Announcements

A presźncia de todos durante as apresentaēões dos seminįrios entre os dias 25.11. e 27.11. é obrigatória !



Information on the course on Atomic and Molecular Physics, SFI5814, 2024-2

Semester: 2024-2
Responsable: Prof. Philippe W. Courteille, philippe.courteille@ifsc.usp.br
Start and end of classes: 19.8.2024 to 27.11.2024
Queries: via e-mail
Time and location of classes:Mondays and Wednesdays from 10h00 to 12h00 in room 18 of bloco F2
or via Google meet (via right-click on your mouse)
Dates of the seminar: 25.11.2024 and 27.11.2024
Holidays: 2.9.-7.9.2024 (Semana da Patria), 12.10.2024 (Nossa Senhora Aparecida), 28.10.2024 (Dia do Funcionįrio Pśblico), 2.11.2024 (Finados), 15.-16.11.2024 (Proclamaēćo da Republica), 15.-16.11.2024 (Conciźncia Negra)
Language: Portuguese, French, German or English (to be agreed with the students)
Workload:
Theory 4 per week
Practice3 per weak
Studies 8 per weak
Duration15 weaks
Total 225 hours
Content:

This is a graduate course! The 'raison d'źtre' of graduate courses shall be to bring the student to the forefront of current research activities in the the lecturer's area of expertise. For the present course this means that the student is supposed to be familiar with the basics of quantum mechanics and its formalism. We're not going to ruminate the hydrogen atom, nor to work off a predefined list of 'same old' classical topics of quantum mechanics. It is up to the student who realizes that he has gaps of knowledge to fill them until being able to benefit from the lectures.

This is a course on atomic and molecular physics, which means that the emphasis of the course will be set on learning how to use our knowledge of the quantum mechanical apparatus to solve 'concrete and relevant' problems. We will learn how to calculate, analytically and numerically, the dynamics of observables in state of the art experiments performed at the IFSC. Possible topics of this lecture include:

1. A quick review of quantum mechanics and its formalism,
2. Dirac equation, atomic structure and substructure,
3. collisions and molecules,
4. quantization procedure for field and atomic motion,
5. master equation and open systems,
6. light scattering and cooperativity in coupled dipoles models,
7. collective atomic motion, atoms in cavities,
8. quantum gates with cold atoms.

Evaluation/approvation:

The seminar will include a written monograph and an oral presentation. The seminar grade counts 1/2 of the final grade. The presentation of the exercises and the participation in the subsequent discussions will be evaluated and counts for 1/2 in the final grade.


Recomended literature: Philippe W. Courteille, Apostila do Curso: Quantum mechanics
D.J. Griffiths, Introduction to Quantum mechanics, 3a ediēćo, Pearson
P.W. Atkins and R.S. Friedman, Molecular Quantum Mechanics (3rd ed.) Oxford University, (1997, 2001)
I.N. Levine, Quantum Chemistry, Allyn and Bacon (3rd ed.) Boston (1983)
C. Cohen-Tannoudji, B. Diu, F. Laloe, Quantum mechanics (vol. 1) Wiley Interscience
Jook Walraven, Quantum Gases, Lectures at the University of Amsterdam
H.A. Bethe, R. Jackiw, Intermediate Quantum Mechanics, (2nd ed.) W.A. Benjamin, Inc)
J.I. Steinfeld, Molecules and Radiation, The MIT Press
A. Corney, Atomic and Laser Spectroscopy, Clarendon Press, Oxford
B.H. Bransden, C.J. Joachain, Physics of Atoms and Molecules, John Wiley & Sons
Eric Cornell, Very Cold Indeed: The Nanokelvin Physics of Bose-Einstein Condensation



Exercises

To successfully absolve this course, the student must study the material indicated in the 'Topics' column and made available in the courses' booklet 'Quantum Mechanics applied to Atoms and Light' until the date indicated in bold letters in the table below. Also, he must solve the exercises indicated in blue color and be prepared to present it fluently.

