| Semester: | 2023-1 |
| Responsable: | Prof. Philippe W. Courteille, philippe.courteille@ifsc.usp.br |
| Start and end of classes: | 13.3.2023 to 21.6.2023 |
| Queries: | via e-mail |
| Time and location of classes: | Mondays and Wednesdays from 14h00 to 16h00 in room F-210 or via
Google meet |
| Dates of the seminar: | 19.6.2023 and 21.6.2023 |
| Holidays: | 3.4.-8.4.2023 (semana santa), 21.4.-23.4.2023 (Tiradentes), 1.5.2023 (dia do trabalho), 8.-10.6.2023 (Corpus Christi) |
| 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 |
| ----------------------------- | ------------------------ | ------------ | -------- |
| 13.03.2023 | 1.2.1 - 1.2.7 | | Atoms & photons, blackbody radiation, Einstein relations and Lambert-Beer law |
| 15.03.2023 | | 1.2.10.3 | The laws of Wien and Stefan-Boltzmann (Nathan) |
| 15.03.2023 | | 1.2.10.5 | Photons in a resonator (Eliel) |
| 15.03.2023 | | 1.2.10.6 | Number of modes in a cavity (Clara) |
| 15.03.2023 | 1.2.8 - 2.2.5 | | Saturation, basics of quantum theory |
| 20.03.2023 | | 1.2.10.8 | Number of photons per radiation mode (Gabriel) |
| 20.03.2023 | | 1.2.10.9 | Atoms in an optical cavity (Vinícius) |
| 20.03.2023 | | 1.2.10.11 | Applying the Lambert-Beer law (Anna) |
| 20.03.2023 | 2.2.6 - 2.3.8 | | States, observables and representations, product spaces |
| 22.03.2023 | 2.4.1 - 2.5.4 | | Time evolutions and translations, symmetry transformations |
| 27.03.2023 | | 2.2.9.2 | Normalization of the Bloch vector (Gustavo) |
| 27.03.2023 | | 2.2.9.5 | The ammonium molecule (Gabriel) |
| 27.03.2023 | | 2.3.9.5 | Spin rotation operators (Clara) |
| 27.03.2023 | | 2.3.9.8 | Eigenvalues (Otávio) |
| 27.03.2023 | 3.5.1 - 3.5.3 | | Properties of the harmonic oscillator |
| 29.03.2023 | 3.5.4 - 3.6.3 | | Superposition states of a harmonic oscillator |
| 03.04.2023 | | 2.3.9.15 | Liouville equation (Otávio) |
| 03.04.2023 | | 2.3.9.16 | Unitary transformation of singlet states (Eliel) |
| 03.04.2023 | | 2.4.7.1 | Coupled two-level atom (Nathan) |
| 03.04.2023 | | 2.5.6.2 | Particle in a homogenous gravitational field () |
| 03.04.2023 | 3.6.4 - 3.8.3 | | Kicking, shaking and forcing a harmonic oscillator |
| 05.04.2023 | 15.1.2 + 4.3.1 - 4.4.4 | | Quantum jumps, angular momentum algebra, coupling of angular momenta |
| 10.04.2023 | | 2.5.6.3 | Phase shift in a Ramsey-Bordé interferometer (Vinicius) |
| 10.04.2023 | | 3.5.6.3 | Vibration of a harmonic oscillator (Gabriel) |
| 10.04.2023 | | 3.6.6.1 | Sum of displacements operators (Clara) |
| 10.04.2023 | | 3.6.6.2 | Harmonic oscillator and coherent states (Gustavo) |
| 10.04.2023 | 6.4.1 - 6.4.3 | | Time-dependent perturbations, Rabi oscillations |
| 12.04.2023 | 6.4.4 + 9.1.1/2 + 13.1.1 - 13.2.1 | | Transition rates, charges in electromagnetic fields, dipolar approximation |
| 17.04.2023 | | 3.6.6.3 | Annihilation operator acting on Fock and Glauber states (Nathan) |
| 17.04.2023 | | 3.6.6.5 | Schrödinger cat state (Otávio) |
| 17.04.2023 | | 3.6.6.7 | Lamb-Dicke regime (Anna) |
| 17.04.2023 | | 3.6.6.11 | Electric field amplitude and fluctuation (Eliel) |
| 17.04.2023 | 13.2.3 - 13.3.2 | | Selection rules, the density operator |
| 19.04.2023 | 13.3.3 - 13.5.1 | | Trace of observables, Bloch equations with spontaneous emission |
| 08.05.2023 | | 3.6.6.12 | Beam splitting a Fock state (Nathan) |
| 08.05.2023 | | 3.6.6.13 | Wavefunction of a harmonic oscillator in a Glauber state (Clara) |
| 08.05.2023 | | 4.2.3.6 | Transition matrix elements (Gustavo) |
| 08.05.2023 | | 4.3.4.5 | Uncertainty of angular momentum components (Vinícius) |
| 08.05.2023 | | 4.3.4.6 | Matrix representation of the components of the angular momentum (Gabriel) |
