| Semester: | 2021-1 |
| Responsable: | Prof. Philippe W. Courteille, philippe.courteille@ifsc.usp.br, Sala 45 do Grupo de Óptica |
| Start and end of classes: | 25.3.2021 to 12.7.2021 |
| Queries: | via e-mail |
| Time and location of classes: | Mondays and Thursdays from 8h00 to 10h00 on-line,
sala da aula no Google meet |
| Dates of the seminar: | 1-12.7.2021 |
| Holiday: |
| Language: | Portuguese, French, German or English (to be agreed with the students) |
| Workload: |
| Theory | 4 per week |
| Practice | 3 per semana |
| Studies | 8 per semana |
| 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 'applied' quantum mechanics, 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. quantization procedure for field and atomic motion, |
| 3. master equation and open systems, |
| 4. light scattering and cooperativity in coupled dipoles models, |
| 5. collective atomic motion, atoms in cavities, |
| 6. foundations of quantum information. |
|
| 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 |
| Kevin Berwick, Computational Physics using MATLAB |
| MathWorks tutorials |
| Date of presentation | Chapter of script | Exercise | Topic |
| ----------------------------- | ------------------------ | ------------ | -------- |
| 25.03.2021 | 2.1.1 - 2.2.7 | | Foundations of quantum mechanics |
| 29.03.2021 | | 2.1.8.2 | Fourier theorem (Aline) |
| 29.03.2021 | | 2.2.9.2 | Normalization of the Bloch vector (Lucas) |
| 29.03.2021 | 2.2.8 - 2.3.4 | | Postulates of quantum mechanics |
| 01.04.2021 | | 2.3.9.3 | Orthonormal base (Julia) |
| 01.04.2021 | | 2.3.9.4 | Eigenvalue equation (Ian Carlo) |
| 01.04.2021 | 2.3.5 - 2.3.8 | | Representations and product spaces |
| 05.04.2021 | | 2.3.9.5 | Spin rotation operators (Camila) |
| 05.04.2021 | | 2.3.9.8 | Eigenvalues (Matheus Fernandes) |
| 05.04.2021 | 2.4.1 - 2.5.2 | | Time evolutions and translations |
| 08.04.2021 | | 2.3.10.15 | Liouville equation (João) |
| 08.04.2021 | | 2.3.10.16 | Unitary transformation of singlet states (Aline) |
| 08.04.2021 | 2.5.3 - 2.5.4 | | Symmetry transformations |
| 12.04.2021 | | 2.4.6.1 | Coupled two-level atom (José / Ian-Carlo) |
| 12.04.2021 | | 2.4.6.3 | Motion in Heisenberg's picture (Lucas) |
| 12.04.2021 | 3.4.1 - 3.4.3 | | The harmonic oscillator |
| 15.04.2021 | | 2.5.5.1 | Calculus with commutator (Matheus Fernandes) |
| 15.04.2021 | | 2.5.5.4 | Parity (Julia) |
| 15.04.2021 | | 3.4.6.1 | Ground state of a harmonic oscillator (João) |
| 15.04.2021 | 3.4.4 - 3.5.2 | | Superposition states of a harmonic oscillator |
| 19.04.2021 | | 3.4.6.3 | Vibration of a harmonic oscillator (Camila) |
| 19.04.2021 | | 3.5.6.2 | Harmonic oscillator and coherent states (José) |
| 19.04.2021 | | 3.5.6.4 | Schrödinger cat state (Lucas) |
| 19.04.2021 | 3.5.3 - 3.5.4 | | Kicked and shaken oscillator, the Lamb-Dicke regime |
| 22.04.2021 | | 3.5.6.3 | Annihilation operator acting on Fock and Glauber states (Aline) |
| 22.04.2021 | | 3.5.6.5 | Transition elements for arbitrary Lamb-Dicke parameters (Matheus Fernandes) |
