| Semester: | 2022-1 |
| Responsable: | Prof. Philippe W. Courteille, philippe.courteille@ifsc.usp.br |
| Start and end of classes: | 29.3.2022 to 7.7.2022 |
| Queries: | via e-mail |
| Time and location of classes: | Thursdays from 14h00 to 16h00 in room F-210 and Fridays from 8h00 to 10h00
Google meet |
| Dates of the seminar: | 21.6.2022 to 7.7.2022 |
| Holidays: | 11.4.-16.4.2022 (semana santa), 21.4.-23.4.2022 (Tiradentes), 16.6.-18.6.2022 (Corpus Christi), 9.7.2022 (Revolução Constitucionalista) |
| 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. the harmonic oscillator, field probability distributions and quantum coherences, |
| 3. angular momentum algebra and the collective spin formalism, |
| 4. time-dependent perturbation theory, |
| 5. absorption and emission of light, absorption and fluorescence spectra, |
| 6. density operator and master equations for open systems, |
| 7. quantization procedure for field and atomic motion, the Jaynes-Cummings model, |
| 8. light scattering and cooperativity in coupled dipoles models, |
| 9. Dicke states and superradiant phase transitions, spin-squeezing and superradiant lasing, |
| 10. atoms in cavities, collective atomic motion, |
| 11. Bragg scattering and Bloch oscillations, |
| 12. detection and manipulation of ultracold gases. |
|
| Evaluation/approvation: |
Written tests will be applied, 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 |
| 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 |
| Date of presentation | Chapter of script | Exercise | Topic |
| ----------------------------- | ------------------------ | ------------ | -------- |
| 29.03.2022 | 1.2.1 - 1.2.7 | | Blackbody radiation, Einstein relations and Lambert-Beer law |
| 31.03.2022 | | 1.2.10.3 | The laws of Wien and Stefan-Boltzmann (Leandro) |
| 31.03.2022 | | 1.2.10.5 | Photons in a resonator (Claudio) |
| 31.03.2022 | | 1.2.10.6 | Number of modes in a cavity (Alejandra) |
| 31.03.2022 | 1.2.8 - 2.2.5 | | Saturation, basics of quantum theory |
| 06.04.2022 | | 1.2.10.8 | Number of photons per radiation mode (Lucas) |
| 06.04.2022 | | 1.2.10.9 | Atoms in an optical cavity (Claudio) |
| 06.04.2022 | | 1.2.10.11 | Applying the Lambert-Beer law (Alejandra) |
| 06.04.2022 | 2.2.6 - 2.3.7 | | States, observables and representations |
| 07.04.2022 | | 2.1.8.1 | Conservation of probability (Hugo) |
| 07.04.2022 | | 2.2.9.3 | Quantum superposition (Cosme / Erika) |
| 07.04.2022 | 2.3.8 - 2.5.4 | | Product spaces, time evolutions and translations |
| 22.04.2022 | | 2.2.9.2 | Normalization of the Bloch vector (Erika, Claudio) |
| 22.04.2022 | | 2.3.9.5 | Spin rotation operators (Leandro) |
| 22.04.2022 | | 2.3.9.6 | Eigenvalues and eigenvectors (Gustavo) |
| 22.04.2022 | 3.5.1 - 3.5.5 | | Symmetry transformations and the harmonic oscillator |
| 28.04.2022 | | 2.3.9.8 | Eigenvalues (Erika) |
| 28.04.2022 | | 2.3.9.15 | Liouville equation (Hugo) |
| 28.04.2022 | | 2.3.9.16 | Unitary transformation of singlet states (Leandro) |
| 28.04.2022 | 3.6.1 - 3.6.5 | | Superposition states of a harmonic oscillator |
| 29.04.2022 | | 2.4.7.1 | Coupled two-level atom (Hugo) |
| 29.04.2022 | 3.7.1 - 3.8.3 | | Kicking, shaking and forcing a harmonic oscillator |
