## Scope of questions for State exams of Master's degree program

Branch: Quantum Technologies

Subject: Quantum Optics

Subjects regarding the questions:

- 02KO1 Quantum Optics 1
- 02KO2 Quantum Optics 2

- Description of light propagation: derivation of the wave equation from Maxwell's equations, Helmholtz equation and its paraxial approximation, eikonal equation, wavefront, plane and spherical waves, Gaussian beam, monochromatic and quasimonochromatic waves, wave packet, polarization states.
- Quantization of electromagnetic field: decomposition of a field into superposition of harmonic modes, single mode electric and magnetic field, Hamiltonian, applications of the principle of correspondence, creation and annihilation operators, bosonic character of photons.
- Discrete and continuous mode structures: canonical commutation relations and Hamiltonian in the continuous case, optical cavity and free space modes, transition between time and frequency, coordinate and momentum representation, Gauss and Hermite–Gauss modes.
- Important states ofoptical modes: Fock states, coherent states, squeezed states, thermal states, squeezed vacuum, decomposition of unity, displacement and squeezing operations, coherent, squeezed and single particle states of multiple modes.
- Coherence and interference: quantum description of a beam splitter, correlation functions, Hanbury Brown–Twiss effect, Hong–Ou–Mandel effect, Mach–Zehnder interferometer, Michelson interferometer, wave packet transmission, vacuum modes as source of noise and losses.
- Quantum light detection: measurement of intensity and polarization, description of interaction of a strong local oscillator with the measured field, homodyne detector, heterodyne detector, quadratures of a light mode, mean value and mean square deviation of quadratures.
- Spin angular momentum of light: single photon spin quantization, difference from the description of spin-1 massive particles, helicity and its observable, Pauli matrices, Poincaré sphere of polarization states, measurement, spin rotation and depolarizationas geometrical transforms, polarization as a qubit carrier.
- Orbital angular momentum of light: Laguerre–Gauss basis, forked diffraction grating, spiral wave plate, spatial light modulator, q-plate, quantization of orbital angular momentum of a single photon, conversion between spin and orbital angular momentum.
- Nonlinear quantum optics: nonlinear dependence of polarization on intensity, higher harmonic components, parametric processes of second and third order, spontaneous parametric down-conversion as a method of squeezing, phase matching, single photon generation.
- Quantum Optics in phase space: characteristic function, Wigner function, Glauber–Sudarshan function, Husimi function, quasi-distribution properties, description of observable quantities in phase space, displacement, squeezing and time evolution as geometric phase space transformations.