Prof. Cecilia Cormick’s will teach a mini-course @ IFUSP between 12 and 14 of february.

This is a graduate-level course for which students may earn credits by enroling.

**Where: **Seminar room** **@** **Ed. Alessandro Volta, Bloco C, IFUSP.

**When: ** - Lectures Tuesday (12), Wednesday (13) and Thursday (14) from 10:00 to 13:00.

- Informal discussions in the afternoon, from 16:00 to 17:00.

**Goal: **The goal of the course is to give the students a general overview of standard theoretical tools in the field of quantum optics. These are to a large extent independent of the concrete physical system in mind and are essential for an understanding of several applications related with the control of quantum systems. The case of atoms interacting with light fields will be treated in more detail as a concrete implementation.

**Syllabus: **Interaction between atoms and the quantized electromagnetic field. Cavity QED. Wigner-Weisskopf theory of spontaneous emission. Treatment of the atom as open quantum system, Bloch equations. Optical forces on atoms: Doppler cooling, radiation pressure, optical potentials. Sub-Doppler cooling. Basic principles of ion trapping. Internal and external degrees of freedom in systems of trapped ions. Sideband cooling. Laser control of the state of the ions. Manipulation of ions for quantum computing purposes.

**Previous knowledge assumed:** General notions of quantum mechanics, including Dirac notation and density matrix formalism. General notions of atomic physics.

**Program:Lecture 1: General (and fast) description of atom-light interactions:**

- Semiclassical treatment, weak coupling, rotating wave approximation. Two-level atom: Rabi oscillations, AC Stark shift.

- Interaction between an atom and the quantized field: Jaynes-Cummings model, Wigner- Weisskopf theory, master-equation description of spontaneous emission.

**Lecture 2: Optical forces on atoms:**

- Bloch equations: evolution and stationary state.

- Radiation pressure and Doppler cooling.

- Optical potentials.

- Sub-Doppler cooling with Sisyphus effect.

**Lecture 3: Trapped ions:**

- Basic principles of Penning and Paul traps.

- Internal and external degrees of freedom of a single ion.

- Manipulation with lasers: sideband cooling, single-qubit gates.

- Description of a system of several ions.

- Basic elements for quantum information processing with trapped ions.

**Additional topics included in the problems: **- Adiabatic elimination procedure.

- “Forbidden” transitions through two-photon processes.

- Optical pumping.

**Recommended reading:**For the level of the crash-course (not necessarily the best material, rather the most acces- sible):

• M. Lukin, notes for the course “Modern Atomic and Optical Physics II” (Harvard), available at http://lukin.physics.harvard.edu/teaching/

• M. Fox, “Quantum Optics” (Oxford University Press).

• C. Gerry and P. Knight, “Introductory Quantum Optics” (Cambridge University Press).

At a more advanced level (and more reliable as reference material):

• R. Loudon, “The Quantum Theory of Light” (Oxford University Press).

• D. F. Walls and G. F. Milburn, “Quantum Optics” (Springer).

• M. Scully and M. S. Zubairy, “Quantum Optics” (Cambridge University Press).

• C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, “Atom-Photon Interactions” (Wiley).

For specific sub-topics (laser cooling, ion traps):

• Cohen-Tannoudji and Phillips, “New Mechanisms for laser cooling”. Physics Today (1990).

• Metcalf and van der Straten, “Laser cooling and trapping of atoms”. J. Opt. Soc. Am. B (2003).

• Eschner, Morigi, Schmidt-Kaler and Blatt, “Laser cooling of trapped ions”. J. Opt. Soc. Am. B (2003).

• Häffner, Ross and Blatt, “Quantum computing with trapped ions”. Phys. Rep. (2008).

• Kielpinski, “Ion-trap quantum information processing”. Front. Phys. China (2008).

**Short bio: Prof. Cecilia Cormick**

I studied physics at the University of Buenos Aires, and I did my diploma thesis on phase-space representations for quantum computing, under the supervision of Juan Pablo Paz. After that I stayed in the same group for my PhD, which focused on decoherence problems from a theoretical approach. By the end I was eager to get closer to actual experiments so I moved towards quantum optics during my postdoctoral stays in Germany (first Saarbrücken with Giovanna Morigi, then Ulm in the group of Martin Plenio). There I worked mostly on the theoretical description of systems of trapped ions for quantum information and simulation purposes, but I also did some more general stuff related with spectroscopy or quantum state engineering. At the end of 2014 I returned to Argentina and settled at the University of Cordoba, where I work as tenured researcher and assistant professor. In the last years, although I haven't abandoned my older topics, my lines of research have shifted gradually towards the area of quantum statistical mechanics, in particular to phase transitions and systems of composite bosons.

**Funding:**

This course is funded by the graduate-program at IFUSP and is a part of an initiative to promote short courses on advanced research topics, taught by experts from other institutions in Brazil and abroad.