| 05.05.2022 | | 2.4.7.4 | Particle in a homogenous gravitational field (Lucas) |
| 05.05.2022 | | 2.4.7.5 | Phase shift in a Ramsey-Bordé interferometer (Claudio) |
| 05.05.2022 | | 2.4.7.6 | Commutator of a function of operators (Alejandra) |
| 05.05.2022 | 4.3.1 - 4.4.4 + 5.2.1 | | Angular momentum algebra, coupling of angular momenta, periodic potentials |
| 06.05.2022 | | 3.5.6.3 | Vibration of a harmonic oscillator (Erika) |
| 06.05.2022 | 5.2.2 + 6.4.1 - 6.4.3 | | Bloch oscillations, time-dependent perturbations |
| 12.05.2022 | | 3.6.6.1 | Sum of displacements operators (Hugo) |
| 12.05.2022 | | 3.6.6.2 | Harmonic oscillator and coherent states (Cosme) |
| 12.05.2022 | | 3.6.6.5 | Schrödinger cat state (Leandro) |
| 12.05.2022 | 6.4.4 + 9.1.1 - 9.1.2 | | Transition rates, charges in electromagnetic fields, light-matter semiclassically |
| 13.05.2022 | | 3.6.6.7 | Lamb-Dicke regime (Claudio) |
| 13.05.2022 | 13.1.1 - 13.2.4 | | Dipolar approximation and selection rules |
| 19.05.2022 | | 3.6.6.11 | Electric field amplitude and fluctuation (Gustavo) |
| 19.05.2022 | | 3.6.6.12 | Beam splitting a Fock state (Leandro) |
| 19.05.2022 | | 3.6.6.13 | Wavefunction of a harmonic oscillator in a Glauber state (Alejandra) |
| 19.05.2022 | 13.3.1 - 13.4.5 | | Density operator and the Liouville equation |
| 20.05.2022 | | 4.2.3.6 | Transition matrix elements (Cosme) |
| 20.05.2022 | 13.5.1 - 13.5.3 | | Bloch equations with spontaneous emission |
| 26.05.2022 | | 4.3.4.5 | Uncertainty of angular momentum components (Erika) |
| 26.05.2022 | | 4.3.4.6 | Matrix representation of the components of the angular momentum (Cosme) |
| 26.05.2022 | | 4.3.4.7 | Spin-1/2-particle in a magnetic field (Lucas) |
| 26.05.2022 | 13.6.1 - 13.6.5 | | Line broadening effects and saturation |
| 27.05.2022 | | 4.3.4.8 | Spin expectation value for a two-level system (Erika, Claudio) |
| 27.05.2022 | 13.7.1 - 13.7.4 | | Raman-coherences in three-level systems |
| 02.06.2022 | | 4.4.5.7 | Transition amplitudes between Zeeman sub-states (Leandro) |
| 02.06.2022 | | 4.4.5.13 | External product of two spins (Cosme) |
| 02.06.2022 | | 4.4.5.14 | Coupling three spins (Alejandra) |
| 02.06.2022 | | 9.1.3.1 | Lagrangian of an electron in the electromagnetic field (Lucas) |
| 02.06.2022 | 14.1.1 - 14.1.4 | | Quantized radiation, the dressed atom picture |
| 03.06.2022 | | 13.3.5.2 | Pure states and mixtures (Erika) |
| 03.06.2022 | | 13.3.5.4 | Thermal mixture (Hugo) |
| 03.06.2022 | | 13.3.5.5 | Thermal population of a harmonic oscillator (Claudio) |
| 03.06.2022 | 14.2.1 - 14.2.4 | | The (quasi-)distribution functions P, Q, and W, squeezed states |
| 09.06.2022 | | 13.3.5.6 | Density operator of a Glauber state (Cosme) |
| 09.06.2022 | | 13.3.5.8 | Partial measurements (Alejandra) |
| 09.06.2022 | | 13.4.6.4 | Bloch vector and Bloch equations (Lucas) |
| 09.06.2022 | | 13.4.6.6 | Sequence of Ramsey pulses (Leandro) |
| 09.06.2022 | 14.3.1 - 14.3.3 | | Jaynes-Cummings model, quantum correlation in light fields |
| 10.06.2022 | | 13.4.6.8 | Atomic clocks by the Ramsey method with spontaneous emission (Claudio) |
| 10.06.2022 | | 13.4.6.9 | Photon echo (Claudio) |