| 22.04.2021 | 3.5.5 - 3.5.5 | | Forced oscillator, numerical approaches for arbitrary potentials |
| 26.04.2021 | | 3.6.3.1 | Numerical resolution of the Hermite differential equation (João) |
| 26.04.2021 | | 3.6.3.2 | Numerical resolution of the Schrödinger equation (Ian-Carlo) |
| 26.04.2021 | 3.6.1 - 3.6.2 | | The Fourier grid method, rotations and central potentials |
| 29.04.2021 | | 4.1.5.1 | Parity of the spherical harmonic functions (José) |
| 29.04.2021 | | 4.1.5.2 | Bose-Einstein condensate in an isotropic potential (Julia) |
| 29.04.2021 | 4.1.1 - 4.2.2 | | The radial Schrödinger equation |
| 03.04.2021 | | 3.5.6.10 | Beam splitter (Aline, Ian Carlo) |
| 03.04.2021 | | 3.6.3.5 | Least bound states numerically |
| 03.05.2021 | 4.3.1 - 4.4.3 | | Quantization of the electromagnic field, coupling of angular momenta |
| 06.05.2021 | | 4.1.5.6 | Particle in a spherical harmonic potential (Camila) |
| 06.05.2021 | | 4.2.3.6 | Transition matrix elements (Matheus Fernandes) |
| 06.05.2021 | 4.4.4 - 5.2.1 | | Clebsch-Gordan coefficients, periodic systems |
| 10.05.2021 | | 4.3.4.5 | Uncertainty of angular momentum components (Matheus Fernandes, Ian Carlo) |
| 10.05.2021 | | 4.4.5.1 | Addition/subtraction of angular momenta (João, Lucas, José) |
| 10.05.2021 | | 4.4.5.9 | (Un-)coupled bases of the spherical harmonics (Camila) |
| 10.05.2021 | 5.2.2 - 5.2.2 | | Matlab for quantum mechanics |
| 13.05.2021 | | 4.4.5.7 | Transition amplitudes between Zeeman sub-states (Lucas) |
| 13.05.2021 | | 4.4.5.8 | Gymnastics of angular momentum operators (Aline) |
| 13.05.2021 | 6.1.1 - 6.4.3 | | Bloch oscillations |
| 17.05.2021 | | 4.4.5.11 | Spin-orbit coupling (Julia) |
| 17.05.2021 | | 9.2.8.1 | Zeeman effect with different quantization axes (José) |
| 17.05.2021 | 6.1.1 - 6.3.1 | | Stationary perturbation theory and the variational method |
| 20.05.2021 | | 9.2.8.2 | Zeeman shift and quantization axes (Matheus Fernandes) |
| 20.05.2021 | | 6.1.3.1 | One-dimensional well with a deformation in the centre (Julia) |
| 20.05.2021 | | 6.1.3.4 | Perturbation of a 2-level system (Camila) |
| 20.05.2021 | 6.3.2 - 6.4.3 | | Time-dependent perturbation theory |
| 24.05.2021 | | 6.1.3.10 | Vanishing perturbation orders (Matheus Aryel) |
| 24.05.2021 | | 6.2.3.2 | Variational method applied to the harmonic oscillator (Aline, Lucas) |
| 24.05.2021 | 8.1.1 - 8.2.4 | | The method of steepest descent, the Dirac equation |
| 27.05.2021 | | 6.2.3.3 | Effect of finite nuclear mass on hydrogen via Rayleigh-Ritz (João) |
| 27.05.2021 | | 6.2.3.4 | Collapse of a condensate with attractive interactions (Lucas) |
| 27.05.2021 | | 6.4.6.1 | Perturbed harmonic oscillator (Camila) |
| 27.05.2021 | 8.2.5 + 14.1.1 | | The atomic fine structure, the density operator |
| 31.05.2021 | | 6.4.6.4 | Rabi method (Julia) |
| 31.05.2021 | | 6.4.6.5 | Ramsey fringes (Thales, Aline) |
| 31.05.2021 | | 14.1.5.2 | Pure states and mixtures (Ian Carlo) |
