Collège de France, 11 Apr 2005
Center of Quantum OpticsInnsbruck
Center of Quantum OpticsInnsbruck
Austrian Academy of SciencesAustrian Academy of SciencesUniversityUniversity
BEC and superfluidityin ultracold Fermi gases
Rudolf Grimm
BEC and superfluidityin ultracold Fermi gases
Rudolf Grimm
two classes
Fermionshalf-integer spin
Bosonsinteger spin
trapped atomsat T=0
all in ground state:Bose-Einstein condensate
only one particle per state:degenerate Fermi gas
two classes
Bosonsinteger spin
all in ground state:Bose-Einstein condensate
trapped atomsat T=0
Fermionshalf-integer spin
only one particle per state:degenerate Fermi gas
ultracold Fermi gases
1999: first degenerate Fermi gas (40K)Debbie Jin group at JILA, Boulder
40K: JILA (1999)Florence (2002)Zurich (2004)Hamburg (2004)
degenerate Fermi gases now playing in nine labs:6Li: Rice (2001)
ENS (2001)Duke (2001)MIT (2002)Innsbruck (2003)
2003 – making molecules (bosons!)BEC of molecules at Innsbruck, JILA, MIT, ENS Paris, Rice
2004 – BEC-BCS crossover, creation of fermionic superfluids
spin mixture oftwo lowest statesstable against two-body decay0 250 500 750 1000 1250 1500
-4
-2
0
2
4
magnetic Field [G]
a (1
000
a 0)
prediction:M. Houbiers et al., PRA 57, R1497 (1998).
Feshbach resonance
weakly bound dimers:it‘s a kind of magic !
6Li spin mixture
three-body recombination
molecules made by collisions
three atoms
three-body
process atomEkin =2Eb/3
large positive scattering lengthand last bound level
Eb = h2/(ma2)
r
U(r)
manystates
Ekin =Eb/3
molecule(binding energy Eb)
weakly bound dimers are huge !
weakly bound dimersize ~100nm
they are incredibly stable !(when made of fermionic atoms)theory: Petrov, Salomon, Shlyapnikov, PRL 93, 090404 (2004)expt.: Cubizolles et al., PRL 91, 240401 (2003)
Jochim et al., PRL 91, 240402 (2003)
they are incredibly stable !(when made of fermionic atoms)theory: Petrov, Salomon, Shlyapnikov, PRL 93, 090404 (2004)expt.: Cubizolles et al., PRL 91, 240401 (2003)
Jochim et al., PRL 91, 240402 (2003)
„normal“ dimersize ~1nm
optical trap for evaporative cooling
special feature #1precise controlof laser power
10 W → few 100µW
special feature #1precise controlof laser power
10 W → few 100µW
special feature #2: axial magnetic confinement- spatial compression at very weak optical traps- perfectly harmonic !!- precisely known trap frequency for weak optical trap
special feature #2: axial magnetic confinement- spatial compression at very weak optical traps- perfectly harmonic !!- precisely known trap frequency for weak optical trap
νz = 24.5 Hz @ 1kG
Umagn
apparatus
Science(Aug 04):
The Chamber of Secrets
6Li team
JohannesHecker
Denschlag AlexanderAltmeyer
StefanRiedlReece
Geursen
MarkusBarten-stein
Cheng Chin
SelimJochim
IBM res. labsSwitzerland
Sept. 04
IBM res. IBM res. labslabsSwitzerlandSwitzerland
Sept. 04Sept. 04
U ChicagoUSA
Jan. 05
U ChicagoU ChicagoUSAUSA
Jan. 05Jan. 05
U MelbourneAustraliaMay 05
U MelbourneU MelbourneAustraliaAustraliaMay 05May 05
axial profiles → phase transition
final trap power 28mW 3.8mWnumber of molecules 400.000 200.000temperature 430nK few 10nKcondensate fraction ~20% >90%
excellentstarting point
for further experiments
partiallycondensed
almostpure
molecular BEC gallery
JILA, Jin et al.40K2
MIT, Ketterle et al.
6Li2
6Li2ENS Paris, Salomon et al.
