1. Erich Mueller Cornell University
Ultracold Fermions
Erich Mueller
Cornell University
Sourish Basu
Stefan Baur
Stefan Natu
Theja De Silva (Binghampton)
Dan Goldbaum
Kaden Hazzard
David Huse (Princeton)
Meera Parish (Princeton)
Francesco Fumarola (Columbia)

2. Fermi Systems Neutrons in Nuclear Matter
Strong overlap in relevant models and phenomena (magnetism, superconductivity…)
Electrons in Metals
Hard problems: emergent physics
Lithium atoms in optical traps
(record temp: 500pK)
Unity of description: why we love physics.

3. Outline Recent Progress BCS-BEC crossover Revisiting superconductivity
Near future
Pseudogap physics
Modulated superfluidity (FFLO)
Supressing superfluidity (Polarization and surface tension)
Use atomic systems to explore most exciting ideas in many body physics
Many other exciting phenomena: spin models, quantum hall effects, artificial light, Hubbard models…
Other directions: metrology, quantum computing…

4. Quantum Statistics High T: Boltzmann distribution Low T:
Degenerate gas
Hulet

5. Superfluidity Bosons: cold hot Atoms delocalized (Heisenberg)
Collective transport: no dissipation
BEC: state “unchanged” by adding/removing boson
Fermions:
Interactions drive pairing:
Pairs are Bosons: Superfluid

6. BCS-BEC Crossover Leggett Weak attractive interactions BCS
No bound state in free space V
Pairing is many-body effect (Fermi surface reduces dimensionality) r V0 r0
Pairing and superfluidity occur simultaneously
Continuously connected
(Experiment: tune interactions with magnetic field)
Strong attractive interactions
Pairing (crossover) precedes superfluidity (phase transition) V r
BEC

7. BCS-BEC landscape BEC BCS D 10 BCS-BEC crossover regime 10 10 10 10 10
Figure: M. Holland et al., PRL 87, (2001)
BEC
BCS 10
BCS-BEC crossover regime
Alkali BEC
Superfluid
4He
High Tc superconductors 10 -2
Transition temperature Tc/TF
Superfluid 3He 10 -4
Superconductors
(Cooper pairs) -6 10 10 5 -5 10 10 10
Binding energy of Fermionic pairs or gap energy
in units of Fermi Energy 2/ D kT BF

8. Phase diagram 6Li or 40K Pairs shrink Normal BEC BCS Superfluid B B0V B0 V r r
Free space: bound state at threshold (universal thermodynamics) V r
Most theory and experiment done here
Experiments confirm phase diagram

9. Universality and Unitarity
Bound state has infinite size: no energy scale from potential
Cross-section as large as possible
(determined by conservation laws)
Thermodynamic functions -- universal functions of density and temperature
Ex:
Same for nucleons as for atoms!

10. How to experimentally detect superfluidity?
Vortices
Ketterle group: Nature 435 , (2005).
Q: Nature of normal state Pseudogap
Specific heat:
Thomas group: Phys. Rev. Lett. 98, (2007)

11. What is pseudogap? (in BCS-BEC crossover literature)
Gap: Superfluid No low energy fermionic excitations
Atoms bound in condensed pairs
Colloquial pic: energy cost of breaking pairs gives gap
More precise: quantum interference of particle and hole states
Pseudogap: Normal Few low energy fermionic excitations
Atoms bound in non-condensed pairs:
Gap “blurred out” by incoherently adding contributions from pairs with different momenta

12. What is pseudogap? (in BCS-BEC crossover literature)
BCS spectral density (what is energy of excitations with momentum k?)
Idea: two ways to add particle
Simply insert particle

13. What is pseudogap? (in BCS-BEC crossover literature)
BCS spectral density (what is energy of excitations with momentum k?)
Idea: two ways to add particle
Simply insert particle
Insert pair, and a hole
(adding pair leaves state unchanged -- Condensate)

14. What is pseudogap? (in BCS-BEC crossover literature)
BCS spectral density (what is energy of excitations with momentum k?)
Idea: two ways to add particle
Simply insert particle
Insert pair, and a hole
States hybridize

15. What is pseudogap? (in BCS-BEC crossover literature)
BCS spectral density (what is energy of excitations with momentum k?)
Idea: two ways to add particle
Simply insert particle
Insert pair, and a hole
States hybridize
Add “coherence factors”

16. What is pseudogap? Superfluid (in BCS-BEC crossover literature)
Pseudogap spectral density (what is energy of excitations with momentum k?)
Normal
Insert particle

