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Creating new states of matter:

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Presentation on theme: "Creating new states of matter:"— Presentation transcript:

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 Today The molecular BEC – what can we do with it?
Crossover to a gas of (weakly bound) Cooper pairs Fundamental excitations, gap Fermi Superfluidity With tunable interactions: Model system for High-TC superconductors, Neutron stars, Quark-Gluon Plasma and more ….

3 The molecular condensate:
What makes it special? Why does it work? What can we do with it? How cold is it?

4 Change the magnetic field!
molecular BEC na3 = 0.04

5 exploring the crossover
na3 = 0.28 molecular BEC na3 = 0.04

6 exploring the crossover
Bosons Fermions na3,kF|a| =  na3 = 0.28 molecular BEC na3 = 0.04

7 exploring the crossover
Bosons Fermions na3,kF|a| =  na3 = 0.28 kF|a| = 6 molecular BEC na3 = 0.04

8 exploring the crossover
Bosons Fermions na3,kF|a| =  na3 = 0.28 kF|a| = 6 molecular BEC degenerate Fermi gas na3 = 0.04 kF|a| = 1 Bartenstein et al, PRL 92, (2004)

9 crossover reversible and lossless !
reversibility BEC 1s Fermi gas 1s BEC BEC after 2s crossover reversible and lossless ! T/TF  0.03 in Fermi gas limit Carr et al.,PRL 92, (2004) for 90% condensate fraction in BEC limit

10 BEC – BCS crossover 1980 crossover molecules Cooper pairs
strong coupling Cooper pairs weak coupling crossover 1980

11 A tunable BEC-BCS gas! 6Li2 BEC critical temperature
We can freely change the interaction without increasing the entropy B-field kBTF: Fermi energy Epair : pairing energy M. Holland et al., PRL (2001)

12 What determines the shape of a BEC?
Noninteracting atoms: ground state of the trap

13 Shape of a BEC Interacting atoms: mean field
V n = N/V N ri r Valid for na3<<1 !!!

14 Gross-Pitaevskii equation
Describe system as single particle wave function external potential interaction chemical potential kinetic term Ignore kinetic term: Thomas-Fermi approx.

15 Size of a Fermi gas Ignoring interactions:
With interactions: no analytic expression, even difficult to calculate numerically RF Fermi energy EF=kBTF

16 Interacting Fermi gas Description difficult: kinetic energy is dominant (Fermi momentum), or of similar magnitude as interaction, simple mean field interaction only works for a<< 1/kF More general: scattering cross section is limited:

17 Unitary interaction For unitary interaction (k>>1/a), the mean field energy scales just as the kinetic energy: This results in a rescaling of the Fermi energy by a constant factor (1+b) EF,unitary=(1+b)EF,ideal

18 Universal behavior on resonance!
EF,unitary=(1+b)EF,ideal is supposed to be a universal parameter independent of the physical system: In neutron stars, nuclei, quark-gluon plasma Hard to determine quantitatively Now measured experimentally Also quantum Monte Carlo and other methods are now in good agreement, best precision caclulation so far: b=-0.58(1) Astrakharchik et al. PRL (2004)

19 How to measure b ? Simply measure cloud size!
shape should be the same as for noninteracting gas … Unfortunately: Precision very poor!

20 More precise measurements
Which quantities can be measured with the highest accuracy?

21 collective modes cigar-shaped trap nr = 755(10) Hz, nz  22 Hz axial

22 collective modes two kinds of radial modes: „breathing“ compression
„quadrupole“ surface mode

23 axial coll. excitation on resonance: frequency (normalized to sloshing
mode) 600 800 1000 1200 magnetic field (G) on resonance:

24 axial coll. excitation frequency (normalized to sloshing mode)

25 axial coll. excitation frequency (normalized to sloshing mode) 600 800
1000 1200

26 radial coll. excitation

27 What kind of mode was excited?
surface mode? compression mode? need to have a closer look! Lee, Huang, Yang prediction

28 More frequency measurements …
Radio frequency spectroscopy rf ~80MHz breaking molecules costs energy molecular signal up-shifted breaking pairs costs energy pair signal up-shifted mI= -1 |3> |2> 1 |1> high B-field

29 rf spectra in BEC limit atoms only atom-molecule mixture
no evaporation T >> Tc atoms only atom-molecule mixture evaporation to T  Tc P = 300 mW molecular signal: two-body physics !! evaporation to T < 0.4 Tc P = 35 mW pure molecular sample (BEC) rf offset (kHz) 100kHz  4.8mK  0.4neV

30 rf spectra in BEC limit T ≈ 0.2 TF double-peak structure:
very large pos. sc. length T ≈ 0.2 TF double-peak structure: atoms and pairs T = 0.0? TF pairs only ! pair signal shifts with EF ! many-body physics rf offset

31 rf spectra in crossover regime
very large neg. scatt. length rf offset (kHz)

32 rf spectra in crossover regime
large neg. sc. length rf offset (kHz) 100kHz  4.8mK  0.4neV 1kHz  48nK  4peV!

33 gap vs. interaction strength
Fermi energy at two different levels of trap power 1.1µK (23 35mW 3.3µK (68 1 W

34 gap vs. interaction strength
comparison with radial trap frequency

35 universal lineshape data taken on resonance,
frequency scale normalized to Fermi energy 0.16 EF

36 Where’s superfluidity?
We’ve seen the gap: But is there superfluidity?? Is there a “condensate”??? Yes, there it is!! Condensate above resonance, 900G Zwierlein et al., MIT First observation: JILA Observe bimodal distributions, with both condensed pairs and thermal cloud

37 Condensate Fraction Data: MIT (2004)
Temperature measurement difficult: Alternative: measure condensate fraction

38 Superfluidity??? Bimodal distributions are a strong indication for a phase transition, but is there a superfluid phase? To date best method: Rotating superfluid needs to develop a vortex lattice Challenge: The visibility of the vortices might be very small: condensate fraction is rather tiny in BCS regime

39 Observation of vortices!
MIT experiment (2005) Vortices on BEC side of resonance!

40 Vortices in the cross over
792G 740G 766G 812G 833G 843G 853G 863G Now a tool to check superfluidity!!!

41 Polarized gases What happens if you change the balance between the two different spin states in the experiment? What would that correspond to in a superconductor? …..

42 Many different answers ….

43 Superfluidity in an imbalanced gas

44 Condensate fraction …. MIT

45 Polarization detection scheme
MIT experiment

46 Phase separation MIT experiment

47 Condensate fraction vs. P
MIT experiment

48 Phase separation (elongated trap)
Rice University

49 A matter of temperature??
This trap is very elongated!!

50 tomorrow 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 Slides available at

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