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

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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-T C superconductors, Neutron stars, Quark-Gluon Plasma and more …. Today

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

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Change the magnetic field! molecular BEC na 3 = 0.04

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exploring the crossover molecular BEC na 3 = 0.04 na 3 = 0.28

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exploring the crossover molecular BEC Bosons na 3 = 0.04 na 3 = 0.28 na 3,k F |a| = Fermions

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exploring the crossover molecular BEC Fermions Bosons na 3 = 0.04 na 3 = 0.28 k F |a| = 6 na 3,k F |a| =

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exploring the crossover molecular BEC degenerate Fermi gas Fermions Bosons na 3 = 0.04 na 3 = 0.28 k F |a| = 1 k F |a| = 6 na 3,k F |a| = Bartenstein et al, PRL 92, (2004)

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

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

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k B T F : Fermi energy E pair : pairing energy 6 Li 2 BEC M. Holland et al., PRL (2001) A tunable BEC-BCS gas! critical temperature B-field We can freely change the interaction without increasing the entropy

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

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Shape of a BEC Interacting atoms: mean field n = N/V riri r V N Valid for na 3 <<1 !!!

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

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Size of a Fermi gas Fermi energy E F =k B T F Ignoring interactions: With interactions: no analytic expression, even difficult to calculate numerically RFRF

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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/k F More general: scattering cross section is limited:

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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+ E F,unitary =(1+ )E F,ideal

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Universal behavior on resonance! E F,unitary =(1+ )E F,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: =-0.58(1) Astrakharchik et al. PRL (2004)

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

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

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collective modes axial radial cigar-shaped trap r = Hz, z Hz

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

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axial coll. excitation frequency (normalized to sloshing mode) magnetic field (G) on resonance:

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axial coll. excitation frequency (normalized to sloshing mode)

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axial coll. excitation frequency (normalized to sloshing mode)

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radial coll. excitation

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

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More frequency measurements … Radio frequency spectroscopy high B-field 1 0 m I = rf ~80MHz breaking molecules costs energy molecular signal up-shifted breaking molecules costs energy molecular signal up-shifted pairs breaking pairs costs energy pair pair signal up-shifted pairs breaking pairs costs energy pair pair signal up-shifted |1> |2> |3>

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

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

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rf spectra in crossover regime rf offset (kHz) 837 G: very large neg. scatt. length

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

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

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gap vs. interaction strength comparison with radial trap frequency

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universal lineshape data taken on resonance, frequency scale normalized to Fermi energy 0.16 E F

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Wheres superfluidity? Weve 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

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

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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

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

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Vortices in the cross over 740G 766G 792G 812G 833G843G853G 863G Now a tool to check superfluidity!!!

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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? …..

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Many different answers ….

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Superfluidity in an imbalanced gas MIT

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Condensate fraction …. MIT

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Polarization detection scheme MIT experiment

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Phase separation MIT experiment

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Condensate fraction vs. P MIT experiment

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Phase separation (elongated trap) P=0 P=0.18 P=0.37 P=0.60 P=0.79 P=0.95 Rice University

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

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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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