17. What is pseudogap? Superfluid (in BCS-BEC crossover literature)
Pseudogap spectral density (what is energy of excitations with momentum k?)
Normal
Simply insert particle
Insert hole and pair
Many ways to do this

18. What is pseudogap? Superfluid (in BCS-BEC crossover literature)
Pseudogap spectral density (what is energy of excitations with momentum k?)
Normal
Simply insert particle
Insert hole and pair
Many ways to do this
Hybridize + +
+ …

19. What is pseudogap? Superfluid (in BCS-BEC crossover literature)
Pseudogap spectral density (what is energy of excitations with momentum k?)
Normal
Structures persist at weaker coupling: (less broadening)

20. How to experimentally see pseudogap?
RF spectroscopy
Grimm group, Science 305, 1128 (2004)
7Li
Empty
Decreasing T
Continuum of final state k -k
Pairs
B [Gauss]
dn [kHz]
Challenges: final state interactions, trap inhomogeneities (current controversies)
(example with tightly bound pairs)
Mueller, ArXiv: ; Basu and Mueller, arXiv:

21. Is crossover pseudogap a novel quantum Liquid?
T>Tc~0.5 TF -- Not very degenerate
(metal at 105 K)
No sharp quasiparticles: thermal effect?
Need to suppress TC
Solution: Polarize gas
(spin relaxation negligible)
Connected to questions of interplay of superconductivity and magnetism
Fulde-Ferrel [1964], Larkin and Ovchinnikov [1965]
History: x
Looking for FFLO state is among goals of future experiments
Buzdin, Nature Materials (2004)

22. Observation: Phase separation
MW. Zwierlein, A. Schirotzek, C.H. Schunck, and W, Ketterle:
Science 311, (2006)
Superfluid core with polarized halo

23. Phase diagram (at unitarity) (cf: 3He-4He)
Comparison: liquid-gas
(cf: 3He-4He)
Ketterle group: Nature (Feb 7, 2008)

24. Surface Tension Phase Coexistence -> Surface Tension 60 mm 1 mm
Aspect Ratio of
Cloud: 50:1
Aspect Ratio of
Superfluid: 5:1
Data: Hulet (unpublished)
Amusing aside:
Initial experiments: axial density -- discrepancy between experiments

25. More Data
Data: Hulet group -- Nuclear Physics A (2007)

26. Origin of Surface TensionD D0 SF
Normal
Order parameter passes over barrier in going between spatially separated phases

27. Numerical Calculation
kfa=-20
At unitarity, surface tension parameterized by single universal number - extract approx value from BdG
Normal
Stefan Baur

28. Global consequences: soap bubble physicsz
Why “square” ends?
Interplay of trap and surface tension
Data: Hulet group -- Nuclear Physics A (2007)
Large anisotropy: at each z imagine infinite cylindrical bubble E
Critical droplet
Bubble radius
Natu and Mueller, arXiv:

29. Soap bubble physics z Why “square” ends?
Data: Hulet group -- Nuclear Physics A (2007)
Minimum moves up as z increases: “1st order transition” E
Critical droplet
Bubble radius
Natu and Mueller, arXiv:

30. How does pseudogap evolve with polarization?
Fumarola and Mueller, arXiv: T N S
Forbidden
Sharp fermions at Fermi energy
Pseudogap smearing pushed to finite energy
Pairs exist as excitations
Polarization

31. How does pseudogap evolve with polarization?
Fumarola and Mueller, arXiv: T N S
Forbidden
Sharp fermions at Fermi energy
Pseudogap smearing pushed to finite energy
Pairs exist as excitations
Polarization

32. Summary/Outlook Recent work: Strong coupling superfluidity
BCS-BEC Crossover
Pseudogap
Polarization: phase separation
More General
Cold atoms: controlled environment for studying collective effects in degenerate quantum systems
Future
FFLO x

33. Analogies “Pasta” phases of nuclear matter
“Stripe phases” of high temperature superconductors

34. x
Stability of FFLO?
Short range interactions: generally favor bulk phase sep
T=0
Mean-field calculation
Normal
Superfluid
FFLO red region

35. Future experiments -- Quasi-1D enhance CDW/SDW instability
Arrays of coupled tubes
1D--fluctuating FFLO phase very stable
FFLO S N
Boost Tc by coupling tubes
(Bethe Ansatz)

36. Phase diagram for coupled tubes
Meera M. Parish, Stefan K. Baur, Erich J. Mueller, David A. Huse
Phys. Rev. Lett. 99, (2007)