Rice Univ., Hulet et al.6Li2
thethe BECBEC--BCS BCS crossovercrossover
two classes
Fermionshalf-integer spin
Bosonsinteger spin
these twoworlds
are connected !
trapped atomsat T=0
all in ground state:Bose-Einstein condensate
only one particle per state:degenerate Fermi gas
two classes
Fermionshalf-integer spin
Bosonsinteger spin
trapped atomsat T=0
„pairing“is the key
all in ground state:Bose-Einstein condensate
only one particle per state:degenerate Fermi gas
two classes
Fermionshalf-integer spin
Bosonsinteger spin Feshbach
resonance
trapped atomsat T=0
interactioncontrol !!!
all in ground state:Bose-Einstein condensate
only one particle per state:degenerate Fermi gas
two classes
Fermionshalf-integer spin
Bosonsinteger spin
superfluidity ?
all in ground state:Bose-Einstein condensate
only one particle per state:degenerate Fermi gas
two classes
Bosonsinteger spin
Fermionshalf-integer spin
exotic statesof matter
neutron star
all in ground state:Bose-Einstein condensate
only one particle per state:degenerate Fermi gas
exploring the crossover
na3 = 0.04
molecularBEC
exploring the crossover
na3 = 0.04
na3 = 0.28
molecularBEC
exploring the crossover
na3 = 0.04
Bosons Fermions
na3,kF|a| = ∞
na3 = 0.28
molecularBEC
exploring the crossover
na3 = 0.04
na3 = 0.28
molecularBEC
kF|a| = 6
FermionsBosons
na3,kF|a| = ∞
exploring the crossover
molecularBEC
degenerate Fermi gas
FermionsBosons
na3 = 0.04
na3 = 0.28
kF|a| = 1
kF|a| = 6
na3,kF|a| = ∞
fully reversibleno loss, no heating !!!
(isentropic)
cloud size → interaction energy
quantumMonte Carlo
(Carlson et al.Astrakharchik et al.)
ζ0=0.810(3)( β = ζ0
4 – 1 )
BEC mean-field
withamol = 0.6a
(Petrov et al.prediction)
comparisonwith theory
M. Bartenstein et al.PRL 92, 120401 (2004);updated inProcs. ICAP-2004
normalized tonon-interacting
Fermi gas
collective modesin the BEC-BCS crossoverM. Bartenstein et al., PRL 92, 203201 (2004)
collective modes
S. Stringari, Europhys. Lett. 65, 749 (2004):interesting behavior of collective modes in the crossover !!!
axial
radial
our cigar-shaped trap νr = 755(10) Hz, νz ≈ 22 Hz
axial modeM. Bartenstein et al., PRL 92, 203201 (2004), updated data analysis: PhD thesis M. Bartenstein
frequency(normalizedto sloshingmode)
dampingrate
hydrodynamicbehaviorhydrodynamicbehavior
axial mode: resonance regionM. Bartenstein et al., PRL 92, 203201 (2004), updated data analysis: PhD thesis M. Bartenstein
frequency(normalizedto sloshingmode)
dampingrate
unitarity point:
confirms equation of state 5/12/ =Ω zz ω
3/2n∝µ
extremely weak damping in resonance region !!
superfluidity?
extremely weak damping in resonance region !!
superfluidity?
radial coll. excitation
600 800 1000 12000,0
0,2
0,4
0,6
0,8
1,4
1,6
1,8
2,0
2,2
magnetic field (G)
Γ r /ω
r
BEC limit
Ωr /ω
r
collisionless limitfrequency(normalizedto sloshingmode)
damping
M. Bartenstein et al.PRL 92, 203201 (2004)
hydrodynamichydrodynamic collisionlesscollisionless
??
comparison with theory
hydrodynamic
on Leggett‘s mean-fieldon Giorgini‘s qu.MC calculationon Leggett‘s mean-field
on Giorgini‘s qu.MC calculationHu et al., PRL 93, 190403 (2003) based model
Manini et al., cond-mat/0407039 basedHu et al., PRL 93, 190403 (2003) based model
Manini et al., cond-mat/0407039 based
γnµ ~
comparison with theory
cond-mat/0503618
??
how good is our experiment ?• axial trap very well known!
• radial trap freq. meas‘d only in one direction:ellipticity of laser beam ???
how good is our experiment ?• axial trap very well known!
