Theoretical Quantum Optics

Lecturer: Giovanna Morigi

Lectures:

The lecture is offered as a block lecture within three weeks of the semester. The weeks are:

December, from 14.12. to 18.12.

January, from 5.1. to 9.1.

February, dates to be determined

The exact times and rooms for the lecture will be announced here on the website as soon as they are fixed.

Content

  1. The elastically-bound electron
    1.1 Underdamped oscillator
    1.2 Driven oscillator
    1.3 Atomic polarizability
     
  2. Light-atom interaction
    2.1 Interaction Hamiltonian in the electric-dipole approximation
    2.2 The induced dipole moment: Resonant regime
    2.3 Resonant excitation of a two-level transition. Rabi oscillations
    2.4 An effective two-level system. The Bloch sphere.
     
  3. Optical Bloch Equations
    3.1 The density matrix
    3.2 Density matrix for a two-level system
    3.3 Phenomenological description of decay
    3.4 Stationary solution in presence of spontaneous emission. Saturation and classical limit.
    3.5 Spin Echoes.
     
  4. The quantum electromagnetic field
    4.1 Classical Maxwell Equations in vacuum. Gauge invariance. Energy.
    4.2 Second quantization.
    4.3 Photons.
    4.4 Fields. Coherent states. Squeezed states. Single Photon wave packet. Photon field.
    4.5 A single mode cavity
     
  5. Atom-photon interactions in a single-mode cavity
    5.1 Jaynes-Cummings model
    5.2 From quantum to classical dynamics.
    5.3 Master equation for a damped harmonic oscillator: microscopic derivation.
     
  6. Dissipative master equations
    6.1 Useful concepts.
    6.2 Derivation of the Born-Markov master equation.
    6.3 Master equation of a dipole undergoing spontaneous emission.
    6.4 Unraveling the master equation.

Literature

  • Chapter 1: R. Becker, Electromagnetic Fields and Interactions, vol. 2 (Dover, 1964).
  • Chapter 2,3: L. Allen and J. H. Eberly, Optical Resonance and Two-level Atoms (Dover, 1987).
  • Chapter 2: C. Cohen-Tannoudji, B. Diu, F. Laloe, Quantum Mechanics, vol. 2 (Wiley, 1977).
  • Chapter 2,3,6,7: C. Cohen-Tannoudji,J. Dupont-Roc, G. Grynberg, Atom-photon interactions (Wiley, 1992).
  • Chapter 3: A. Kossakowski, “On quantum statistical mechanics of non-Hamiltonian systems”. Rep. Math. Phys. 3 (4), 247 (1972).
  • Chapter 3: G. Lindblad,  “On the generators of quantum dynamical semigroups”. Commun. Math. Phys. 48 (2), 119 (1976).
  • Chapter 4,5,6: C. W. Gardiner and P. Zoller, Quantum Noise (Springer, 2000).
  • Chapter 5: B.-G. Englert and G. Morigi, Five lectures on dissipative master equations, in “Coherent Evolution in Noisy Environments”, p. 55-106, Lecture Notes in Physics, ed. by A. Buchleitner and K. Hornberger (Springer Verlag, Berlin-Heidelberg-New York 2002). See also http://arxiv.org/abs/quant-ph/0206116.