Calculus Quantum physics Advanced quantum physics Electromagnetic fields and waves

1.Quantum control of atoms with light -Atomic transitions, Bloch vector and Bloch equations -ac-Stark shift and optical potentials 2. Photons for quantum technologies - Photons in cavities and free space - Quantum states of light: Fock and coherent states. Squeezed states. - The spectrum of light - Quantum metrology with photonic states 3. Atoms and qubits interacting with quantum light - Jaynes-Cummings model - Interaction of atoms with photons in free space - Radiative decay and the optical master equation - Generation of quantum states of light by atoms (laser and single-photon emission) 4. Introduction to quantum optical setups - Cavity and circuit QED systems - Trapped ions 5. Quantum computing with quantum optical systems - Quantum gates mediated by photonic modes - Trapped ion quantum computing - Quantum computing with photon states 6. Applications of quantum optics -Single photons for quantum communications (g^2, characterization of single-photon states) - Electromagnetically Induced Transparency - Optical tweezers and optical trapping - Atomic ensembles for quantum networks 7. Quantum optics laboratory. - Experiment 1: Entangled photon pairs. Hong-Ou-Mandel Interferometry - Experiment 2: Saturation Spectroscopy - Experiment 3: Optical Tweezers

1. Educational activities: - Theory lessons - Tutorial sessions - Laboratory practice - Individual student work 2. Educational Methodologies: - Classroom lessons by lecturers in which the main concepts will be developed. Bibliography will be provided to students as a complement to the main lessons - Solution of practical exercises in the classroom and also individually by students. - Laboratory practice and writing of laboratory reports on the experimental work.