Course Description and Material
Quantum Optics and Measurements
Mesoscopic Physics and Nanostructures
Understanding new phenomena and predicting new functions in various nano-structured solid state systems require the fundamental theories of spins, excitons and electron transport in such systems. In this course we will study the basic properties of nuclear spins, electron spins, excitons, polaritons and conduction electrons (quasi-particles) in solid states. The lectures are devoted to understanding the basic concepts and theoretical methods of the above topics. Advanced subjects and related experiments are covered by the reading assignment.
Bose-Einstein Condensation and Lasers
After Bose-Einstein condensation of dilute atomic gas systems was realized in 1995, the study of highly degenerate quantum gases has attracted the interest among theoretical and experimental scientists from various fields. More recently an elementary excitation in semiconductor cavity QED systems, exciton polariton, has been investigated extensively from the viewpoints of dynamic condensation and matter-wave lasers. In this lecture we will start with the conventional argument of Bose-Einstein condensation (BEC) at thermal equilibrium. After reviewing the basic properties of the BEC described by the Gross-Pitaevskii equation, we will move on the discussion of the dynamic condensation at quasi-equilibrium condition and matter-wave lasers at non-equilibrium condition, described by the open dissipative Langevin equation or maser equation. Topics covered in the course include the coherence properties of BEC, BEC of non-interacting particles, Bogoliubov theory of interacting bosons, superfluidity and quantized vortices, BCS phase transition, several nontrivial issues of BEC, quantum reservoir theory of matter-wave lasers and potential applications to future quantum information processing.
Fundamentals of Noise Processes
Fundamentals of statistic, Fourier analysis, statistical and quantum mechanics, and linear and nonlinear circuit theory. Thermal, quantum and 1/f noise in resistors, pn junctions, lasers, and parametric amplifiers. Energy efficiency (bit/photon) and spectral efficiency (bit/s/Hz) in coherent and single photon optical communications. Protocols and security in quantum cryptography. Decoherence of qubits in quantum computation.
Quantum Probability and Quantum Information
Applied Physics Core course appropriate for graduate students and advanced undergraduate students with prior knowledge of elementary quantum mechanics, basic probability, and linear algebra. Quantum probability as a generalization of classical probability theory, with implications for information theory and computer science. Generalized quantum measurement theory, conditional expectation, and quantum noise theory with an emphasis on communications and precision measurements. Classical versus quantum correlations, entanglement and Bell's theorem. Introduction to quantum information processing including algorithms, error correction and communication protocols.
Physics of Quantum Information
This course (AP226: Physics of Quantum Information) provides the fundamental concepts, physical pictures, and basic experimental techniques which are essential in the field of quantum information science. The mathematical methods in probabilities and quantum mechanics that have been instructed in AP225 are assumed. The present course focuses on the development of physical pictures and intuition on various quantum phenomena and applications.
Physics of Quantum Computation
Overview of physical qubit encodings in atomic and semiconductor systems; principles of magnetic resonance including double-resonance techniques; decoherence, refocusing and decoupling of spin qubits. Spontaneous emission as a quantum stochastic process; the dressed-state picture and Optical Bloch Equations for atoms interacting with light; introduction to cavity QED and to simple laser cooling. Basic physics of quantum information processing with trapped ions; input-output properties of cavity QED systems; single-photon generation. Quantum dot excitons and semiconductor cavity QED; coherent Raman scattering; all-optical control of electron spin states. Entanglement distribution, purification and swapping; quantum well excitons, cavity polaritons and BEC quantum computation. Cold collisions of gas-phase atoms, optical lattices, and atomic cluster-state generation.