Department of Physics, Unit Catalogue 2010/11 |
PH40084: Advanced quantum theory |
 Credits:
| 6 |
| Level:
| Masters |
| Period: | This unit is available in... |
| Semester 2 |
| Assessment:
| EX 100% |
| Supplementary Assessment: | Like-for-like reassessment (where allowed by programme regulations) |
| Requisites:
| Before taking this unit you must take PH30030 |
| Description:
| Aims: The aim of this unit is to increase the breadth and depth of students' knowledge and understanding of quantum physics, in both fundamental aspects of quantum mechanics and modern applications of quantum theory. Learning Outcomes: After taking this unit the student should be able to: * explain in detail the salient differences between classical physics and quantum physics; * demonstrate an in-depth understanding of the realm of quantum optics and its major applications and frontline research; * give a mathematical description of the quantum principles of vector states, Hilbert space and quantum interference; * use and apply Dirac formalism to light-matter optical phenomena; * explain optical absorption and refraction using a quantum framework; * outline and critically assess the following major applications of coherent light-matter interactions; Rabi oscillations, Ramsey interference, electromagnetically induced transparency and laser cooling; * discuss the principles of quantum cryptography and computing. Skills: Numeracy T/F A, Problem Solving T/F A. Content: Relativistic quantum mechanics (7 hours): Principle of inertia, Lorentz transformation, Klein-Gordon equation, Dirac equation, spinors, addition of relativistic velocities, Lorentz boost of spinors, free particle solutions, interaction with the electromagnetic field, non-relativistic limit of Dirac's equation, origin of the electron spin, spin-orbit interaction, solutions of Dirac's equation for the hydrogen atom. The physics of high magnetic fields (3 hours): Landau quantization, 2D and 3D density of states in a magnetic field, Shubnikov de Haas and van Alphen effects, oscillations of the Fermi level, Quantum Hall Effect. Spin in electric and magnetic fields (2 hours): Larmor precession and 4π periodicity of the spin phase, neutron interference experiments, spin resonance, Rabi oscillations, Rashba Hamiltonian, Spin transistor, Aharonov Casher and Aharonov-Bohm effects. Quantum optics (10 hours): Phenomenology of optical processes (e.g. absorption, emission and scattering). Quantum mechanical principles and Dirac notations. Semi-classical interaction of radiation with matter, Hamiltonian of 2-level and 3-level atoms in electromagnetic field. Evolution of a quantum system, Rabi oscillations and quantum interference. Applications: Electromagnetically induced transparency and coherent population trapping. Lasing without inversion. Ramsey interference. Opto-mechanical effect: laser cooling. Quantum Information (2 hours): Quantum cryptography and computing. |