Code: 12KVEN Quantum Electronics
Lecturer: doc. Dr. Ing. Ivan Richter Weekly load: 3+1 Completion: A, EX
Department: 14112 Credits: 5 Semester: W
The lecture covers the basics of quantum electronics. It systematically discusses the Dirac formalism and its application to quantum system description, pure and mixed states, and the statistical operator and its properties, including the time dynamics of quantum Liouvill equation. It also introduces, apart from Schrödinger, also Heisenberg and Dirac formalism of quantum system dynamics. The attention is given to time dynamics of quantum systems, with the help of evolution operator formalism, and both stationary and nonstationary perturbation theory, including semi classical theory of interaction of a quantum system with the classical field. It is further devoted to quantized electromagnetic field and basics of quantum electrodynamics. Finally, the attention is given to both Fock states and coherent states of quantized electromagnetic field, their properties and specifications, and also to the application of coherent states as a tool for description of quantum optical radiation (quasiprobability densities as, e.g. Glauber-Sudarshan representation, and quantum characteristic functions). The lectures are accompanied with practical example exercises.
1. Introduction. Quantum electronics and optics. Dirac formalism, operator algebra basics.
2. Pure and mixed states, projectors, statistical operator.
3. Characteristics and examples of statistical operators, quantum Liouvill equation, reduced statistical operator.
4. Schrödinger, Heisenberg a Dirac (interaction) formalism of quantum system dynamics.
5. Time dynamics of quantum system, evolution operator.
6. Stationary and nonstationary perturbation theory.
7. Nonstationary perturbation theory for evolution and statistical operators, examples of perturbation.
8. Semiclassical theory of interaction of quantum system with classical field, Bohr transition frequency.
9. Quantization of electromagnetic field, quantum linear harmonic oscillator, annihilation and creation operators.
10. Basics of quantum electrodynamics, hamiltonian of an atom interacting with classical field.
11. Coherent states of electromagnetic fields - properties, displacement operator, single and multimode field.
12. Comparison of classical and quantum states, classical and nonclassical states, generation of coherent states.
13. Quantum description of optical radiation, quasi probability density.
Seminar contents:
Practical examples and calculations of selected problems in the areas:
1. Dirac formalism and description of quantum systems within this formalism.
2. Operator algebra basics, Baker-Hausdorff identity, tracing operator.
3. Projectors, examples of statistical operator, quantum Liouvill equation.
4. Schrödinger, Heisenberg and Dirac formalism.
5. Time dynamics of quantum system, application of nonstationary perturbation theory.
6. Operator algebra of boson operators.
7. Quantization of electromagnetic field, linear harmonic oscillator - quantization.
8. Basics of quantum electrodynamics - quantum averages of field operators, commutator of field operators.
9. Coherent states of quantum fields - properties, displacement operator, completeness, quasiprobabilities.
Recommended literature:
Compulsory literature:
[1] W. H. Louisell: Quantum statistical properties of radiation, J. Wiley & Sons, London, 1973.
[2] L. Mandel, E. Wolf: Optical coherence and quantum optics, Cambridge University Press, 1995.

Supplementary literature:
[3] J. Formánek, Úvod do kvantové teorie, Academia, 1983 (in Czech).
[4] 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.
Dirac formalism of quantum decription, pure and mixed states, statistical operator, Schrödinger, Heisenberg a Dirac formalism, time dynamics, stationary and nonstationary perturbation theory, semiclassical theory of interaction, absorption, stimulated emission, quantum electromagnetic field, annihilation and creation operator, Fock and coherent states, quasi probability density, Glauber-Sudarshan representation.

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