Date of presentationChapter of scriptExerciseTopic
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19.08.2024 1.1.1 - 1.3.2 Antecedents and foundations of quantum mechanics
21.08.2024 1.3.3 - 1.5.6 Postulates of quantum theory
26.08.2024 1.1.6.2Rutherford scattering (Rafael)
26.08.2024 1.1.6.6Bohr's atom (Joćo)
26.08.2024 1.1.6.7The hydrogen atom (Gabriel)
26.08.2024 1.5.7 - 1.6.6 Representations, product spaces and time evolutions
28.08.2024 1.6.7 - 2.3.6 Translations and symmetry transforms, gravity, potentials and barriers, scattering matrices
04.09.2024 1.4.9.2Normalization of the Bloch vector (Joćo)
04.09.2024 1.4.9.5The ammonium molecule (Rafael)
04.09.2024 1.5.9.3Orthonormal base (Gabriel)
04.09.2024 2.4.1 - 2.4.4 Dirac-potential, numerical techniques, the Fourier grid method, steepest descent
09.09.2024 1.5.9.5Spin rotation operator (Joćo)
09.09.2024 1.5.9.8Eigenvalues (Gabriel)
09.09.2024 1.6.7.1Coupled two-level atom (Rafael)
09.09.2024 2.5.1 - 2.5.5 Introduction to MATLAB, harmonic oscillator
11.09.2024 2.6.1 - 2.6.5 Glauber states and field quantization, kicking a harmonic oscillator
16.09.2024 1.7.6.2Particle in a homogenous gravitational field (Rafael)
16.09.2024 2.2.5.3Particle in a well (Joćo)
16.09.2024 2.2.5.4Least bound states and localization energy (Joćo)
16.09.2024 3.1.1 - 3.2.2 Angular motion in a central potential, radial motion, quantum model of hydrogen
23.09.2024 3.3.1 - 3.4.4 Angular momentum algebra, coupling of angular momenta and Clebsch-Gordan coefficients
23.09.2024 5.1.1 - 5.4.2 Stationary and time-dependent perturbation theory, the variational method
23.09.2024 2.4.4.2Numerical resolution of the Schrödinger equation (Gabriel)
23.09.2024 2.4.4.5Infinite rectangular double-well potential (Joćo)
23.09.2024 3.1.5.5Finite spherical 3D potential well (Rafael)
25.09.2024 5.4.3 - 5.4.4 Sudden and periodic perturbations, transition rates, Raman transitions
30.09.2024 3.2.3.6Transition matrix elements (Joćo)
30.09.2024 3.3.4.8Spin expectation value for a two-level system (Rafael)
30.09.2024 3.4.5.7Transition amplitudes between Zeeman sub-states (Gabriel)
30.09.2024 9.1.1 - 9.1.4 The Dirac equation and the electron spin
02.10.2024 9.2.1 - 9.3.2 Hydrogen fine structure via TIPT, hyperfine structure
07.10.2024 3.4.5.9(Un-)coupled bases of the spherical harmonics (Gabriel)
07.10.2024 3.4.5.11Spin-orbit coupling (Rafael)
07.10.2024 3.4.5.14Coupling three spins (Joćo)
07.10.2024 10.1.1 - 10.2.6Charged particles in electromagnetic fields, Zeeman and Paschen-Back effect
09.10.2024 10.2.7 - 11.2.2Landau levels, Stark effect, wavefunction symmetrization and Pauli's principle, helium atom
21.10.2024 5.1.3.4Perturbation of a 2-level system (Joćo)
21.10.2024 5.1.3.8Three-level system with degeneracy (Joćo)
21.10.2024 11.3.1 - 11.4.3Atoms with many electrons, periodic system of elements
23.10.2024 5.1.3.3Extended nucleus (Rafael)
23.10.2024 5.2.3.1Variational method applied to a quartic potential (Rafael)
23.10.2024 14.1.1 - 14.4.5Interaction of light with atoms, selection rules, density matrix and Bloch equations
28.10.2024 5.2.3.5Collapse of a condensate with attractive interactions (Rafael)
28.10.2024 9.1.5.7Magnetic field generated by the orbiting proton at the location of the electron (Joćo)
28.10.2024 9.3.3.4Hyperfine structure of rubidium (Joćo)
28.10.2024 14.5.1 - 14.7.3Spontaneous emission, line broadening, multilevel systems
30.10.2024 15.1.1 - 15.1.4Phenomena in three-level systems, quantized radiation, dressed states
06.11.2024 10.1.3.1Lagrangian of an electron in the electromagnetic field (Joćo)
06.11.2024 10.2.7.1Zeeman effect with different quantization axes (Gabriel)
06.11.2024 10.2.7.3Coupling of two electrons (Rafael)
06.11.2024 15.2.1 + 15.4.1-3Quasi-probability distributions, the Jaynes-Cummings model
11.11.2024 18.1.1-3 + 24.1.1-2.1Forces on atoms, radiation pressure and optical tweezer, ultracold atoms
13.11.2024 10.3.2.1Stark effect in hydrogen (Rafael)
13.11.2024 11.1.3.1Indistinguishability of particles (Gabriel)
13.11.2024 11.1.3.2Bosonic and fermionic isotopes (Gabriel)
13.11.2024 24.2.2 - 24.4.2Experimental techniques for cooling and trapping
18.11.2024 24.4.3 - 25.2.5Evaporation, imaging techniques, Bose-Einstein condensation
20.11.2024 11.4.4.1Filled electronic shells (Rafael)
20.11.2024 11.4.4.2Electronic excitation levels of alkaline (Joćo)
20.11.2024 19.1.1 - 20.1.4Coupled dipoles model, atoms in cavities
20.11.2024 15.6.4.2Non-Hermitian time evolution (Gabriel)
25.11.2024 18.1.4.1The Stern-Gerlach effect (Joćo)
25.11.2024 18.1.4.2Potential for magnetic trapping (Gabriel)
25.11.2024 18.2.5.2Radiation pressure (Rafael)
25.11.2024 23.1.1 - 21.2.2Collective coupling of atoms in cavities, the collective atomic recoil laser, lab tour
27.11.2024 Seminar

