Physics 6110: Atomic Physics
Spring Semester, 2019
Robin Côté
Syllabus
Homeworks
Additional Material
| Date | Lecture | Content | ||||||
|---|---|---|---|---|---|---|---|---|
| Jan. 21 | Martin Luther King Jr. Day. | - No classes | ||||||
| Jan. 23 |
Lecture 1: Intro., Spectral lines, Bohr model, and units. |
Brief overview of the beginning of atomic physics: spectral lines and Rydberg formula, the Bohr model of the hydrogen atom, and various unit systems used in atomic physics. | ||||||
| Jan. 28 |
Lecture 2: Spinless hydrogenic atoms and ions |
Solving the Schrödinger equation for one-electron systems, and recovering the Bohr model results for hydrogen (with infinitely massive nucleus). | ||||||
| Jan. 30 | Lecture 3: Relativistic corr. | Summary of spinless hydrogenic systems, and introduction to angular momenta (orbital, general, and electron spin). We begin to investigate relativistic corrections. | ||||||
| Feb. 4 | Lecture 4: Dirac equation | We introduce the Dirac equation for a free particle, and show that it imlies the spin 1/2 of the electron. We generalize the treatment to an electron in a static electric Coulomb field, and obtain certain relativistic corrections. | ||||||
| Feb. 6 | Lecture 5: Size of corrections | We finish the relativistic corrections and evaluate their effects on hydrogen energy levels. We also briefly discuss the Lamb shift. | ||||||
| Feb. 11 | Lecture 6: Hyperfine Interactions | We see how the g-factor of the electron can be obtain from Dirac's Equation, and state the corrections to to QED. We introduce hyperfine interactions, due to the existence of the spin of the nucleus. | ||||||
| Feb. 13 | Lecture 7: Isotope shift | We introduce an additional effect due to the finite size of the nucleus, namely isotope shifts. We discuss the normal mass shift (NMS), the specific mass shift (SMS), and the field shift. | ||||||
| Feb. 18 | Lecture 8: Atoms in Optical Fields | We first introduce Einstein's phenomenological theory and its A and B coefficients. We follow by obtaining the Hamiltonian for a two-level atom in a classical optical field, and discuss the different type of transition allowed (electric dipole E1, magnetic dipole M1, electric quadrupole E2, etc.). | ||||||
| Feb. 20 | Lecture 9: Rabi Oscillations | We consider E1 transitions in a two level atom, and use the rotating wave approximation (RWA) to obtain simplified differential equations for the time-dependent population coefficient in each level. By solving them, we obtain the Rabi formula. | ||||||
| Feb. 25 | Lecture 10: Angular Momentum | We review angular momentum theory, first for the addition of two angular momenta. We also introduce the 3-j symbols. | ||||||
| Feb. 27 | Lecture 11: Wigner-Eckart Theorem | We continue our review of angular momentum theory, and discuss how to add three anular momenta and 6-j symbols. We introduce the Wigner-Eckart theorem which helps decoupling orientation and other properties of systems. | ||||||
| March 4 | Lecture 12: Applications of Wigner-Eckart Theorem | We review the Wigner-Eckart theorem, and explore its application to dipole and quadrupole transitions, and the Landé formula. We also explore its use in hyperfine interactions, and explore additional properties and additional theorems derived from the Wigner-Eckart theorem. | ||||||
| March 6 | Lecture 13: More Wigner-Eckart | We continue our discussion of the Wigner-Eckart theorem and its application. We also start introducing multi-electron atoms. | ||||||
| March 11 | Mid-term | Covers all topics to this date. | ||||||
| March 13 | E&M Mid-term | - No classes: E&M midterm. | ||||||
| March 18 | Spring Break | - No classes | ||||||
| March 20 | Spring Break | - No classes | ||||||
| March 25 | Final Project | - No classes: preparing final project | ||||||
| March 27 | Lecture 14a:
Multi-electron Lecture 14b: atoms |
We introduce multi-electron atoms, first by writing the full Hamiltonian, and using coordinate transformations, rewrite it in the relative coordinates, including the mass polarization term. We also introduce the Central Field approximation to treat the interaction between electrons. | ||||||
| April 1 | Lecture 15: The Helium atom | We continue our treatment of multi-electron atoms, and discuss the Helium atom as an example. We compute its ground state, and first excited state using perturbative and variational methods, accounting for the spin states. | ||||||
| April 3 | Lecture 16: Slater Determinant | We describe multi-electron atoms in general, in particular how Slater determinants can be used as a basis to construct wave functions. We apply the concepts to He and recover the previous results. | ||||||
| April 8 | Final Project | - No classes: preparing final project | ||||||
| April 10 | Lecture 17: More about atoms | We finish our discussion of the shell structure of the electronic states of multi-electron atoms. We also describe spin-orbit, and hyperfine structure for multi-electron atoms. | ||||||
| April 15 | Lecture 18: Cooling trapped ions | We give a short introduction to quantum information processing with atoms, ions, and molecules. We first review how ions can be trapped and cooled. In particular, we show how optical transitions can be used to cool to very low temperatures, and how it relates internal and external degree of freedom of the trapped ions. | ||||||
| April 17 | Lecture 19: Quantum Information with ions | We show how the specific excitations depend on the internal and external states of trapped ions, and show how excitation sequences can lead to quantum phase gates. We discuss the original gate of Zoller and Cirac, and explore other possible platforms based on atomic systems, notably Rydberg atoms. | ||||||
| April 22 | Lecture 20: Scattering | We introduce scattering theory for short-range (i.e. non-Coulomb problems) interactions, including the various notation and concepts. We consider spherically symmetric potentials, and focus on low-energy collisions, introducing the effective range expansion, and particularly the scattering length. We also discuss inelastic processes in general, and at low-temperaturesin particular. | ||||||
| April 24 | Lecture 21: Resonances | We introduce the different types of resonances, and the underlying reason for their appearance. We discuss resonances due to the form of the interactin potential (potential and shape resonances), and those due to coupling between different states (Feshbach resonances). We look at a two-state treatment of Feshbach resonances. | ||||||
| April 29 | Final Project Presentations | - No classes: presenting final project | ||||||
| May 1 | Final Project Presentations | - No classes: presenting final project | ||||||