1. Creating new states of matter:
Experiments with ultra-cold Fermi gases
Selim Jochim
MPI für Kernphysik and
Universität Heidelberg
Henning Moritz
ETH Zürich

2. Introduction
Major breakthroughs in this field have made this field an exciting one in the past decade
Fermi Superfluidity, Crossover to a gas of Bosons (weakly bound molecules)
With tunable interactions: Model system for High-TC superconductors, Neutron stars, Quark-Gluon Plasma and more ….

3. What is an ultracold quantum gas?
Gas shows “quantum” effects when the wave packets start to overlap

4. Fermions and Bosons: Bosons Fermions At zero temperature …. Fermi
energy
EF=kBTF
Bose-Einstein condensation
Degenerate Fermi gas

5. What makes ultracold gases special?
Compare with superfluids, like He, or superconductors:
Density is way lower -> dilute gas makes description very simple
Lab-in-a-trap type of systems with many easy-to-use knobs, such as
temperature
confinement (single well, periodic …),
Interactions (even do controlled “chemistry”!)

6. First BEC experiments
JILA
Boulder
1995 Rb Na
MIT
1995

7. Fermi degenerate gases
Two isotopes of Lithium in the same trap in thermal equilibrium

8. Superfluid Fermi Gases:
Molecular condensates
Look like a normal BEC
Are normal BECs
A little bit of cheating?

9. Observe superfluidity
A rotating superfluid cloud needs to exhibit vortices

10. What will the course be about?
Today:
How do we make/manipulate/detect ultracold gases
Laser cooling
Trapping
Evaporative cooling in conservative potentials
Detection and manipulation of ultracold atoms

11. 2nd day
How to cool a Fermi gas - special challenges, - like forbidden collisions - Pauli blocking, etc.
Scattering length
Concept of Feshbach resonance to tune interactions  make things interesting!
Making ultracold molecules, BEC of molecules

12. 3rd day BEC of molecules BEC/BCS crossover
Gap, collective excitations/ Cooper pairs  superconductivity
Vortices
Imbalanced spin mixtures

13. 4th day Condensed Matter Physics with atoms?
Periodic potentials, bosonic Case: Mott isolator
Fermions: The Fermi Surface
Interactions of Fermions in optical lattices
Low dimensional systems
Future directions with optical lattices
Final discussion

14. Spontaneus light force:
photon momentum (recoil)
scattering rate
Lithium:
acceleration:
Frisch 1933: Deflection of a sodium beam using a Na-lamp:

15. Model: 2 level atom: Spontaneous scattering rate: s0: saturation G
Line width

16. Optical molasses
Doppler shift:
red detuned
blue detuned

17. Doppler molasses:

18.  Optical molasses!
Harold Metcalf (1986)

19. How cold can we get? T = /2kB Spontaneous emission causes heating,
due to randomly distributed emission.
stationary state when heating rate=cooling rate
minimal, when
T = /2kB
 ≈ a few MHz  Tmin typically 0.1…0.25 mK
Prediction by Hänsch, Schawlow, Wineland, Dehmelt (1975)

20. Much lower temperatures observed!!!
Time-of flight measurement:

21. Sub Doppler and sub recoil cooling
So far we only considered a 2-level atom,
typically, there are several Zeeman-sublevels.
different Zeeman-sublevel experience different
“light shifts”, “dressed atom” picture:
Rabi frequency

22. Sisyphus cooling Light shift on Zeeman level
(Clebsch Gordan coefficients)
Counter propagating Laser beams with orthogonal
polarization create a polarization grating:

23. Sideband cooling Quantization of trap potential |e> |g>
Condition for sideband cooling:
“Lamb-Dicke regime”:
Localize atoms better than Dx<< l
|g>
Used in this way in ion traps!

24. Raman-sideband cooling
Optical pumping
Raman-coupling
A little more complicated, but universal!
e.g. in optical lattice!

25. Magneto-optical trap
Optical molasses + magnetic field + polarisation:

26. MOT in 3D Quadrupole field through anti-Helmholtz coils,
Counterpropagating laser beams in x,y,z, with proper polarization

27. How to load a MOT?
Most simple technique: Load atoms from vapor! but: trapping velocity is limited to v ≈ a few 10 m/s, e.g. Rb., Cs.
 only a small fraction of the Boltzmann distribution can be trapped!
also: atomic vapor limits the vacuum and causes trap loss (Especially critical for subsequent experiments!)

28. Loading from and atomic beam
Atoms with a low vapor pressure:
 need to be evaporated from an oven.
(need to compensate Doppler shift!)
Slow an atomic beam?
 make use of spontaneous light scattering!