| 10.06.2022 | | 13.5.4.6 | Purity of two-level atoms with spontaneous emission (Hugo) |
| 10.06.2022 | 14.4.1 - 14.4.4 | | Spontaneous emission, correlation functions |
| 17.06.2022 | | 13.5.4.12 | Quantum Zeno effect and saturation broadening (Lucas) |
| 17.06.2022 | | 13.5.4.13 | Saturation broadening and Autler-Townes splitting (Cosme) |
| 17.06.2022 | | 13.6.6.2 | Saturated absorption spectroscopy (Alejandra) |
| 17.06.2022 | | 13.8.4.1 | EIT & dark resonances (Erika) |
| 17.06.2022 | 18.1.1 - 18.1.1 | | The spectrum of resonance fluorescence |
| 23.06.2022 | | 13.8.4.2 | STIRAP (Claudio) |
| 23.06.2022 | | 13.8.4.3 | Adiabatic sweeps (Claudio) |
| 23.06.2022 | | 14.1.5.1 | Photon statistics (Erika) |
| 23.06.2022 | | 14.1.5.2 | Converting a pure state into a mixture by incomplete measurement (Hugo) |
| 23.06.2022 | 18.1.2 - 18.1.7 | | Introduction to numerical programming software, Matlab |
| 24.06.2022 | | 14.2.5.1 | Glauber-Sudarshan and Husimi distribution (Lucas) |
| 24.06.2022 | | 14.2.5.9 | P-, Q-, and Wigner distribution functions for Glauber states (Alejandra) |
| 24.06.2022 | | 14.4.6.1 | Time-evolution in the Jaynes-Cummings model (Leandro) |
| 24.06.2022 | 19.1.1 - 19.2.5 | | Cooperativity in light scattering, the coupled dipoles model |
| 30.06.2022 | | 14.4.6.4 | Vacuum Rabi splitting (Claudio) |
| 30.06.2022 | | 14.4.6.5 | The Q-function in a Jaynes-Cummings state (Hugo) |
| 30.06.2022 | | 14.4.6.6 | Creation of quantum correlations in an optical mode (Alejandra) |
| 30.06.2022 | | 14.6.4.2 | Non-Hermitian time evolution (Erika) |
| 30.06.2022 | 20.1.1 - 20.1.5 | | Collective states in the Dicke model, spin squeezing |
| 01.07.2022 | | 20.1.6.3 | Collective spin of a coherent spin state (Cosme) |
| 01.07.2022 | | 20.1.6.9 | Spin squeezing with two atoms (Lucas) |
| 01.07.2022 | | 20.2.3.4 | Equilibrium phase transition (Leandro) |
| 01.07.2022 | 20.2.1 - 20.3.3 | | Super- and subradiance, interacting atoms |
|
| | | | Other possible topics |
| | 15.1.1 - 15.1.2 | | Quantum jumps and quantum measurement |
| | 17.1.1 - 17.1.3 | | Electromagnetic forces |
| | 17.2.1 - 17.2.4 | | Optical forces |
| | 17.3.1 - 17.3.3 | | Photonic recoil on free and confined atoms |
| | 18.2.1 - 18.3.1 | | Mie scattering, scattering from continuous and from disordered clouds |
| | 18.4.1 - 18.4.3 | | Bragg scattering from periodic clouds, photonic bands |
| | 21.1.1 - 21.2.2 | | Atomic motion in optical cavities |
| | 21.3.1 - 21.3.3 | | Microscopic self-organization phenomena |
| | 21.5.1 - 21.5.5 | | Quantization of the atomic motion in cavities |
| | 21.6.1 - 21.6.5 | | Quantized light interacting with atoms moving in cavities |
| | 22.1.1 - 22.6.5 | | Atom optics, cooling and trapping |
| | 23.1.1 - 23.2.9 | | Quantum statistics of bosons and fermions |
| | 24.1.1 - 24.2.5 | | Bose-Einstein condensation |
| | 24.3.1 - 24.4.3 | | Solutions of the Gross-Pitaevski equation |
| | 25.1.1 - 25.4.3 | | Superfluid and coherent properties of Bose-Einstein condensates |
| | 26.1.1 - 26.3.4 | | Interaction of Bose-Einstein condensates with light |
| 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 jump, 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.
|