The course is delivered in Italian (default mode) or in English (upon request and agreement among the students).
Course Content
Introduction to the Physics of Ultracold Atoms. Complements of Atomic Physics. Mechanical effects in atom-laser interaction. Theory of laser cooling. Atom trapping. Interactions between cold atoms. Ultracold quantum gases. Optical lattices and quantum simulation. Atomic clocks. Atomic interferometers. Quantum computers with individual trapped atoms.
C. Foot
Atomic Physics
(Oxford University Press, 2005)
H. J. Metcalf, P. van der Straten
Laser Cooling and Trapping
(Springer, 1999)
M. Inguscio, L. Fallani
Atomic Physics: Precise Measurements and Ultracold Matter
(Oxford University Press, 2013)
C. Cohen-Tannoudji, D. Guéry-Odelin
Advances in Atomic Physics: An Overview
(World Scientific, 2011)
Learning Objectives
The course aims to introduce to the physics of ultracold atoms. In the first part of the course, techniques for cooling atomic gases down to temperatures of a few nanokelvins will be illustrated, both by describing their physical aspects and theoretical implications, and by showing the experimental techniques and main results obtained in this field of research. In the second part of the course, applications of such systems in quantum science and technology will be illustrated, focusing on the research conducted in the Department of Physics and Astronomy. By the end of the course the student will have acquired a basic knowledge of the subject, sufficient to pursue experimental and/or theoretical thesis work in this field of research.
Prerequisites
A basic background in Atomic Physics is required, such as that provided in the "Atoms, Molecules and Photons" course. However, the basic concepts will be recalled during the first lectures
Teaching Methods
The Course will be developed with frontal lectures, in which the lecturer will illustrate the topics mainly at the blackboard. During the lectures, slides with notable examples or significant results in the study of ultracold atomic gases will also be shown, stimulating students to give an interpretation of the proposed phenomena, in an interactive mode. The course will be complemented with visits to research laboratories, in order to show students the practical implementation of the concepts and techniques illustrated during the course.
All course materials will be made available on the Moodle e-learning platform (transcripts of what is written on blackboard during the lecture, slides with figures and experimental films, software codes to be used on an optional basis to explore some theoretical topics in depth). Access to a collection of video lectures (in English) that can be used on an optional basis as supplementary material will also be provided.
Further information
(not available)
Type of Assessment
Learning will be verified through an oral examination.
During the exam, the student will be asked to present a topic of his/her choice from those discussed during the course. A student who wishes to go in-depth into a specific topic may do so by agreeing on the topic with the lecturer, who will provide additional study material. The exposition will normally take place in front of a blackboard, but it is possible for the student to use slides to support the presentation.
Questions on other topics discussed during the course may be asked to assess the student's ability to contextualize the chosen topic within the general themes.
Course program
1) Introduction to the course.
Review of Doppler effect and recoil shift.
2) Short review of atomic structures.
Spectrum of alkali atoms. Fine structure. Hyperfine structure. Transitions between levels and selection rules. Zeeman shift. Spectrum of two-electron (alkaline-earth) atoms. Singlet and triplet states. LS coupling. Intercombination transitions.
3) Complements of coherent light-atom interaction.
Coherent light-atom coupling. Rotating wave approximation. Rabi dynamics. Spontaneous emission. Density matrix. Optical Bloch equations. Quantum trajectories. Bloch vector and Bloch sphere. Examples: visualization of Rabi dynamics, adiabatic passage, Ramsey spectroscopy.
4) Radiative forces.
Introduction to radiative forces: energy/time scales and relevant approximations. Full derivation of radiative forces in atom-light interaction. Radiation pressure and optical dipole force. Radiation pressure: properties and alternative derivation. Fluctuations of the radiation pressure: diffusion in momentum space. Optical dipole force: general properties and interpretation in terms of light shift.
5) Laser cooling.
Deceleration of an atomic beam. Zeeman Slower. Doppler cooling (optical molasses). Temperature of laser-cooled atoms. Experimental determination of temperature. Limits of Doppler cooling. Introduction to SubDoppler cooling. Polarization gradients. Atom-light interaction in multilevel systems. Dependence of Rabi frequency on angular momentum. Optical pumping. Open and closed transitions. Sisyphus cooling. Temperature limit in subDoppler cooling. Experimental configurations with real atoms. Recoil temperature. Raman cooling.
6) Atom trapping.
Introduction to atomic traps. Magneto-optical trap (MOT). Experimental realization of MOTs: temperature and number of trapped atoms. Magnetic traps: general properties, quadrupole Trap, Majorana losses. Optical dipole traps: general properties, common geometries for optical dipole traps.
7) Atom-atom interactions at low temperature.
Interaction potentials. Short review of scattering theory. Partial-waves expansion. Low-energy quantum scattering: s-wave scattering and scattering length. Dependence of scattering length on potential parameters. Potential barrier. Potential well. Effect of the bound states. Measurement of scattering lengths. Isotope mass scaling. Feshbach resonances: general principles and toy model. Scattering of identical particles. Inelastic collisions. Evaporative cooling.
8) Ultracold quantum gases.
Short summary of general concepts of Bose-Einstein and Fermi-Dirac distribution. Phase-space density. Bose-Einstein condensation (BEC) in a harmonic trapping potential. Experimental observation of BEC. Weakly interacting Bose gas and Gross-Pitaevskii equation. Matter-wave coherence of atomic BECs. Experiments with BEC interference. Superfluid properties of BECs. Experimental observation of BEC critical velocity and vortex formation. Sympathetic cooling. Ultracold Fermi gases. Short introduction on condensation of interacting fermions: superfluidity, superconductivity, BEC-BCS crossover.
9) Optical lattices.
General properties of optical lattices. Short review of Bloch theory. Bose-Einstein condensates in optical lattices. Energy bands. Transport of cold atoms in optical lattices and Bloch oscillations. Tight-binding lattice models. Two examples of quantum simulation with cold atoms in optical lattices: Anderson localization and Superfluid-Mott transition.
10) Atomic clocks.
Introduction to high-precision spectroscopy and atomic clocks. Microwave atomic clocks: Ramsey spectroscopy and atomic fountain clocks. Optical atomic clocks. Ultranarrow transitions and ultranarrow lasers. Spectroscopy in the Lamb-Dicke regime. Optical lattice clocks and magic wavelengths. Discussion of some systematic effects: blackbody radiation shift and gravitational redshift.
11) Atom interferometry.
Introduction to atom interferometers. Ramsey-Bordé interference. Atomic gravimeters. Bloch oscillations as atom interferometers.
12) Introduction to experiments with single atoms.
Single-atom trapping and manipulation. Rydberg atoms in optical tweezer arrays and their applications.