Quantum Optics

Lecture

Thomas Gasenzer

Wednesday, 14:15-15:45, kHS Pw 12 [LSF]
Practice group: Fri, 14:15-15:00, SR AÜStr 3-5 (Please register here if you require a Schein.)

Attention! Last lecture on 20.07.2010, 09:15 hrs, SR Pw 16

Content - Prerequisites - Literature - Additional material

Content:

• 1. Introduction
  - From Einstein to recent experimental highlights
  
• 2. Semi-classical theory of light-matter interaction
  - Maxwell equations in free space - Hamiltonian formulation - Minimal coupling to charged particles - Dipolar approximation - Optical Bloch Equations - Spontaneously emitting two-level atom coupled to laser light
  
• 3. Field quantisation and coherence
  - Mode expansion - Plane-wave expansion - Single-mode field quantisation - Coherent states - Theory of photodetection - First and second-order correlation functions - Hanbury Brown-Twiss experiments - Glauber's theory of coherence
  
• 4. Quasi-Probability Distributions
  - Characteristic functions - Quasi-Probability distributions: Glauber-Sudarshan P-representation, Wigner function, Husimi Q-function - Examples for specific states - Generalized P-distributions: Complex, Positive P, and Glauber R-representations
  
• 5. Linear optical elements
  - Loss-less beam splitter - Partition noise - Heterodyne detection - Mach-Zehnder Interferometer - Angular-momentum representation of linear elements
  
• 6. Squeezed states
  - Squeezed vacuum state - Parametric down conversion - Bogoliubov transformation and two-mode squeezing - Nonlinear optics - Detection of squeezed states - Generation of squeezed states
  
• 7. Open quantum systems
  - The Jaynes-Cummings model - Collapse and revival - Open quantum systems - Dissipation in classical systems - Master equation - Quantum Monte-Carlo algorithm
  

Prerequisites:

• Quantum Mechanics (Theoretical Physics III), Statistical Mechanics (Theor. Phys. IV)

Literature:

• L. Allen, J.H. Eberly, Optical Resonance and Two-Level Atoms. Wiley Inc., 1975.
• S.M. Barnett, P.M. Radmore, Methods in Theoretical Quantum Optics, Clarendon Press, Oxford, 1997.
• C. Cohen-Tannoudji, J.Dupont-Roc, G.Grynberg. Atom-Photon Interactions. Wiley Science Paperb. Series 1998 (first ed.:1992).
• C.W. Gardiner, Quantum Noise. Springer Verlag, Berlin, 1991.
• H. Haken, Light. North Holland, Amsterdam, 1985.
• J.R. Klauder and E.C.G. Sudarshan, Fundamentals of Quantum Optics. Benjamin, New York, 1968.
• R. Loudon, The Quantum Theory of Light. 3rd ed., Oxford University Press, 2000.
• L. Mandel, E. Wolf, Optical Coherence and Quantum Optics, CUP, Cambridge, 2008 (ISBN 0-521-41711-2).
• D. Meiser, Quantum Optics. Lecture Notes, CU Boulder 2008.
• P. Meystre, M. Sargent III, Elements of Quantum Optics, 3rd ed., Springer Verlag, Berlin, 1997.
• P. Meystre, Laser Cooling and Trapping. Springer Verlag, Berlin, 1999.
• P.W. Milonni and J.H. Eberly, Lasers. Wiley, New York, 1988.
• P.W. Milonni, The Quantum Vacuum: An Introduction to Quantum Electrodynamics. Academic Press, New York, 1994.
• L.E. Reichl, A Modern Course in Statistical Physics, Wiley Interscience, 2nd edition 1998 (ISBN 0-471-59520-9).
• W.P. Schleich, Quantum Optics in Phase Space. Wiley-VCH, Weinheim, 2001.
• M.O. Scully, M. S. Zubairy. Quantum Optics. Cambridge University Press, 1997.
• W. Vogel, D.-G. Welsch, S. Wallentowitz, Quantum Optics. An Introduction. 2nd ed., Wiley-VCH, Weinheim, 2001.
• D.F. Walls, G.J. Milburn, Quantum Optics. Springer Verlag, Berlin, 1994.

Additional material:

• Slides (Literature, Wigner function, Squeezing, etc.).
• Maple-Sheet (PDF) (for simulating Optical Bloch Equations).
• Hanbury-Brown Twiss experiments: Phil. Mag. 45, 366, 663 (1954), Nature 177, 27 (1956), Nature 178, 1046 (1956).
• Trapping of an atom with single photons: Nature 404, 365 (2000).
• Generation of Schrödinger Cats from Number states: Nature 448, 784 (2007).