| Semester: | 2021-2 |
| Responsable: | Prof. Philippe W. Courteille, philippe.courteille@ifsc.usp.br |
| Start and end of classes: | 11.8.2021 to 26.11.2021 |
| Queries: | via e-mail |
| Time and location of classes: | Wednesdays and Fridays from 10h00 to 12h00 on-line,
sala da aula no Google meet |
| Dates of the seminar: | 12.11.2021 to 26.11.2021 |
| Holidays: |
| 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 |
|
| |
| Content: |
This is a graduate course! The 'raison d'être' 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: |
In view of the on-line character of this course, no written tests will be applied. Instead exercises will be solved in each class, homeworks will be given,
and a seminar will be organized. 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 edição, 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 Mechnanics, (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 |
| ----------------------------- | ------------------------ | ------------ | -------- |
| 11.08.2021 | 1.1.1 - 2.1.7 | | Antecedents and foundations of quantum mechanics |
| 13.08.2021 | | 1.1.6.2 | Rutherford scattering (Adonai) |
| 13.08.2021 | | 1.1.6.6 | Bohr's atom (Aline) |
| 13.08.2021 | | 1.1.6.7 | The hydrogen atom (Michelle) |
| 13.08.2021 | 2.2.1 - 2.4.6 | | Quantum theory, representations, product spaces and time evolutions |
| 17.08.2021 | | 2.1.8.1 | Conservation of probability (José) |
| 17.08.2021 | | 2.2.9.3 | Quantum superposition (Leonardo) |
| 17.08.2021 | 2.5.1 - 3.2.1 | | Translations and symmetry transformations, rectangular potentials |
| 20.08.2021 | | 2.2.9.6 | The ammonium molecule (Adonai) |
| 20.08.2021 | | 2.3.9.9 | Schwartz inequality (Aline) |
| 20.08.2021 | | 2.3.9.10 | Heisenberg's uncertainty principle (Michelle) |
| 20.08.2021 | 3.2.2 - 3.3.6 | | Potentials wells and barriers, scattering matrices, Dirac-potential |
| 24.08.2021 | | 2.3.9.12 | Projection of the motion of a particle (Leonardo) |
| 24.08.2021 | | 2.3.9.13 | Complete system of commuting operators (Adonai) |
| 24.08.2021 | | 2.4.7.4 | Particle in a homogenous gravitational field (Michelle) |
| 24.08.2021 | 3.4.1 - 3.4.2 | | Numerical techniques, the Fourier grid method, steepest descent |
| 27.08.2021 | | 2.4.7.5 | Phase shift in a Ramsey-Bordé interferometer (Adonai) |
| 27.08.2021 | | 2.4.7.6 | Commutator of a function of operators (Aline) |
| 27.08.2021 | 4.1.1 - 4.1.3 | | Particle in a central potential, separation of the angular motion |
| 01.09.2021 | | 3.1.4.1 | Trapped particle (José) |
| 01.09.2021 | | 3.2.5.3 | Particle in a well (Michelle) |
| 01.09.2021 | | 3.2.5.4 | Least bound states and localization energy (Aline) |
| 01.09.2021 | 4.1.4 - 4.2.2 | | Radial motion, quantum treatment of hydrogen, angular momentum algebra |
| 03.09.2021 | | 3.4.3.1 | Numerical resolution of the Hermite differential equation (Matheus, José) |
| 03.09.2021 | | 3.4.3.2 | Numerical resolution of the Schrödinger equation (Adonai) |
| 03.09.2021 | | 3.4.3.5 | Infinite rectangular double-well potential (Matheus) |
| 03.09.2021 | 4.3.1 - 4.4.4 | | Coupling of angular momenta and Clebsch-Gordan coefficients |
| 10.09.2021 | | 4.1.5.5 | Finite spherical 3D potential well (José) |
| 10.09.2021 | | 4.2.3.6 | Transition matrix elements (Adonai) |
| 10.09.2021 | | 4.3.4.8 | Spin expectation value for a two-level system (Michelle) |
| 10.09.2021 | 6.1.1 - 6.4.2 | | Stationary and time-dependent perturbation theory, the variational method |
| 14.09.2021 | | 4.4.5.7 | Transition amplitudes between Zeeman sub-states (Aline) |
| 14.09.2021 | | 4.4.5.9 | (Un-)coupled bases of the spherical harmonics (Adonai) |
| 14.09.2021 | | 4.4.5.11 | Spin-orbit coupling (Michelle) |
| 14.09.2021 | 6.4.3 - 6.4.4 | | Sudden and periodic perturbations, transition rates, Raman transitions |
| 17.09.2021 | | 4.4.5.14 | Coupling three spins (Michelle) |
| 17.09.2021 | | 6.1.3.4 | Perturbation of a 2-level system (José) |
| 17.09.2021 | | 6.1.3.8 | Three-level system with degeneracy (Adonai, Michelle) |
| 17.09.2021 | 8.1.1 - 8.1.2 | | The Dirac equation |
| 21.09.2021 | | 6.1.3.3 | Extended nucleus (Adonai) |
