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**
K. von Klitzing, G. Dorda, M.
Pepper, New method for high-accuracy
determination of the fine-structure
constant based on quantized Hall
resistance, Phys.
Rev. Lett. 45, 494 (1980).
M. Buttiker, Absence of
backscattering in the quantum Hall effect
in multiprobe conductors, Phys. Rev.
B 38,
9375 (1988).
L. P.
Kouwenhoven et al., Electron transport in
quantum dots, in Mesoscopic Electron
Transport,ed L. L. Sohn, G. Schoen and L. P.
Kouwenhoven (Kluwer Series E vol 345)
(June 1996) p 105 - 214
S. Datta, Quantum
transport. Atom to transistor (Cambridge
Univ. Press, 2013).
G. Benenti et al.,
Fundamental aspects of steady-state conversion
of heat to work at the nanoscale, Phys.
Rep. 694, 1 (2017).
Part II: Collective
quantum coherence of bosons and fermions
An introduction to BEC
& superfluidity
N.B. See Moodle for
the Lecture LaTeX notes and blog
Lecture 0 (online
--- see Moodle) Presentation of part 2 of the course (see
Moodle for the you tube videos with the
presentation)
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)
Lecture
1&2&3 (online
--- see Moodle) The ideal Bose gas
Gas in a 3D box
Thermodynamic limit
Lecture
4 (online --- see Moodle) BEC in ideal Bose gases:
statistical saturation of the excited states
Harmonic trapping
Problem set 1
Solutions: see video tutorials from students in
Moodle!
* Trapped ideal gases (Tc
for BEC, condensate fraction)
* Phenomenology of the ultracold gases
experiments * Measurement of energy and
ground-state occupation in ultracold atomic
BECs
Lectures: Introduction
to experiments in ultracold atomic gases; part1,
part2
Lecture 5&6 (online --- see Moodle)
One-body density matrix & off-diagonal long
range order
Order parameter
Ground state & coherent states
Lecture
7&8&9(online --- see Moodle)
The weakly-interacting Bose gas
Excitation spectrum
The Bogoliubov transformation
Sound velocity
Healing length
Condensate depletion due to
interactions
ODLRO for weakly interacting
Bose gases (Optional)
* One-body
density matrix in weakly interacting
Bose gases * Phase coherence
properties of weakly interacting Bose gases * Measurements of coherence &
ODLRO: from quantum optics to ultracold
gases
Lecture 10&11(online
--- see Moodle)
BEC and
superfluidity:
Landau criterion
Defect moving through a superfluid
GPE and inhomogeneous Bose Einstein Condensates (optional)
The discovery of
superfluidity: A. Griffin, "Superfluidity:
three people, two papers, one prize", Physics
World (2008).
B. De Marco & D. S. Jin,
"Onset of Fermi degeneracy in a trapped atomic
gas", Science
285, 1703 (1999)
A. G. Truscott et al.,
"Observation of Fermi pressure in a gas of
trapped atoms", Science
291, 2570 (2001)
Lecture
12&13&14(online --- see Moodle) Reminder
about the ideal Fermi gas
Weakly interacting Fermi gases
The one-pair Cooper problem
Cooper pairs
Lecture
15&16
(online --- see Moodle) 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)
Lecture 17&18&19(online --- see
Moodle) Mean-field
approximation
Bogoliubov transformation: quasi-particles
Variational calculation
Gap and number equations
Problem set 5
Lecture 20&21(online
--- see Moodle) BCS theory
at finite temperature (optional) (Elements of
the) BEC-BCS crossover theory (optional)
* Feshbach
resonances & the BEC-BCS crossover * BEC-BCS crossover at zero temperature:
T=0 variational calculation
A.J. Leggett, "Diatomic
molecules and Cooper Pairs", Modern Trends in
the Theory of Condesed Matter 115 13-27,
(1980)
The final course
presentations will be on Thursday the
14th of May 2019 AND Friday the 15th of May 2020
(20 min. = 15 min. presentation, 5 min.
discussion)
List of possible themes
suitable for presentations
PART
1
Quasiparticles
Landau theory of the Fermi liquid Dirac fermions in graphene Klein tunneling in graphene Topological insulators Majorana fermions
Quantum mechanics in condensed
matter Conductance quantization in quantum
point contacts Qubits in quantum dots Single electron transport in
quantum dots Onsager reciprocity relations Quantum simulators Electron optics with quantum Hall
edge channels Persistent currents in normal metal
rings Thermoelectric effect in quantum
conductors
PART
2
General
Phase
transitions, spontaneous symmetry
breaking and the Goldstone mode
Josephson
effect in superfluids and
superconductors
The concept
of phase in superfluids and
superconductors: interference between
two condensates and Josephson effect
Flux
quantisation and vortices in
superconductors and superfluids
Fermions
Feshbach
resonances & the BEC-BCS crossover
Polarised
Fermi gases
Bosons
Effects of
interactions on Bose-Einstein
condensation of an atomic gas
Deviations
from Einstein's picture of an ideal
saturated Bose gas
Bose-Einstein
Condensation in a Uniform potential
One-body
density
matrix in weakly interacting
Bose gases
Phenomenology
of the ultracold gases experiments
Trapped
ideal
gases (Tc for BEC, condensate
fraction)
Measurement
of energy and ground-state occupation
in ultracold atomic BECs
Measurements
of the excitation spectrum of a BEC in
ultracold atoms
Intereference
between two condensates:Fock vs.
coherent states
Measurements
of the phase coherence properties of
weakly interacting Bose gases
Measurements
of coherence & ODLRO: from
quantum optics to ultracold gases
The
Gross-Pitaevskii equation
Superfluid
velocity
& quantisation of circulation:
Vortex line solutions
Landau
criterion, Cherenkov waves and drag
force in weakly interacting Bose
condensates