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 |
Practice | 3 per weak |
Studies | 8 per weak |
Duration | 15 weaks |
Total | 225 hours |
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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. |
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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. |
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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 |
Date of presentation | Chapter of script | Exercise | Topic |
----------------------------- | ------------------------ | ------------ | -------- |
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 | | 1.1.6.2 | Rutherford scattering (Rafael) |
26.08.2024 | | 1.1.6.6 | Bohr's atom (Joćo) |
26.08.2024 | | 1.1.6.7 | The 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 | | 1.4.9.2 | Normalization of the Bloch vector (Joćo) |
04.09.2024 | | 1.4.9.5 | The ammonium molecule (Rafael) |
04.09.2024 | | 1.5.9.3 | Orthonormal base (Gabriel) |
04.09.2024 | 2.4.1 - 2.4.4 | | Dirac-potential, numerical techniques, the Fourier grid method, steepest descent |
09.09.2024 | | 1.5.9.5 | Spin rotation operator (Joćo) |
09.09.2024 | | 1.5.9.8 | Eigenvalues (Gabriel) |
09.09.2024 | | 1.6.7.1 | Coupled 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 | | 1.7.6.2 | Particle in a homogenous gravitational field (Rafael) |
16.09.2024 | | 2.2.5.3 | Particle in a well (Joćo) |
16.09.2024 | | 2.2.5.4 | Least 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 | | 2.4.4.2 | Numerical resolution of the Schrödinger equation (Gabriel) |
23.09.2024 | | 2.4.4.5 | Infinite rectangular double-well potential (Joćo) |
23.09.2024 | | 3.1.5.5 | Finite 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 | | 3.2.3.6 | Transition matrix elements (Joćo) |
30.09.2024 | | 3.3.4.8 | Spin expectation value for a two-level system (Rafael) |
30.09.2024 | | 3.4.5.7 | Transition 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 | | 3.4.5.11 | Spin-orbit coupling (Rafael) |
07.10.2024 | | 3.4.5.14 | Coupling three spins (Joćo) |
07.10.2024 | 10.1.1 - 10.2.6 | | Charged particles in electromagnetic fields, Zeeman and Paschen-Back effect |
09.10.2024 | 10.2.7 - 11.2.2 | | Landau levels, Stark effect, wavefunction symmetrization and Pauli's principle, helium atom |
21.10.2024 | | 5.1.3.4 | Perturbation of a 2-level system (Joćo) |
21.10.2024 | | 5.1.3.8 | Three-level system with degeneracy (Joćo) |
21.10.2024 | 11.3.1 - 11.4.3 | | Atoms with many electrons, periodic system of elements |
23.10.2024 | | 5.1.3.3 | Extended nucleus (Rafael) |
23.10.2024 | | 5.2.3.1 | Variational method applied to a quartic potential (Rafael) |
23.10.2024 | 14.1.1 - 14.4.5 | | Interaction of light with atoms, selection rules, density matrix and Bloch equations |
28.10.2024 | | 5.2.3.5 | Collapse of a condensate with attractive interactions (Rafael) |
28.10.2024 | | 9.1.5.7 | Magnetic field generated by the orbiting proton at the location of the electron (Joćo) |
28.10.2024 | | 9.3.3.4 | Hyperfine structure of rubidium (Joćo) |
28.10.2024 | 14.5.1 - 14.7.3 | | Spontaneous emission, line broadening, multilevel systems |
30.10.2024 | 15.1.1 - 15.1.4 | | Phenomena in three-level systems, quantized radiation, dressed states |
06.11.2024 | | 10.1.3.1 | Lagrangian of an electron in the electromagnetic field (Joćo) |
06.11.2024 | | 10.2.7.1 | Zeeman effect with different quantization axes (Gabriel) |
06.11.2024 | | 10.2.7.3 | Coupling of two electrons (Rafael) |
06.11.2024 | 15.2.1 + 15.4.1-3 | | Quasi-probability distributions, the Jaynes-Cummings model |
11.11.2024 | 18.1.1-3 + 24.1.1-2.1 | | Forces on atoms, radiation pressure and optical tweezer, ultracold atoms |
13.11.2024 | | 10.3.2.1 | Stark effect in hydrogen (Rafael) |
13.11.2024 | | 11.1.3.1 | Indistinguishability of particles (Gabriel) |
13.11.2024 | | 11.1.3.2 | Bosonic and fermionic isotopes (Gabriel) |
13.11.2024 | 24.2.2 - 24.4.2 | | Experimental techniques for cooling and trapping |
18.11.2024 | 24.4.3 - 25.2.5 | | Evaporation, imaging techniques, Bose-Einstein condensation |
20.11.2024 | | 11.4.4.1 | Filled electronic shells (Rafael) |
20.11.2024 | | 11.4.4.2 | Electronic excitation levels of alkaline (Joćo) |
20.11.2024 | 19.1.1 - 20.1.4 | | Coupled dipoles model, atoms in cavities |
20.11.2024 | | 15.6.4.2 | Non-Hermitian time evolution (Gabriel) |
25.11.2024 | | 18.1.4.1 | The Stern-Gerlach effect (Joćo) |
25.11.2024 | | 18.1.4.2 | Potential for magnetic trapping (Gabriel) |
25.11.2024 | | 18.2.5.2 | Radiation pressure (Rafael) |
25.11.2024 | 23.1.1 - 21.2.2 | | Collective 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 + 19.1.2 | | Spontaneous emission and cooperative scattering, the coupled dipoles model |
| 19.2.1 - 19.2.5 | | Super- and subradiance |
| 22.1.1 - 22.2.3 | | EPR paradox, entanglement generation |
| 23.1.1 - 21.6.1 | | Self-organization in atomic clouds |
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.
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