Methods of Quantum Technologies

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

Branch: Quantum Technologies

Subject: Methods of Quantum Technologies

Subjects regarding the questions:

  • 02KTPA1 Quantum Field Theory 1
  • 02KO1 Quantum Optics 1
  • 11TPLA1 Theory of Solid State 1
  • 12KGOZ1 Quantum Generators of Optical Radiation 1
  • 02KIK Quantum Information and Communication
  1. Relativistic hydrogen atom – relativistic particle in spherically symmetric electromagnetic field, solution of the hydrogen atom with the Dirac, fine and hyperfine structure of hydrogen.

  2. Symmetries and their applications in relativistic quantum theory – representations of Lorentz group, invariance of Klein-Gordon and Dirac equation with respect to Lorentz transformations, discrete symmetries C, P and T.

  3. Quantization of free fields – canonical quantization of scalar and bispinor fields, creation and annihilation operators, Fock’s space.

  4. Laser as a quantum generator of radiation – interaction of resonant radiation with the matter, population inversion, principle of optical radiation amplification, principle of laser radiation generation, basic elements of laser generator.

  5. Laser radiation properties – spectroscopic properties of laser radiation, spatial and temporal coherence, propagation of laser beams and their transformation.

  6. Mathematical methods of Quantum Optics – operator exponential, ladder operators,operator ordering theorems for the Heisenberg algebra, su(2) and su(1,1) algebras, Baker–Campbell–Hausdorff theorem and its special cases, Fourier transform, Dirac delta function.

  7. Light–matter interaction –two-level atoms, dipole approximation, Jaynes-Cummings model, resonant and off-resonant transitions, bare and dressed states, dipole force, momentum and angular momentum exchange between photon and matter particle.

  8. Electrons in a periodic potential –many-particle wavefunctions, Bloch functions, bandstructure of solids, methods of electronic-structure calculations for solids.

  9. Quasiparticles in solids –thermodynamic equilibrium, transport properties of solids, application of Green’s functions in solids.

  10. Quantum information approach to finite dimensional systems –von Neuman entropy, two-particle separable and entangled pure states, Schmidt decomposition, mixed bipartite states, reduced density matrix, quantum operations, completely positive trace preserving maps, partial transposition.