Other possible topics
4.1.1 - 4.3.3 Atoms in periodic potentials
15.4.1 + 19.1.2Spontaneous emission and cooperative scattering, the coupled dipoles model
19.2.1 - 19.2.5Super- and subradiance
22.1.1 - 22.2.3EPR paradox, entanglement generation
23.1.1 - 21.6.1Self-organization in atomic clouds



Seminar

Date of presentationSpeakerTopic
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27.11.2024 Joćo V. B. de S. MerendaSchrödinger cats
27.11.2024 Rafael A. R. da PazSupersolids
27.11.2024 Gabriel BelumatRydberg atoms

Evaluation criteria for the seminar:
  Structure: motivation and contextualization, introdution and outline of the organization of the presentation, conclusion
  Content: choice of topics, logical organization and didactics of argumentation, preparation to answer questions and to survive a discussion
  Didatics: abundant use of examples and schemes, interpretation and discussion of results, implication of the audience, capacity of raising curiosity in the audience
  Presentation:clarity and conciseness, organization of the talk or the blackboard, fluence of the presentation
The active participation of every student in discussions following the presentations of other students will also be evaluated!
Link to the booklet of the course on 'Atomic physics'

Suggestions for seminar topics:The quantum Zeno effect,
Second quantization,
Observation of super- and subradiant spontaneous emission of two ions,
Squeezed states,
The Jaynes-Cummings model,
Quantum projection noise,
Quantum gates,
The method of quantum Monte-Carlo wavefunction simulation,
The quantum Zeno effect,
Bloch equations: derivation and interpretation,
The quantum jumps, its history and observation,
Schrödinger's cat,
The Einstein-Podolski-Rosen hypothesis and its experimental falsification,
Elitzur and Vaidman bomb testing problem,
Topological phases and the Aharonov-Bohm effect,
Quantum non-demolition measurements,
Quantum correlations and the experiments of Young and Hanbury-Brown-Twiss,
Rydberg atoms,
The helium atom,
The quadratic and the dynamic Stark effect,
Ultracold molecules,
Efimov states,
Bose-Einstein condensation.