## "Quantum Optics and Cold Atoms" (In English)

Lecturer: Giovanna Morigi

Exercises and tutorium: Thomas Fogarty and Oxana Mishina

#### Lecture:

Monday 10:00 - 12:00 Uhr, Gebäude E2 6, Seminarraum E04

Tuesday 12:00 - 14:00 Uhr, Gebäude E2 6, Seminarraum E 04

The first lecture takes place on Monday, April 14th at 10:00 in Geb. E26, Lecture Room E04.

Exams: Oral exams. Requirement: >50% of points collected in all exercise sheets. Date will be fixed with the examiners (G. Morigi and T. Fogarty).

#### Changes:

Monday 9th June : Holiday-No Lecture

Tuesday 10th June : 1 hour lecture + 1 hour exercise class (finish exercise sheet 3)

Monday June 16th & Tuesday June 17th: lectures

Monday June 23rd: lecture

Tuesday June 24th: lecture

Monday June 30th: lecture

Tuesday July 1st: Exercise class + Tutorium

Monday July 7th: lecture

Tuesday July 8th: lecture

Monday July 14th: lecture

Tuesday July 15th: Exercise class + Tutorium

Monday July 21st: lecture

Tuesday July 22nd: lecture

#### Assignments

- QOCA1.pdf(Date: 16.4.14, Class: 28.4.14)
- QOCA2.pdf(Date: 6.5.14, Class: 13.5.14)
- QOCA3.pdf(Date: 29.5.14, Class: 3.6.14)
- QOCA4_part1.pdf(Date: 20.6.14, Class: 1.7.14) QOCA4_2r.pdf(Date: 26.6.14, Class 1.7.14 and 14.7.14)
- The elastically-bound electron

1.1 Underdamped oscillator

1.2 Driven oscillator

1.3 Atomic polarizability

- 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.

- 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.

- 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

- 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.

- 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.

- Mechanical effects of light on atoms

7.1The model.

7.2 Conservation laws for the mechanical motion.

7.3 Absorption and emission of laser photons.

7.4 Scattering of laser photons.

7.5 Laser cooling.

- 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.