Quantum Optics 1

Course guarantor:

Igor Jex

Lecturer:

Václav Potoček

Tutor:

Václav Potoček

Supervisor:

Department of Physics

Synopsis:

Building upon classical optics, the course shows the construction of a semiclassical Quantum Optics theory of light and light-matter interaction. The aim of the lecture is to provide a robust theory allowing the qualitative and quantitative description of a broad range of quantum optical phenomena as well as some methods for practical computation.

Requirements:

Zápočet: active participation in seminars with a contribution comprising demonstrating solutions to exercises in class (prepared in homework). The required amount of such exercises is determined by fair share of the total among the number of enrolled students. Absence when scheduled for presentation can be compensated by an equivalent of the full demonstration in text form or scanned. If the criteria are met, zápočet is awarded in batch after last seminar class.

Examination: conditioned by a fulfilled zápočet and at least 80% performance in a short written test (very basic type exercises). The grade is 100% formed by performance in oral examination in a randomly drawn pair of topical areas (with time for individual preparation) and possible supplementary questions. Possibility of a complete replacement of one of the two topics, at the expense of the maximum achievable grade.

Syllabus of lectures:

1. Overview of classical optics: plane waves, Gaussian beam, polarization

2. Electromagnetic field quantization, canonical commutation relations, discrete and continuous case

3. Fundamental quantum states of a single mode

4. Mathematical methods of quantum optics, operator ordering theorems

5. Coherent and squeezed states, classical and non-classical states of light

6. Beam splitter in quantum optics

7. Modal continuum, pulse propagation model

8. Optical detection: single-photon, photon number-resolving, homodyne detectors

9. Interferometry, phase estimation and its improvements using nonclassical states or measurements

10. Quantum theory of coherence, correlation effects, Hanbury Brown-Twiss and Hong-Ou-Mandel effects

11. Single atom-light interaction, Jaynes-Cummings model

12. Cavity quantum electrodynamics, master equation of light attenuation

13. Nonlinear optics and photon-photon interaction in media: parametric down-conversion, Kerr effect

Syllabus of tutorials:

Solving problems to illustrate the theory from the lecture

Study Objective:

After finishing this course, students should be able to understand a big part of current literature in the topic, even though certain topical areas are left for the subsequent subject 02KO2.

Study materials:

Accompanying literature:

[1] V. Potoček: Kvantová optika (lecture script in preparation, CZECH ONLY)

Primary sources:

[2] M.O. Scully, M.S. Zubairy: Quantum Optics (Cambridge University Press 1997)

[3] R. Loudon: The Quantum Theory of Light (Oxford University Press 2000)

[4] Paul H.: Introduction to Quantum optics (Cambridge University Press 2004)

[5] S. M. Barnett, P. M. Radmore: Methods in Theoretical Quantum Optics, Oxford University Press, Oxford 2002

Further recommended literature:

[6] L. Mandel, E. Wolf: Optical coherence and quantum optics (Cambridge University Press 1995)

[7] G. S. Agarwal: Quantum Optics (Cambridge University Press 2012)

[8] G. New: Introduction to Nonlinear Optics, (Cambridge University Press 2011)

Note:

Time-table for winter semester 2025/2026:

Time-table is not available yet

Time-table for summer semester 2025/2026:

Time-table is not available yet

The course is a part of the following study plans:

• Matematická fyzika (elective course)
• Kvantové technologie (compulsory course in the program)