Physics 2313S
Laser Cooling and Bose-Einstein Condensation
(last updated 18 April 00)
Lecturers:
Aephraim Steinberg (rm 1103, x8-0713,
aephraim@physics.utoronto.ca)
Allan Griffin (rm 1007, x8-5199, griffin@physics.utoronto.ca)
Lectures:
Monday 3pm, Tuesday 2pm, and Thursday 2pm.
Room: Monday in MP1115; Tues & Thurs in MP 408.
Overview |
Grading |
Syllabus |
Announcements |
Readings |
Problem Sets |
Final Project
Background:
While Bose-Einstein
Condensation underlies our understanding of superfluid Helium and
superconductivity, a holy grail of modern physics has been to directly produce
BEC in a low density, weakly interacting gas. Using lasers and magnetic fields
to trap and cool alkali atoms to ultracold temperatures, the BEC transition
was finally observed in 1995. As of May 1999, there are 20 groups around the
world which can produce such condensates. This course will give an
introduction to this exciting and rapidly expanding field, covering both
experimental and theoretical aspects. We will assume knowledge of elementary
statistical mechanics, quantum mechanics, atomic physics and electromagnetic
theory.
References:
The BEC homepage at http://amo.phy.gasou.edu/bec.html/ contains a vast array of regularly updated links.
A recent introduction to
BEC theory is given in F. Dalfovo et al., Rev. Mod. Phys., Vol 71, p. 463
(1999); cond-mat/9806038.
Recent summaries of the techniques of laser cooling and trapping can be
found in articles by Steve Chu, Claude Cohen-Tannoudji, and Bill Phillips
in the July, 1998 issue of Reviews of Modern Physics (volume 70, number 3,
pp 685-706; 707-719; and 721;741, respectively).
The most complete recent reference on experiments and theory in atomic BEC
is Bose-Einstein Condensation in Atomic Gases, Proceedings of the Varenna Summer
School Lectures in July 1998, ed. by M. Inguscio, S. Stringari and C. Wieman (IO
S Press, Amsterdam, 1999). Some of the articles cited below are chapters
of this book.
W. Ketterle, D.S. Durfee and D.M. Stamper-Kurn, Making, probing and
understanding Bose-Einstein condensates, cond-mat/9904034.
A.L. Fetter, Theory of a dilute low-temperature trapped Bose condensates, cond-mat/9811366.
A. Griffin, BEC and the New World of Coherent Matter Waves,
cond-mat/9911419.
The necessary background on atomic physics (specifically alkali spectra and
hyperfine
and Zeeman splittings) can generally be found in the
early articles on laser cooling and references therein. However, good
general treatments can also be found in Gerhard Herzberg's 1937 classic
Atomic Spectra and Atomic Structure; chapter XII of Cohen-Tannoudji et al.'s
Quantum Mechanics; selection rules, Clebsch-Gordan coefficients, and
the Lande g-factor are treated in the complements of chapter X of Cohen-Tannoudji.
A good review of work on cold and ultracold atomic collisions can be
found in Weiner et al., Rev. Mod. Phys. 71 (1), pp. 1-85 (Jan 1999).
Several pages with relevant data on atomic transitions, Clebsch-Gordon
coefficients, et cetera were handed out on the second day of class; this
"Hot topics in cold matter" package is available from Steinberg.
Topics:
Introduction and overview;
techniques of laser cooling and trapping (light forces on atoms, optical
molasses, sub-Doppler cooling, temperature measurements); magnetic traps
(adiabatic compression & evaporative cooling); statistical mechanics of
Bose atoms in harmonic wells, inter-atomic interactions and the scattering
length approximation, the Gross-Pitaevskii equation for the condensate
wavefunction, collective oscillations of the condensate; the role of
noncondensed atoms and two-fluid hydrodynamics of trapped Bose gases;
two-component condensates; atom lasers and nonlinear atom optics.
The grade will be based on approximately four problem sets and one
final project. 50% of the grade will be for the project and 50% for
the homework assignments. There will be no exams.
Thursday, Jan 6: First lecture. Allan Griffin. Overview of recent progress.
Monday, Jan 10 through Monday, Jan 24: Aephraim Steinberg.
Jan 10-13: Background: atomic physics of alkalis.
Jan 17-18: Optical and magnetic forces used in laser cooling.
