Presentation on theme: "Creating new states of matter:"— Presentation transcript:
1Creating new states of matter: Experiments with ultra-cold Fermi gasesSelim JochimMPI für Kernphysik andUniversität HeidelbergHenning MoritzETH Zürich
2Today The molecular BEC – what can we do with it? Crossover to a gas of (weakly bound) Cooper pairs Fundamental excitations, gapFermi SuperfluidityWith tunable interactions: Model system for High-TC superconductors, Neutron stars, Quark-Gluon Plasma and more ….
3The molecular condensate: What makes it special?Why does it work?What can we do with it?How cold is it?
4Change the magnetic field! molecularBECna3 = 0.04
5exploring the crossover na3 = 0.28molecularBECna3 = 0.04
6exploring the crossover BosonsFermionsna3,kF|a| = na3 = 0.28molecularBECna3 = 0.04
8exploring the crossover BosonsFermionsna3,kF|a| = na3 = 0.28kF|a| = 6molecularBECdegenerateFermi gasna3 = 0.04kF|a| = 1Bartenstein et al, PRL 92, (2004)
9crossover reversible and lossless ! reversibilityBEC 1s Fermi gas 1s BECBEC after 2scrossover reversible and lossless !T/TF 0.03 in Fermi gas limit Carr et al.,PRL 92, (2004)for 90% condensate fraction in BEC limit
11A tunable BEC-BCS gas! 6Li2 BEC critical temperature We can freely change the interaction without increasing the entropyB-fieldkBTF: Fermi energyEpair : pairing energyM. Holland et al., PRL (2001)
12What determines the shape of a BEC? Noninteracting atoms: ground state of the trap
13Shape of a BEC Interacting atoms: mean field Vn = N/VNrirValid for na3<<1 !!!
14Gross-Pitaevskii equation Describe system as single particle wave functionexternal potentialinteractionchemical potentialkinetic termIgnore kinetic term:Thomas-Fermi approx.
15Size of a Fermi gas Ignoring interactions: With interactions: no analytic expression, even difficult to calculate numericallyRFFermienergyEF=kBTF
16Interacting Fermi gasDescription difficult: kinetic energy is dominant (Fermi momentum), or of similar magnitude as interaction, simple mean field interaction only works for a<< 1/kFMore general: scattering cross section is limited:
17Unitary interactionFor 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
18Universal behavior on resonance! EF,unitary=(1+b)EF,idealis supposed to be a universal parameter independent of the physical system:In neutron stars, nuclei, quark-gluon plasmaHard to determine quantitativelyNow measured experimentallyAlso 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)
19How to measure b ? Simply measure cloud size! shape should be the same as for noninteracting gas …Unfortunately: Precision very poor!
20More precise measurements Which quantities can be measured with the highest accuracy?
27What kind of mode was excited? surface mode? compression mode?need to have a closer look!Lee, Huang, Yang prediction
28More frequency measurements … Radio frequency spectroscopyrf~80MHzbreaking moleculescosts energy→molecular signalup-shiftedbreaking pairscosts energy→pair signalup-shiftedmI=-1|3>|2>1|1>high B-field
29rf spectra in BEC limit atoms only atom-molecule mixture no evaporationT >> Tcatoms onlyatom-molecule mixtureevaporation toT TcP = 300 mWmolecular signal:two-body physics !!evaporation toT < 0.4 TcP = 35 mWpure molecular sample(BEC)rf offset (kHz)100kHz 4.8mK 0.4neV
30rf spectra in BEC limit T ≈ 0.2 TF double-peak structure: very large pos. sc. lengthT ≈ 0.2 TFdouble-peak structure:atoms and pairsT = 0.0? TFpairs only !pair signal shifts with EF !many-body physicsrf offset
31rf spectra in crossover regime very large neg.scatt. lengthrf offset (kHz)
32rf spectra in crossover regime large neg. sc. lengthrf offset (kHz)100kHz 4.8mK 0.4neV1kHz 48nK 4peV!
33gap vs. interaction strength Fermi energyat two different levels of trap power1.1µK (23 35mW3.3µK (68 1 W
34gap vs. interaction strength comparison with radial trap frequency
35universal lineshape data taken on resonance, frequency scale normalized to Fermi energy0.16 EF
36Where’s superfluidity? We’ve seen the gap: But is there superfluidity?? Is there a “condensate”???Yes, there it is!!Condensate above resonance, 900GZwierlein et al., MITFirst observation: JILAObserve bimodal distributions, with both condensed pairs and thermal cloud
37Condensate Fraction Data: MIT (2004) Temperature measurement difficult:Alternative: measure condensate fraction
38Superfluidity???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 latticeChallenge: The visibility of the vortices might be very small: condensate fraction is rather tiny in BCS regime
39Observation of vortices! MIT experiment (2005)Vortices on BEC side of resonance!
40Vortices in the cross over 792G740G766G812G833G843G853G863GNow a tool to check superfluidity!!!
41Polarized gasesWhat happens if you change the balance between the two different spin states in the experiment?What would that correspond to in a superconductor?…..
48Phase separation (elongated trap) Rice University
49A matter of temperature?? This trap is very elongated!!
50tomorrow Condensed Matter Physics with atoms? Periodic potentials, bosonic Case: Mott isolatorFermions: The Fermi SurfaceInteractions of Fermions in optical latticesLow dimensional systemsFuture directions with optical latticesFinal discussionSlides available at