PHY 566
Quantum Electronics II

Ultracold Atoms
and Quantum Gases

fundamentals, techniques, and applications

Fall 2015

Meeting time and place Instructor


12:00-1:20 P-125  

Prof. Dominik Schneble

A-106 Office hours: tba
topics   Review of atom-light interactions; ultracold collisions; cooling and trapping; Bose-Einstein condensates and their mean-field physics; low-dimensional Bose gases; degenerate Fermi gases; pairing, superfluidity and BEC-BCS crossover; vortices; optical lattices; artificial gauge fields. Connections to condensed-matter, nuclear, and particle physics, quantum information science, and metrology.


  None required - lecture notes with chapter references to reviews and textbooks will be provided as the course proceeds.
Recommended: C.J. Pethick & H. Smith: Bose-Einstein-Condensation in Dilute Gases.
PHY565: ~biweekly homework (50%), midterm (15%) & final (15%); term paper (20%)

learning outcomes
Students who completed this course should have a thorough understanding of basic phenomena in ultracold AMO physics, should be able to describe these phenomena based on quantum mechanics, and should be able to make quantitative estimates for them.

detailed list of topics covered I Atomic structure of hydrogen and alkali atoms [PHY565 review]
Bohr model
Nonrelativistic QM of the hydrogen atom
Relativistic QM of the hydrogen atom: fine structure
Effects of QED on fine structure: Lamb shift
Effects of the nucleus: hyperfine structure
Alkali atoms: screening and quantum defect

II Atomic structure of multielectron atoms [PHY565 review]

III Interaction of atoms with static fields
Zeeman effect of the HFS: Breit-Rabi formula
quadratic and linear Stark effect

IV Interaction of atoms with oscillating fields: atomic resonance
Electric dipole Hamiltonian
AC Stark shift and spontaneous scattering rate
Rotating-wave approximation for 2-level atoms
Resonance of a driven magnetic moment: QM vs classical
Bloch representation of 2-level systems and their dynamics; OBE
Dressed states
Avoided level crossings; Landau-Zener transitions
Jaynes-Cummings model
Spontaneous emission, stimulated emission, and absorption
Dipole transitions: selection rules
Higher-order transitions

V The mechanical effects of light on atoms: laser cooling and trapping
Spontaneous scattering forces: optical molasses, MOT
Doppler- and sub-Doppler cooling
Optical dipole force

VI Ultracold collisions
Partial-wave expansion
s-wave scattering from a spherically symmetric rectangular well
Energy shift and effective interaction
Inelastic collisions
Feshbach resonances
Alkali potentials and scattering lengths

VII Evaporative cooling in conservative-potential atom traps
Simple model for evaporative cooling
Magnetic traps for neutral atoms: Quadrupole, TOP, IP
RF evaporation
Optical dipole traps

VIII Harmonically trapped ideal Bose and Fermi gases
Identical particles: wavefunction, distribution function
Density of states
Noninteracting Bose gas: ground state, Tc, thermodyn. quantities,  density distribution of thermal fraction
Noninteracting Fermi gas: Fermi energy, density distribution, momentum distribution

Weakly interacting trapped Bose gas: BEC
Equilibrium properties; Gross-Pitaevskii equation (GPE), density distribution, healing length
Bogoliubov excitations, critical velocity and superfluidity
Hydrodynamics: collective excitations, anisotropic expansion
Vortices and vortex lattices
Microscopic description beyond the GPE
Collective scattering: Bragg spectroscopy, impurity-atom scattering, four-wave mixing
Binary mixtures
Spinor condensates

X Interacting Fermi gases
Classification of fermionic homonuclear spin mixtures: regimes, interaction tuning, and role of  kFa
Mean-field theory of BEC-BCS crossover
Trapped-gas properties

XI Optical-lattice systems
Characteristic quantities
Band structure: Bloch waves and Wannier functions
Bloch oscillations, Landau-Zener transitions
Bose-Hubbard model: mean-field phase diagram
1D Bose gas: Lieb-Liniger model, Tonks-Girardeau

Each student must pursue his or her academic goals honestly and be personally accountable for all submitted work. Representing another person’s work as your own is always wrong. Any suspected instance of academic dishonesty will be reported to the Academic Judiciary. For more comprehensive information on academic integrity, including categories of academic dishonesty, please refer to the academic judiciary website at

Email to your University email account is an important way of communicating with you for this course. For most students the email address is ‘’, and the account can be accessed here: *It is your responsibility to read your email received at this account.* For instructions about how to verify your University email address see this: . You can set up email forwarding using instructions here: . If you choose to forward your University email to another account, we are not responsible for any undeliverable messages.

See the policy statement regarding religious holidays at Students are expected to notify the course professors by email of their intention to take time out for religious observance. This should be done as soon as possible but definitely before the end of the ‘add/drop’ period. At that time they can discuss with the instructor(s) how they will be able to make up the work covered.

If you have a physical, psychiatric/emotional, medical or learning disability that may impact on your ability to carry out assigned course work, you should contact the staff in the Disability Support Services office [DSS], 632-6748/9. DSS will review your concerns and determine, with you, what accommodations are necessary and appropriate. All information and documentation of disability is confidential. Students who require assistance during emergency evacuation are encouraged to discuss their needs with their professors and Disability Support Services. For procedures and information go to the website

Stony Brook University expects students to respect the rights, privileges, and property of other people. Faculty are required to report to the University Police and the Office of University Community Standards any serious disruptive behavior that interrupts teaching, compromises the safety of the learning environment, and/or inhibits students’ ability to learn. See more here:
revised 07/17/2015