Description:

The lecture covers the advanced topics in quantum optics, consequentially to the previous course of Quantum electronics. It systematically discusses especially the statistical properties of radiation, coherent states of electromagnetic field, quantum description of optical radiation, special states of fields, with respect to quasi-probability densities and characteristic functions. Next, the attention is given both to Dirac quantum theory of interaction of quantized electromagnetic field with a quantum system (including spontaneous emission) and quantum theory of scattering (Rayleigh, Thomson, Raman, resonance fluorescence). The attention is further given both to the quantum theory of coherence (quantum theory of detection, quantum correlation functions), in relation to classical theory. The course is further devoted to generalized higher-order coherence theory, coherent properties of special states of fields, and quantum theory of damping (quantum damped harmonic oscillator, Heisenberg-Langevin approach). Finally, the attention is given to review of nonclassical measuring techniques (photocounting, intensity interferometry, Brown-Twiss effect, stellar correlation interferometer, correlation spectroscopy), possibilities of measuring the quantum state of light, and some selected parts of modern quantum optics (squeezed states). The lectures are accompanied with practical example exercises.

Contents:

1. Coherent states of electromagnetic fields, quantum description of optical radiation, quasi probability densities.
2. Selected quantum states of light: coherent state, ideal laser, chaotic blackbody radiation and thermal light.
3. Dirac theory of interaction of quantized electromagnetic field with quantum system.
4. Quantum theory of radiation scattering on atom, Kramers - Heisenberg effective scattering cross section.
5. Quantum theory of detection, single and multiatom two-level absorption / emission detector.
6. Quantum theory of coherence, quantum correlation functions, generalized coherence theory.
7. Basics of quantum damping approaches, quantum damped oscillator, Heisenberg-Langevin approach.
8. Review of nonclassical light states, classification, entangled states, quantum phase problem, squeezed states.
9. Review of nonclassical measuring techniques, photodetection equation, measuring the quantum state of light.
10. Modern quantum optics, EPR paradox, Bell inequalities, entangled states, and quantum cryptography.

Seminar contents:

Practical examples and calculations of selected problems in the areas:
1. Application of coherent states of electromagnetic fields, quantum description of optical radiation.
2. Application of Dirac theory of interaction of quantized electromagnetic field with quantum system for selected states of light, processes of absorption, spontaneous and stimulated emission, Einstein coefficients.
3. Application of Kramers - Heisenberg effective scattering cross section to Rayleigh, Thomson, and Raman scattering.
4. Application of quantum theory of detection.
5. Calculations and application of quantum correlation functions and photodetection equation.
6. Application of quantum theory of damping.

Recommended literature:

Compulsory literature:
[1] Mandel L.: Wolf E.: Optical Coherence and Quantum Optics, Cambridge University Press, 1995.
[2] Louisell W. H.: Quantum Statistical Properties of Radiation, J. Wiley & Sons, London, 1973.
[3] Vrbová, M.: Kvantová teorie koherence, interní učební materiál, KFE FJFI, 1997 (in Czech).

Supplementary literature:
[4] Peřina J.: Coherence of Light, Dordrecht Reidel Publishing Company, 1985.
[5] Peng J.S., Li G. X.: Introduction to Modern Quantum Optics, World Scientific, 1998.
[6] C. C. Tannoudji, J.D. Roc, G. Grynberg, Photons and atoms - introduction to quantum electrodynamics, Atom-photon interactions - basic processes and applications, J. Wiley & Sons, New York, 2003.

Keywords:

Quantum theory of interaction, absorption, spontaneous and stimulated emission, Einstein coefficients, quantum theory of scattering, Rayleigh, Thomson, Raman scattering, quasi probability density, photodetection equation, theory of detection, quantum correlation function, quantum theory of damping, photocounting, intensity interferometry, Brown-Twiss effect, correlation spectroscopy, nonclassical state, squeezed state, EPR paradox, Bell inequalities, entangled state.

Abbreviations used:

Semester:

• W ... winter semester (usually October - February)
• S ... spring semester (usually March - June)
• W,S ... both semesters

Mode of completion of the course:

• A ... Assessment (no grade is given to this course but credits are awarded. You will receive only P (Passed) of F (Failed) and number of credits)
• GA ... Graded Assessment (a grade is awarded for this course)
• EX ... Examination (a grade is awarded for this course)
• A, EX ... Examination (the award of Assessment is a precondition for taking the Examination in the given subject, a grade is awarded for this course)

Weekly load (hours per week):

• P ... lecture
• C ... seminar
• L ... laboratory
• R ... proseminar
• S ... seminar