| 21.09.2021 | | 6.2.3.1 | Variational method applied to a quartic potential (Matheus) |
| 21.09.2021 | | 6.2.3.4 | Collapse of a condensate with attractive interactions (Aline) |
| 21.09.2021 | 8.1.3 - 8.1.4 | | Electron spin |
| 24.09.2021 | | 8.1.5.2 | Zitterbewegung (Aline) |
| 24.09.2021 | | 8.1.5.3 | Constants of motion of Dirac's Hamiltonian 1 (Leonardo) |
| 24.09.2021 | | 8.1.5.4 | Calculating with Dirac matrices (José) |
| 24.09.2021 | 8.2.1 - 8.2.5 | | Hydrogen fine structure via and TIPT |
| 28.09.2021 | | 8.1.5.6 | Constants of motion in the LS-coupling (José) |
| 28.09.2021 | | 8.1.5.7 | Magnetic field generated by the orbiting proton at the location of the electron (Michelle) |
| 28.09.2021 | 8.3.1 - 9.2.2 | | Hyperfine structure, charged particles in electromagnetic fields |
| 01.10.2021 | | 8.3.3.1 | Field of a magnetic moment (Aline) |
| 01.10.2021 | | 8.3.3.4 | Hyperfine structure of rubidium (Michelle) |
| 01.10.2021 | | 8.4.5.2 | Muonic hydrogen (José/Adonai) |
| 01.10.2021 | 9.2.3 - 9.2.7 | | Zeeman, Paschen-Back and Stark effect, Landau levels |
| 05.10.2021 | | 9.1.3.1 | Lagrangian of an electron in the electromagnetic field (Adonai) |
| 05.10.2021 | | 9.2.8.1 | Zeeman effect with different quantization axes (José) |
| 05.10.2021 | | 9.2.8.3 | Coupling of two electrons (Michelle) |
| 05.10.2021 | 10.1.1 - 10.2.2 | | Wavefunction symmetrization, Pauli's principle and the helium atom |
| 08.10.2021 | | 9.2.8.4 | Breit-Rabi formula (Aline) |
| 08.10.2021 | | 9.2.8.6 | Diamagnetism of the ground states of H atoms (José) |
| 08.10.2021 | | 9.3.2.1 | Stark effect in hydrogen (Leonardo) |
| 08.10.2021 | 10.3.1 - 10.4.3 | | Atoms with many electrons |
| 15.10.2021 | | 9.3.2.2 | Stark effect in the 1s hydrogen level (Michelle) |
| 15.10.2021 | | 10.1.3.1 | Indistinguishability of particles (Leonardo) |
| 15.10.2021 | | 10.1.3.2 | Bosonic and fermionic isotopes (José) |
| 15.10.2021 | 13.1.1 - 13.3.4 | | Periodic system, interaction of light with atoms, selection rules |
| 19.10.2021 | | 10.2.3.1 | Helium atom (Aline/Matheus/José) |
| 19.10.2021 | | 10.3.5.1 | Effective potential in the Thomas-Fermi model () |
| 19.10.2021 | 15.1.1 - 15.2.1 | | Quantized radiation, dressed atom picture, Jaynes-Cummings model |
| 22.10.2021 | | 10.4.4.1 | Filled electronic shells (Aline) |
| 22.10.2021 | | 10.4.4.2 | Electronic excitation levels of alkaline (Adonai) |
| 22.10.2021 | 15.4.1 + 19.1.2 | | Spontaneous emission and cooperative scattering |
| 26.10.2021 | | 15.2.4.1 | Time-evolution in the Jaynes-Cummings model (Adonai) |
| 26.10.2021 | | 15.2.4.4 | Vacuum Rabi splitting (José) |
| 26.10.2021 | | 15.2.4.6 | Creation of quantum correlations in an optical mode (Michelle) |
| 26.10.2021 | 21.1.1 - 21.1.2 | | Collective coupling in the Dicke model |
| 29.10.2021 | | 15.4.4.1 | Derivation of the rate equations for two-level atoms (Leonardo) |
| 29.10.2021 | | 15.4.4.2 | Non-Hermitian time evolution (Michelle) |
| 29.10.2021 | 21.1.3 - 21.2.4 | | Spin squeezing, the open Dicke model |
| 09.11.2021 | | 21.1.6.1 | Coherent spin states (José) |
| 09.11.2021 | | 21.1.6.2 | Collective spin of a coherent spin state (Adonai) |
| 09.11.2021 | 18.1.1 - 18.2.4 | | Super- and subradiance, forces on atoms |
| 12.11.2021 | | 21.1.6.4 | Rotation about the x-axis (Aline) |
| 12.11.2021 | | 21.1.6.8 | Spin squeezing with two atoms (José) |
| 12.11.2021 | | 21.2.5.5 | Equilibrium phase transition (Michelle) |
| 12.11.2021 | | | EPR paradox, entanglement generation |
| 16.11.2021 | | 18.1.4.1 | The Stern-Gerlach effect (Matheus) |
| 16.11.2021 | | 18.1.4.2 | Potential for magnetic trapping (Adonai, Michelle) |
| 16.11.2021 | | 18.2.5.2 | Radiation pressure (Matheus) |
| 16.11.2021 | 11.1.1 - 11.1.5 | | Cooling and trapping of atoms, self-organization phenomena |
| 19.11.2021 | | 21.3.3.2 | Behavior of entanglement upon rotation of the quantization axis (Adonai) |
| 19.11.2021 | | 21.3.3.4 | Projections of single-atom spins and their correlations () |
| 19.11.2021 | | 21.4.4.1 | Generating a Bell state (Adonai) |
| 19.11.2021 | 22.1.1 - 22.2.3 | | Self-organization in atomic clouds, lab tour |
| 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.
|