Presentation on theme: "Creating new states of matter: Selim Jochim MPI für Kernphysik and Universität Heidelberg Experiments with ultra-cold Fermi gases Henning Moritz ETH Zürich."— Presentation transcript:
Creating new states of matter: Selim Jochim MPI für Kernphysik and Universität Heidelberg Experiments with ultra-cold Fermi gases Henning Moritz ETH Zürich
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
The molecular condensate: What makes it special? Why does it work? What can we do with it? How cold is it?
Change the magnetic field! molecular BEC na 3 = 0.04
exploring the crossover molecular BEC na 3 = 0.04 na 3 = 0.28
exploring the crossover molecular BEC Bosons na 3 = 0.04 na 3 = 0.28 na 3,k F |a| = Fermions
exploring the crossover molecular BEC Fermions Bosons na 3 = 0.04 na 3 = 0.28 k F |a| = 6 na 3,k F |a| =
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)
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
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
What determines the shape of a BEC? Noninteracting atoms: ground state of the trap
Shape of a BEC Interacting atoms: mean field n = N/V riri r V N Valid for na 3 <<1 !!!
Gross-Pitaevskii equation Describe system as single particle wave function kinetic term external potential interaction chemical potential Ignore kinetic term: Thomas-Fermi approx.
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
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:
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
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)
How to measure Simply measure cloud size! –shape should be the same as for noninteracting gas … Unfortunately: Precision very poor!
More precise measurements Which quantities can be measured with the highest accuracy?
collective modes axial radial cigar-shaped trap r = Hz, z Hz
collective modes breathing two kinds of radial modes: quadrupole compression surface mode
axial coll. excitation frequency (normalized to sloshing mode) magnetic field (G) on resonance:
axial coll. excitation frequency (normalized to sloshing mode)
axial coll. excitation frequency (normalized to sloshing mode)
radial coll. excitation
What kind of mode was excited? need to have a closer look! surface mode? compression mode? Lee, Huang, Yang prediction
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>
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
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
rf spectra in crossover regime rf offset (kHz) 837 G: very large neg. scatt. length
rf spectra in crossover regime rf offset (kHz) large neg. sc. length 1kHz 48nK 4peV!100kHz 4.8 K 0.4neV
gap vs. interaction strength 3.3µK (68 1 W 1.1µK (23 35mW Fermi energy at two different levels of trap power
gap vs. interaction strength comparison with radial trap frequency
universal lineshape data taken on resonance, frequency scale normalized to Fermi energy 0.16 E F
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
Condensate Fraction Data: MIT (2004) Temperature measurement difficult: Alternative: measure condensate fraction
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
Observation of vortices! MIT experiment (2005) Vortices on BEC side of resonance!
Vortices in the cross over 740G 766G 792G 812G 833G843G853G 863G Now a tool to check superfluidity!!!
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? …..
A matter of temperature?? This trap is very elongated!!
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