**Atomic, Molecular and Optical Physics Masters Defense Topics**

**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 advisor and examinee may, after
consultation, alter this list.

**Atomic Units and Fundamental Constants:** Atomic units in terms of Ñ, e, c, m, numerical values for length and energy. The fine structure constant, energy and length hierarchies (a_{0},aa_{0},,...). What are the fundamental constants and how are they determined?

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

**Atoms:** Spectroscopic notation (term and configuration); Bohr atom, one electron atom (alkali cf. H, relativistic effects, Lande g factor, Rydberg atoms); hyperfine structure, multi-electron atoms (Hund's rules).

**Atoms in Static Fields**

Magnetic: Basic interaction, (anomalous) Zeeman effect, Paschen-Bach decoupling, magnetic trapping.

Electric Fields: Polarizability, linear regime, field ionization.

**Resonance and Spectroscopy:** Interaction Hamiltonian, magnetic
resonance, two-state spectroscopy (Rabi solution, density matrix, Bloch
equations, transition rate, Ramsey spectroscopy), dressed atom, types of transitions, selection rules, and approximate spontaneous decay rates. 3-level systems: (Autler-Townes effect, dark states).

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

**Multi-Photon Processes:** Two-photon excitation, Raman processes, perturbation theory for higher order processes.

**Coherence:** Single atom (e.g. Ramsey Spectroscopy,quantum beats), localized ensembles (superradiance), extended ensembles (See atom optics: phase matching, 4-wave mixing), quantum computing, entanglement.

**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, Bom approximation), inelastic scattering, effects of identical particle symmetry and ultracold temperatures, evaporative cooling, Feshbach resonances

**Bose-Einstein Condensation**: Ideal gas, mean-field theory for a weakly interacting gas (Gross-Pitaevski equation, Thomas-Fermi approximation, elementary excitations, spinor condensates, superfluidity), second quantization.

**Qantum** **Degenerate Fermions**: Equilibrium properties, BCS state and Cooper pairing

**Linear atom optics**: gratings, waveguides, mirrors, atomic deflection and diffraction

**Cavity Quantum Electrodynamics**: Jaynes-Cummings model, 2nd quantization of light, dressed atoms

**Nonlinear and quantum atom optics:** wave mixing, solitons, phase coherent amplification, entanglement, spin squeezing

**Miscellaneous**: Landau-Zener crossing