| 08.05.2023 | 13.5.2 - 13.6.5 | | Saturation and line broadening effects |
| 10.05.2023 | 13.7.1 - 13.7.4 | | Three-level systems |
| 15.05.2023 | | 4.3.4.7 | Spin-1/2-particle in a magnetic field (Gabriel) |
| 15.05.2023 | | 4.3.4.8 | Spin expectation value for a two-level system (Otávio) |
| 15.05.2023 | | 4.4.5.7 | Transition amplitudes between Zeeman sub-states (Gustavo, Nathan) |
| 15.05.2023 | | 4.4.5.13 | External product of two spins (Vinícius) |
| 15.05.2023 | 13.8.1 - 13.8.3 | | Probing of Autler-Townes splitting, multi-level phenomena |
| 17.05.2023 | 14.1.1 - 14.2.4 | | Quantized radiation, the dressed atom picture, (quasi-)distribution functions |
| 22.05.2023 | | 4.4.5.14 | Coupling three spins (Gustavo) |
| 22.05.2023 | | 9.1.3.1 | Lagrangian of an electron in the electromagnetic field (Anna) |
| 22.05.2023 | | 9.2.8.2 | Zeeman shift and quantization axes (Gabriel) |
| 22.05.2023 | | 13.3.5.2 | Pure states and mixtures (Clara) |
| 22.05.2023 | | 13.3.5.4 | Thermal mixture (Nathan) |
| 22.05.2023 | | 13.3.5.5 | Thermal population of a harmonic oscillator (Otávio ) |
| 22.05.2023 | | 13.3.5.6 | Density operator of a Glauber state (Otávio ) |
| 22.05.2023 | 14.4.1 - 14.4.4 | | Jaynes-Cummings model, quantum correlation in light fields |
| 24.05.2023 | 14.5.1 - 14.5.3 | | Spontaneous emission, correlation functions |
| 29.05.2023 | | 13.3.5.8 | Partial measurements (Vinícius) |
| 29.05.2023 | | 13.4.6.4 | Bloch vector and Bloch equations () |
| 29.05.2023 | | 13.4.6.6 | Sequence of Ramsey pulses () |
| 29.05.2023 | | 13.4.6.8 | Atomic clocks by the Ramsey method with spontaneous emission (Otávio) |
| 29.05.2023 | | 13.4.6.9 | Photon echo () |
| 29.05.2023 | | 13.5.4.6 | Purity of two-level atoms with spontaneous emission (Clara) |
| 31.05.2023 | | | Visit of strontium labs |
| 05.06.2023 | | 13.5.4.13 | Quantum Zeno effect and saturation broadening () |
| 05.06.2023 | | 13.6.6.2 | Saturated absorption spectroscopy (Anna) |
| 29.05.2023 | | 13.8.4.1 | Autler-Townes splitting (Gabriel) |
| 05.06.2023 | | 13.8.4.3 | EIT & dark resonances () |
| 05.06.2023 | | 13.8.4.5 | STIRAP (Nathan) |
| 05.06.2023 | | 13.8.4.6 | Adiabatic sweeps (Gustavo) |
| 05.06.2023 | | 14.1.5.1 | Photon statistics (Vinícius) |
| 05.06.2023 | | 14.1.5.2 | Converting a pure state into a mixture by incomplete measurement (Eliel) |
| 05.06.2023 | 14.6.1 - 14.6.2 | | Elastic and inelastic scattering |
| 07.06.2023 | 14.6.3 + 17.1.1 - 17.1.3 | | The spectrum of resonance fluorescence, electromagnetic and optical forces |
| 12.06.2023 | | 14.2.5.1 | Glauber-Sudarshan and Husimi distribution (Eliel) |
| 12.06.2023 | | 14.2.5.9 | P-, Q-, and Wigner distribution functions for Glauber states (Gustavo) |
| 12.06.2023 | | 14.4.5.1 | Time-evolution in the Jaynes-Cummings model (Gabriel) |
| 12.06.2023 | | 14.4.5.4 | Vacuum Rabi splitting () |
| 12.06.2023 | | 14.4.5.5 | The Q-function in a Jaynes-Cummings state () |
| 12.06.2023 | | 14.4.5.6 | Creation of quantum correlations in an optical mode (Vinícius) |
| 12.06.2023 | | 14.6.4.2 | Non-Hermitian time evolution (Nathan) |
| 12.06.2023 | 17.2.1 - 17.2.4 | | Radiation pressure and dipolar potentials |
| 14.06.2023 | 19.1.1 - 19.2.5 | | Cooperativity in light scattering, the coupled dipoles model |
| 19.06.2023 | | | Seminar |
| 21.06.2023 | | | Seminar |
|
| | | | Other possible topics |
| | 14.1.1 - 14.1.3 | | Squeezing of light |
| | 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 |
| | 20.1.1 - 20.1.5 | | Collective states in the Dicke model, spin squeezing |
| | 20.2.1 - 20.3.3 | | Super- and subradiance, interacting atoms |
| | 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 |