Quantum Optics 1 0800-PA-QUANTOPT1

Discussed topics
Lecture (30 hrs)
1. General information about the subject – a review (basic phenomena and processes, photons).
• Orders of magnitude and units of physical quantities characterizing atoms, optical fields and interaction between them. Estimating the number of photons in a laser beam of given power and frequency.
• Examples of quantum behaviour: photon detection after its passing through a Mach-Zehnder interferometer, nondemolition measurement.
• Photon statistics: counting photons, statistics of the number of photons in a coherent beam, Poisson distribution and "Poissonian, super-Poissonian and sub-Poissonian light".
2. Quantum theory of radiation
• Maxwell's equations (ME) for electric and magnetic fields, electromagnetic potentials, gauge
• Polarization and radiation modes
• Vector and scalar electromagnetic potentials, gauge, evolution equations
• Coulomb gauge
• Energy of radiation field, expression through the fields and vector potential in analogy to a set of uncoupled harmonic oscillators
• Quantization rules, creation and ahhinilation operators, Hamiltonian and momentum operator, number operator, eigenstates and eigenvalues of the Hamiltonian and momentum operator, radiation modes, photons.
3. Quantum states of radiation
• Vacuum state and its basic properties.
• Single-mode states, Fock (number) and coherent (quasiclassical, Glauber) states, their basic properties and interpretation. Multimode states.
• Single- and multimode single-photon states.
• Beam splitter and its classical and quantum model. Input and output states. Single-photon experiments, Hong – Ou – Mandel (HOM) effect.
• Quadrature operators for radiation fields (definition, commutation rules, Heisenberg relations).
• Squeezed states of radiation (definitnion, properties, generation scheme in a parametric process).
4. Interaction of electromagnetic fields with atomic systems
• Time-dependent perturbation theory, transition amplitude and probability, transitions among discrete states and from discrete to continuous spectrum.
• Interaction of atomic systems with classical electromagnetic fields (interaction Hamiltonian, electric – dipole and magnetic – dipole interaction, absorption and stimulated emission).
• "Exactly solvable" models:Rabi model, Weisskopf-Wigner model.
• Jaynes – Cummings model.
• Remarks on more complicated cases: more levels, more fields.
Exercises (30 hrs)
5. Harmonic oscillator. A review of the subject (a, a+ and n = a+a operators, their basic properties and algebra, eigenstates and eigenvalues of harmonic oscillator Hamiltonian). Coherent states of harmonic oscillator and their properties: definition, decomposition in the Fock basis, Poissonian statistics of excitation numbers, graphical representation, temporal evolution, Heisenberg relations, quasiorthogonality and completeness, displacement operator for generation operator of coherent states from vacuum state.
6. A few operator relations. Functions of operators, commutation relations involving functions of operators, derivative of an operator, Glauber and Baker-Hausdorff formulas, displacement and squeezing operators.
7. Spin ½ dynamics in a magnetic field as a prototype two-level system. Magnetic resonance, classical and quantum description, Bloch, Schroedinger and von Neumann equations, evolution of expectation value of magnetization.
8. Optical Bloch equations.
Depending on the background, interests and preferences of students, certain modifications of the scope of the class and selection of additional subjects are possible.