Material
complem.
Part I: superfluidity (bosons)
Part II:
superconductivity (fermions)
VOLVER ARRIBA
Lecture 1
Lecture 2&3&4
Lecture
5
Lecture 6&7
Lecture
8&9&10
Lecture
11&12&13
Lecture 14&15&16
Lecture
17&18
Lecture
19
Lecture 20
Lecture 21&22
Lecture 23&24
Lecture 25&26
Lecture 27&28&29
Lecture 30&31
Lecture 32&33
Lecture 34&35
Lecture 36&37
Lecture 38
Lecture 39&40
Problem set 1
Solutions
Problem
set 2
Problem
set 3
Problem
set 4
Problem
set 5
Problem
set 6
Problem set
7
Problem
set 8
Problem
set 9
VOLVER
ARRIBA
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N.B. The supplementary materials underlined in
yellow are (advanced) research articles among which you
can choose one or two articles for the presentation (20
minutes) at the end of the course. **Presentations are an
essential part of the evaluation together with the Problem sets**
Lecture 0
Presentation of
the course
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Part I:
superfluidity (bosons)
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Lecture 1
Historical introduction to Bose-Einstein
condensation (BEC) and sperfluidity
- Introductory
lecture
- E. A. Cornell and C. E.
Wieman, "Nobel lecture: Bose-Einstein
condensation in a dilute gas, the first 70
years and some recent experiments", Rev.
Mod. Phys. 74,
875 (2002)
- E. A. Cornell, J. R.
Ensher, and C. E. Wieman, "Experiments in
Dilute Atomic Bose-Einstein Condensation", proceedings
of the Varenna conference on Bose-Einstein
condensation (1998)
- A. Griffin,
"Superfluidity: three people, two papers, one
prize", Physics
World August 2008, 27-30
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Lecture 2&3&4
The ideal Bose gas
Gas in a 3D box
Thermodynamic limit
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Problem
set 1
Solutions: Mathematica
scritpt
Solutions: Matlab script: numerics_example.m,
int_num.m, fun_zero.m
Plots
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Lecture 5
Trapped ideal gases (Tc
for BEC, condensate fraction)
BEC in ideal Bose gases: statistical
saturation of the excited states
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Lecture
6&7
One-body density matrix & off-diagonal long
range order
Formalism of second quantisation
Order parameter
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Problem
set 2 |
Lecture
8&9&10
The weakly-interacting Bose gas
Excitation spectrum
The Bogoliubov transformation
Sound velocity
Healing length
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Lecture 11&12&13
BEC and
superfluidity:
Landau criterion
Defect moving through a superfluid
Condensate depletion
due to interactions
One-body density matrix in weakly interacting
Bose gases
- The discovery of
superfluidity: A. Griffin, "Superfluidity:
three people, two papers, one prize", Physics
World (2008).
- A. J. Leggett,
"Superfluidity", Rev.
Mod. Phys. 71,
S318 (1999)
- Drag force and Cerenkov
radiation:
- G. E. Astrakharchik and L. P.
Pitaevskii, PRA
70,
013608 (2004)
- I. Carusotto et al., PRL 97,
260403 (2006)
- C. Raman et al., PRL 83, 2502
(1999)
- T. W. Neely et al., PRL 104,
160401 (2010)
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Problem set 3 |
Lecture
14&15&16
Zero temperature: The time dependent
Gross-Pitaevskii equation
Conservation laws: continuity
equation
Stationary solutions
Landau free energy, order parameter, 2nd order
phase transition
Small amplitude oscillations: Bogoliubov-de
Gennes equations
Bogoliubov spectrum of excitations
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Lecture 17&18 --- Application
Superfluid velocity & quantisation of
circulation
Vortex line solutions
Healing length
Rotation of superfluids
Energy of a vortex solution
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Problem
set 4
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Lecture 19
Trapped condensates
Thomas-Fermi limit
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Problem
set 5
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Lecture 20 ---
Applications
Time
of flights measurements: expansion of a BEC
Interference between two condensates
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Problem
set 6
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Lecture 21&22
Towards understanding the experiments:
Alkali atoms
Density and momentum distributions
Short introduction to experiments in cold gases
Cooling, trapping & imaging techniques
Experiments on:
*expanding condensates
*interference between two condensates
*determining the Bogoliubov spectrum
*rotating gases (vortices)
*...
- Lectures: Introduction
to experiments in ultracold atomic gases; part1,
part2
- Science News ''Physicists
create new state of matter'', Science
269,
152 (1995)
- Science Perspectives ''An
Intimate gathering of bosons'', K. Burnett, Science
269,
182 (1995)
- F. Dalfovo et al., Rev. Mod. Phys. 71, 463
(1999)
- M. H. Anderson et al., Science
269,
198 (1995)
- K. B. Davis et al., PRL 75, 3969
(1995)
- Insight Review Article
"Bose-Einstein condensation of atomic gases",
Nature
416,
211 (2002)
- Review article: W. Ketterle et al.,
"Making, probing and understanding BECs", Proceedings
of the International School of Physics
"Enrico Fermi", Course CXL, edited by M.
Inguscio, S. Stringari and C.E. Wieman (IOS
Press, Amsterdam, 1999) pp. 67-176.
