#### Candidacy Topic - Atomic and Molecular

**Introduction: **The following list of topical areas and subtopics covers the broad field of Atomic, Molecular, and Optical Physics. This is a very broad research area and examinees are not expected to be deeply conversant with all topics. Typically they should be barely conversant with topics well removed from their research area(s), and fairly knowledgeable about all subtopics of close relevance to this area. The adviser and examinee may, after consultation, alter this list.

**Atomic Units and Fundamental Constants: **Atomic units in terms of *ћ*, *e*, *c*,*m _{e}*; numerical values for length and energy; the fine structure constant.

**Light: **Basic E&M of light, polarization, standing and traveling waves, density of states, blackbody radiation, 2nd quantization, coherent states, squeezed states, Fock states.

**Atoms: **Spectroscopic notation (term and configuration); Bohr atom; one electron atom (energy hierarchy, non-relativistic limit, fine structure, hyperfine structure); Rydberg atoms; multi-electron atoms (Hund's rules).

**Atoms in Static Fields**: Magnetic field: Basic interaction, (anomalous) Zeeman effect, Paschen-Bach decoupling. Electric Fields: Polarizability, linear regime, field ionization, Stark shift

**Atom-Light Interaction: **Electric dipole approximation, Bloch equations, Rabi oscillation, Ramsey spectroscopy, AC-Stark shift, Raman process, Jaynes-Cummings model, dressed states, selection rules, spontaneous emission, Landau-Zener tunneling.

**Laser Cooling and Trapping of Atoms**: Radiation pressures (scattering and dipole forces), Doppler cooling, sub-Doppler cooling, evaporative cooling, magneto-optic trap, magnetic trapping, optical dipole trap, optical lattice

**Line Shapes: **Broadening mechanisms (homogeneous vs. inhomogeneous), Lorentzians and Gaussians, Doppler shift and recoil, Voigt profile.

**Molecules: **Long-range potentials between atoms(van der Waals R-6,resonance R-3), short range(vibrational and rotational spectra, molecular orbitals), photoassociative spectroscopy, cold molecules.

**Atomic Collisions: **Classical (cross section, mean free path, center-of-mass transformation), quantum (partial wave, scattering lengths, differential and total cross section, Born approximation), inelastic scattering, effects of identical particle symmetry and ultracold temperatures, Feshbach resonances

**Quantum Gases**: Ideal Bose and Fermi gas, thermal de Broglie wavelength, Bose-Einstein condensation, weakly interacting Bose condensate (Gross-Pitaevskii equation, Thomas-Fermi approximation, elementary excitations), Cooper pairing, BCS-BEC crossover