Jan 20-24: Doppler molasses; introduction to MOTs;
phase-space density considerations.
Tuesday, Jan 25 through Thursday, Feb 24: Allan Griffin.
[no detailed summary available. Review of noninteracting Bose gas;
confined Bose gases; s-wave scattering lengths; inclusion of interactions;
Gross-Pitaevski equation; finite temperatures and the significance of
the non-condensate fraction.]
Monday, Feb 28 through Thursday, Mar 9: Aephraim Steinberg.
Feb 28: Limits on Doppler molasses; Sisyphus molasses, etc.
Feb 29: Polarisation gradient cooling, MOT,...
Mar 2: Vapour-cell MOTS, number and density limitations, typical parameters,...
Mar 6: Sub-recoil cooling... atomic coherences, VSCPT, Raman cooling,...
Mar 7: MOT improvements; magnetic trap matching, optical pumping, ...
Mar 9: Evaporative cooling, adiabatic compression, typical parameters...
Monday, Mar 13 through Thursday, Mar 16: Allan Griffin.
Mar 13: Coupled pair of GP equations
Mar 14: Effective Raman coupling
Mar 16: Inelastic Bragg scattering
Monday, Mar 20 through Thursday, Mar 30: Aephraim Steinberg.
Mar 20: Majorana flops, TOP and Ioffe traps,...
Mar 21-: Limitations, comparison of different magnetic and dipole traps,...
Mar 27-: Four-wave mixing, spin domains and tunneling,...
Monday, Apr 2 through Thursday, Apr 5 (last class): Allan Griffin.
PRESENTATIONS WILL BE SCHEDULED IN MID-TO-LATE APRIL...see below
From time to time, announcements may be posted on this web page.
Suggested readings will be listed here and are likely to be
updated as we progress through the course.
Problem set 1 was assigned on 24 Jan 2000, and was due on February 7th.
Problem set 2 was assigned on 11 Feb 2000, and was due on February 29th.
Problem set 3 was assigned on or about 19 Mar 2000, and is due on April 10th.
Problem set 4 is being assigned on 30 Mar 2000, and is due on April 17th.
The final project may be either a talk or a paper. Please email both
prof's with your proposed title and which format you prefer, by the
end of March at the latest. Projects will
be due on April 20th, and talks will be scheduled shortly (see below).
As explained in class, any topic related to current research topics in
Bose-Einstein condensation and/or laser cooling may be acceptable, but
should be vetted by us.
The talks will occur on Wednesday, April 26th, from 10:00 a.m. to
approximately 1:00 p.m., in room 408.
Sample topics we proposed include:
Phase-Coherent Amplification of Matter Waves, by M. Kozuma et al,
Science, 286, 2309 (1999). [atom laser]
Interference of BE Condensates in Momentum Space, L. Pitaevskii and
S. Stringari, PRL 83, 4237 (1999).
Scissors Mode and Superfluidity of a Trapped BEC, by D. Guéry-Odelin
and S. Stringari, PRL 83, 4452 (1999).
Four-wave Mixing with Matter Waves, by L. Deng et al, Nature 398, 218
(1999). [4-wave mixing]
Coherent Splitting of BEC Condensed Atoms with Optically Induced
Bragg Diffraction, by M. Kozuma et al, PRL 82, 871 (1999). [Bragg
scattering]
Meanfield Treatment of Bragg Scattering from a BEC, P. Blake and R.
Ballagh, cond-mat/9912422.
Observation of quantum statistics of local atom number (N-atom correlations)
Gravimetry using Bose-Einstein condensates
Comparison of atom-laser geometries
Coherence in two-species BECs and/or double-well geometries
Measurements of alkali collision parameters
Outlook for all-optical Bose-Einstein condensation
Fundamental excitations and their relaxation rates
Measurement of the coherence of a Bose-Einstein condensate
Bragg scattering and four-wave mixing of Bose condensates
Evidence for superfluidity in Bose condensates
Spin domains in alkali Bose-Einstein condensates
Reversible Bose-Einstein condensation
Superradiant Rayleigh Scattering from a BEC
Bose-Einstein Condensation with Negative Scattering Lengths
REMINDER: final talks occur on the morning of Wednesday, April 26th
(see above).
Back to Aephraim
Steinberg's Home Page
Back to Allan Griffin's Home Page