29. Zeeman slower Make use of Zeeman tuning: E.g.: Li, Na
“Extend” MOT to obtain slow atomic beam
Apply magnetic field, such that
E.g.: Li, Na

30. MOT ….

31. (Density) limitation of the MOT
What limits the (phase space) density in a MOT?
Collisions with background gas ( vapor cell!)
Light assisted collisions:
e.g.:
 photo association!
max. phase space density: ≈10-5

32. How to obtain a quantum gas?
So far: No success with exclusively optical cooling, but it provides excellent starting conditions
Also: No success without optical cooling!!!

33. Conservative potentials for atoms
Spatially varying magnetic field (magnetic trap):
 trap polarized atoms
Far detuned laser fields (induce dipole)

34. Magnetic trap Simplest configuration: quadrupole field (MOT)
 There is a problem, when the atoms get colder: µB
Majorana spin flips at B=0!
Orientation of the magnetic field should not change faster than Larmor frequency B

35. Ways around the zero: Time Orbiting Potential (TOP) Trap:
Rotate zero of magnetic field fast enough such that the atoms don’t take notice …
…but slower than the Larmor frequency
Time averaged potential!

36. Trap with offset field “Ioffe”-Bars with minimum (0G) in the center
“Pinch”-coils produce an offset field
and confine the atoms axially
 Ioffe Pritchard-trap

37. Optical traps (dipole force)
Electric field induces dipole: E p

38. oscillating E-Feld
E-field oscillates slower than resonance (red detuned light) dipole oscillates in phase
Intensity maximum is trap (e.g. focus)
E-field oscillates faster than resonance (blue detuned)
Dipole phase is shifted by p
Intensity minimum is trap (e.g. hollow beam)

39. optical dipole interaction
dipole potential
scattering rate
„red“ detuning (w<w0)
„blue“ detuning (w>w0)
optical dipole force
Fdip = - Udip
optical dipole potential
attraction
repulsion
For most applications: Need to go for very large detunings!

40. Why an optical trap? Challenge:
Typically, very large intensities are required to create the desired potential
Also, photon scattering has to be taken care of!
Potential is independent of spin state, magnetic field
Very flexible opportunities to shape potentials,
 e.g. optical lattice

41. Evaporative cooling
Idea: Remove hottest atoms, while thermal equilibrium is maintained
Important figure of merit: Gain in phase space density per loss of particles

42. EV cooling techniques
In magnetic traps, use RF fields to convert atoms to a high-field seeking state at distinct magnetic field (i.e. position)
potential
position

43. EV cooling techniques
In optical traps, reduce trap depth by reducing laser power.

44. Evaporative cooling Important quantities: Truncation parameter:
Ratio of good to bad collisions:
Bad collisions: E.g. dipolar relaxation, three-body recombination ….

45. Optimize EV cooling Efficiency limited by Collision rate
Losses Background gas (increase collision rate) Binary collisions (scales just as EV cooling) Three body collisions (go for low density)
Heating Photon scattering Parametric heating Anti-evaporation (e.g. Majorana spin flips)
Trap geometry

46. Efficiency Graph: Typical efficiencies …. EV cooling efficiency
truncation parameter h

47. Optimize EV cooling
Geometry matters when the gas becomes (close to) hydrodynamic, e.g. trap frequency < collision rate:
Example for inefficient geometry:
Magnetic trap with gravitational sag

48. Which trap to use? Magnetic trap: Easy evaporation,
Well defined potential
Constant trap frequency
Optical trap
More freedom with trap potentials
Can trap atoms in absolute (magnetic) ground state
Have to take care of photon scattering (use far off-resonant traps!)

49. Absorption imaging resonant cross section of the atoms ~l2
(depends on Clebsch-Gordan coefficients)
Considerable absorption already at very low density:
Image shadow on CCD!
Important advantage: “See” ALL scattered photons

50. Absorption imaging This is the quantity we measure
In the same way, measure momentum distribution:
Time of flight (TOF): measure spatial distribution after a certain time of flight

51. Challenges when cooling Fermions
Identical ultracold particles do not collide (s-waves).
“Pauli blocking” makes cooling of a degenerate Fermi gas very inefficient.
Also: Very low temperatures required to observe superfluidity:

52. Idea: Use Bosons to cool Fermions
Bosons can be cooled with “established” technology
Not the first degenerate Fermi gas, but a very instructive one:
6Li cooled by bosonic 7Li (Rice U., ENS Paris):
Difference of just one neutron makes all the difference!

53. 6Li+7Li cooled together
Two MOTs for the two isotopes (10GHz isotope shift)
Magnetic trap traps both isotopes …

54. Challenges to achieve very low T
Bosons condense to BEC -> heat capacity drops to zero, no more cooling effect
Interactions between Fermions are necessary to observe interesting physics -> spin mixture is needed
To study pairing effects, wish to tune pairing energy!
All of this: Tomorrow by Henning Moritz

55. Literature Metcalf and van der Straaten: “Laser cooling and trapping”
Ketterle, Durfee and Stamper-Kurn “Making, probing and understanding Bose-Einstein condensates”