optical and acoustic sensing techniques will be discussed.

This course introduces important mathematical methods for the solution of a variety of mathematical problems in physics. The following topics are covered: functions of a complex variable, singularities and residues, contour integration; calculus of variations; transformations in physics, symmetries and group theory, discrete groups, group representations and their applications in physics; tensor analysis, application to classical mechanics, electrodynamics, and relativity.

This course introduces the basic building blocks for the theory of quantum measurements. With this detailed knowledge, a rigorous discussion of measurement models, the von Neumann model in particular, error-disturbance relations, incompatibility of measurements, and sequential measurements becomes possible. During the introduction of these concepts, the students will also acquire knowledge in operational quantum theory as well as become fluent in the mathematical framework of Hilbert space quantum mechanics. After this course, the students will master and be knowledgeable in the mathematics and operational meaning of the basic concepts of quantum measurements. This knowledge will make them able to understand key quantum physical concepts like uncertainty and error and disturbance in measurements.

In this course, basic electronic techniques related to quantum technologies are introduced at a level that allows students to analyze, design, build and modify electronics encountered in experimental work on quantum technologies. It covers basic circuit design, with a focus on techniques related to typical signal conditioning and processing tasks encountered in experiments and application engineering involving quantum systems like single photon detection and generation, atom and ion traps, laser spectroscopy, optical modulators and some radio-frequency techniques to drive atomic transitions, and electronic techniques at cryogenic temperatures.