| 31.05.2021 | 14.1.2 - 14.2.2 | | The optical Bloch equations, the rotating wave approximation |
| 07.06.2021 | | 8.1.5.3 | Constants of motion of Dirac's Hamiltonian 1 (Matheus Aryel) |
| 07.06.2021 | | 8.1.5.6 | Constants of motion in the LS-coupling (Ian Carlo) |
| 07.06.2021 | | 8.1.5.7 | Magnetic field generated by the orbiting proton at the location of the electron (Camila) |
| 07.06.2021 | 14.2.3 - 14.4.5 | | The Bloch vector, spontaneous decay, line broadening |
| 10.06.2021 | | 14.1.5.3 | Mixture of states (Julia) |
| 10.06.2021 | | 14.1.5.4 | Thermal population of a harmonic oscillator (José) |
| 10.06.2021 | | 14.2.5.3 | Expansion in Pauli matrices (Matheus Aryel) |
| 10.06.2021 | 14.5.1 - 15.1.1 | | Multi-level Bloch equations, quantization of the electromagnetic field |
| 14.06.2021 | | 14.2.5.4 | Bloch vector and Bloch equations (Matheus Aryel) |
| 14.06.2021 | | 14.2.5.5 | Normalization of the Bloch vector (Matheus Fernandes) |
| 14.06.2021 | | 14.2.5.6 | Sequence of Ramsey pulses (Julia) |
| 14.06.2021 | 15.1.2 - 15.2.1 | | Dressed states, the Jaynes-Cummings model |
| 17.06.2021 | | 14.2.5.9 | Photon echo (Aline) |
| 17.06.2021 | | 14.3.5.2 | Detuning-dependent phase-shift of the dipole moment (José) |
| 17.06.2021 | 15.2.2 - 15.2.3 | | Quantum gates, quantum correlations |
| 21.06.2021 | | 14.3.5.11 | Quantum Zeno effect and saturation broadening (Lucas) |
| 21.06.2021 | 15.3.1 - 15.3.2 | | Spontaneous emission and resonance fluorescence |
| 24.06.2021 | | 14.4.6.2 | Saturated absorption spectroscopy (Matheus Aryel) |
| 24.06.2021 | | 15.1.4.1 | Photon statistics (João) |
| 24.06.2021 | 19.1.1 - 19.2.4 | | Electromagnetic and optical forces |
| 28.06.2021 | | 14.5.5.4 | EIT & dark resonances (Julia) |
| 28.06.2021 | | 15.1.4.3 | Converting a pure state into a mixture by incomplete measurement (José) |
| 28.06.2021 | | 15.2.4.4 | The Q-function in a Jaynes-Cummings state (Camila) |
| 28.06.2021 | 24.1.1 - 24.6.5 | | Atom optics, cooling and trapping, matter wave interferometry |
|
| Optional topics: | 19.3.1 - 19.3.3 | | Photonic recoil on free and confined atoms |
| | 20.1.1 - 20.1.1 | | Cooperativity in light scattering, the structure factor |
| | 20.1.2 - 20.1.7 | | The coupled dipoles model |
| | 20.2.1 - 20.3.1 | | Mie scattering, scattering from continuous and from disordered clouds |
| | 20.4.1 - 20.4.3 | | Bragg scattering from periodic clouds, photonic bands |
| | 22.1.1 - 22.2.2 | | Atomic motion in optical cavities |
| | 22.3.1 - 22.3.3 | | Microscopic self-organization phenomena |
| | 22.5.1 - 22.5.5 | | Quantization of the atomic motion in cavities |
| | 22.6.1 - 22.6.5 | | Quantized light interacting with atoms moving in cavities |
| | 25.1.1 - 25.2.9 | | Quantum statistics of bosons and fermions |
| | 26.1.1 - 26.2.5 | | Bose-Einstein condensation |
| | 26.3.1 - 26.4.3 | | Solutions of the Gross-Pitaevski equation |
| | 27.1.1 - 27.4.3 | | Superfluid and coherent properties of Bose-Einstein condensates |
| | 28.1.1 - 28.3.4 | | 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.
|