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Part II:
superconductivity (fermions)
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Lecture 23&24
Ideal Fermi gas (Sommerfeld theory of
metals)
Fermi-Dirac distribution vs. Maxwell-Boltzmann
Zero temperature: Fermi energy, zero point
pressure, compressibility
Thermal properties: Fermi temperature, heat
capacity
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Problem set 7 |
Lecture 25&26
Introduction to
superconductivity:
Phenomenology
Experimental evidences
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Lecture
27&28&29
Microscopic mechanisms behind
superconductivity
The
one-pair Cooper problem
Cooper pairs
The electron-phonon interaction |
Problem
set 8
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Lecture 30&31
BCS theory at zero temperature
Reduced Hamiltonian
BCS ground state: pair operators
Fock states versus coherent
states
(number of particles and phase as conjugate
variables)
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Lecture
32&33
Variational calculation
Gap and number equations
Condensate
energy and spectrum of
excitations
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Lecture 34&35
Mean-field approximation
Bogoliubov transformation: quasi-particles
BCS theory at finite temperature
Bogoliubov-de
Gennes equations
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Problem
set 9 |
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Lecture 36&37
Introduction
to the BEC-BCS crossover
Basic scattering theory
Scattering length
T-matrix formalism
Born approximation
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Lecture
38 --- Application
Relevance of the BEC-BCS crossover to cold
atoms
Feshbach resonances
Changing
the interaction strength |
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Lecture
39&40
BEC-BCS crossover at zero
temperature
T=0 variational calculation
Contact interaction and analytical solutions
BEC-BCS crossover at finite temperature
- A.J. Leggett, "Diatomic
molecules and Cooper Pairs", Modern Trends in
the Theory of Condesed Matter 115 13-27,
(1980)
- Lecture notes "Superfluidity
in
Ultracold Fermi gases"
- M. Greiner et al., Nature
426, 537 (2003)
- C. A. Regal et al., PRL 92, 040403
(2004)
- Some topic for a possible
presentation
- W. Ketterle & M. W.
Zwierlein, Making,
probing and understanding ultracold Fermi
gases in Ultracold Fermi Gases , Proceedings
of the International School of Physics
"Enrico Fermi", Course CLXIV, Varenna,
20 - 30 June 2006, Ed. M. Inguscio, W.
Ketterle, and C. Salomon (IOS Press,
Amsterdam) 2008
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Problem set 10 |
The final course
presentations will be on Monday the
20th of May 2012 AND Tuesday the 21th of May
2012 (20 min. = 15 min. presentation, 5 min.
discussion)
Let us
discuss well in advance (you can contact me at
francesca.marchetti (at) uam.es) the choice of a topic
Student's name
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date & time
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Title
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Angel
Gabriel Rivas Fonfria
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20/05/13
-- 10:00-10:30
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Intereference between two
condensates:Fock vs. coherent states
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Alberto
Martin Jimenez
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20/05/13
-- 10:30-11:30
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Josephson
effect in superfluids and
superconductors
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| Javier Galego Pascual |
20/05/13
-- 11:30-12:00
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Spontaneous
symmetry breaking,
Phase
transitions, spontaneous
symmetry breaking and the
Goldstone mode |
Alvaro
Esteban Prieto
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20/05/13
-- 12:00-12:30
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Measurements
of coherence & ODLRO: from
quantum optics to ultracold gases
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| David
Hernandez Merino |
20/05/13
-- 12:30-13:00
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Flux quantisation and
vortices in superconductors and
superfluids |
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Francisco Romero Ferrero
&
Sara Jimenez Puertas |
21/05/13
-- 10:00-11:00
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Landau criterion,
Cherenkov waves and drag force in weakly
interacting Bose condensates |
Andrea Santamaria Garcia &
Iñigo Alzueta Perez |
21/05/13
-- 11:00-12:00 |
Feshbach resonances
&
(Numerical solutions of the gap and
number equations in) the BEC-BCS
crossover |
| Manuel
Lara Astiaso |
21/05/13
-- 12:00-12:30 |
Polarised Fermi gases |
Jose
Benito Llorens
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21/05/13
-- 12:30-13:00 |
Deviations
from Einstein's picture of an ideal
saturated Bose gas |
| Examples of other
presentations from previous year
courses |
Josephson junctions,
The concept of phase in
superfluids and superconductors:
interference between two
condensates and Josephson effect |
| From 1 to N Cooper
pairs |
| Measurement of energy and
ground-state occupation in
ultracold atomic BECs
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| Fermi liquid
description and its breakdown |
| Majorana fermions:
concept and physical realisation
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Bibliography
VOLVER ARRIBA
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Part I
- L. Pitaevskii & S.
Stringari, Bose-Einstein Condensation, Clarendon Press,
Oxford (2003)
- A. J. Leggett, Quantum Liquids
--- Bose Condensation and Cooper Pairing in
Condensed-Matter Systems, Oxford
Graduate Texts, Oxford (2006)
- C. J. Pethick & H. Smith, Bose-Einstein
Condensation in Dilute Gases,
Cambridge University Press, Cambridge (2002)
- Bose
Einstein Condensation, ed. A.
Griffin, D. W. Snoke & S. Stringari,
Cambridge University Press, Cambridge (1995)
- My lecture course notes on
superfluidity (to appear towards the end of the
course)
Part II
- Ashcroft & Mermin, Solid
State Physics
- C. Kittel, Introduction
to Solid State Physics
- P. G. de Gennes, Superconductivity
of Metals and Alloys, Westview Press,
Oxford (1966)
- M. Tinkham, Introduction to
Superconductivity, Dover
Publications, New York (1996)
- P. Phillips, Advanced
Solid State Physics, Westview Press,
Oxford (2003)
- J. R. Schrieffer, Theory of
Superconductivity, Westview
Press, Oxford (1964)
- Lecture
notes on Superconductivity from Alfredo Levy
Yeyati
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