• radial trap freq. meas‘d only in one direction:ellipticity of laser beam ???
in progress: upgrade of apparatus
trapping beam
imaging beam
glass cell
mol. BEC / Fermi gas
dichroic mirror
CCD cameradichroicmirror
acousto-opticalscanning system
new possibilities• precise studies of radial modes(compression and surface mode)
• rotating ellipse → stirring up vortices
new possibilities• precise studies of radial modes(compression and surface mode)
• rotating ellipse → stirring up vortices
new
newnew
something(B) → something(1/kFa)measurement interpretation
something(B) → something(1/kFa)measurement interpretation
precise knowledge of a(B)through rf spectroscopy on ultracold molecules
Bartenstein et al., PRL 94, 103201 (2005)(collaboration Innsbruck – NIST)
radio-frequency spectroscopy
meas. of mol. bind. energy in 40KRegal et al., Nature 424, 47 (2003)
rf spectroscopy of 6Li: Gupta et al., Science 300, 1723 (2003)
rf
~80MHz
loss
sign
alrf frequency
~200HzmI=-10
1
high B-field
radio-frequency spectroscopy
meas. of mol. bind. energy in 40KRegal et al., Nature 424, 47 (2003)
rf spectroscopy of 6Li: Gupta et al., Science 300, 1723 (2003)
rf
~80MHz
breaking moleculescosts energy
→molecular signal
up-shifted
breaking moleculescosts energy
→molecular signal
up-shifted
mI=-10
1
high B-field
radio-frequency spectroscopy
meas. of mol. bind. energy in 40KRegal et al., Nature 424, 47 (2003)
rf spectroscopy of 6Li: Gupta et al., Science 300, 1723 (2003)
rf
3001500
atoms
rf offset (kHz)fra
ctio
nall
oss 720 G
atoms molecules
Eb/h bindingenergy
~80MHz
mI=-10
1
high B-field
bound-free dissociation spectra
134(2) kHz
277(2) kHz
binding energy
720.13(4) G
lineshapeof dissociationsignal:C. Chin andP. JuliennePRA 71, 012713(2005)694.83(4) G
rf spectroscopy on 6Li2
bound-bound transition
83.6645(2) MHz@ 661.44(2) G
83.2966(5) MHz@ 676.09(3) G
second data point
exp. dataNIST theory group:multi-channel quantumscattering model
as = 45.167(8) a0at = - 2140(18) a0
→ →
s-wave scattering lengths
simple fit formulae available !simple fit formulae available !
rf spectroscopy in the strongly interacting Fermi gasobservation of the pairing gapC. Chin et al., Science 305, 1128 (2004)
radio-frequency spectroscopy
meas. of mol. bind. energy in 40KRegal et al., Nature 424, 47 (2003)
rf spectroscopy of 6Li: Gupta et al., Science 300, 1723 (2003)
rf
~80MHz
breaking moleculescosts energy
→molecular signal
up-shifted
breaking moleculescosts energy
→molecular signal
up-shifted
mI=-10
1 two-body physics
high B-field
radio-frequency spectroscopy
meas. of mol. bind. energy in 40KRegal et al., Nature 424, 47 (2003)
rf spectroscopy of 6Li: Gupta et al., Science 300, 1723 (2003)
rf
~80MHz
breaking pairs costs energy
→pair signalup-shifted
breaking pairs pairs costs energy
→pairpair signalup-shifted
mI=-10
1 manymany--bodybody physicsphysics
high B-field
rf spectra in molecular limit
evaporationevaporation at 764G, at 764G, thenthen rampramp fieldfield to 720Gto 720G
no no evaporationevaporation
moderatemoderateevaporationevaporation
deepdeep evaporationevaporation
loss
sign
al
atomsatoms onlyonly
atomatom--moleculemolecule mixturemixture
pure pure molecularmolecular samplesample(BEC)(BEC)
rf offset
rf spectra in crossover regime
evaporationevaporation at 764G, at 764G, thenthen rampramp fieldfield on on resonanceresonance
loss
sign
ala → ±∞a → ±∞
T T ≈≈ 0.2 T0.2 TFFdoubledouble--peakpeak structurestructure::atomsatoms and and pairspairsthethe pairingpairing gapgap
T = 0.0? TT = 0.0? TFFpairspairs onlyonly !!shiftshift decreasesdecreases withwithFermiFermi energyenergy
rf offset
rf spectra in crossover regime
evaporationevaporation at 764G, at 764G, thenthen rampramp fieldfield to to BCS BCS sideside
rf offset
loss
sign
al
TT//TTFF ≈ 0.2≈ 0.2
BCS sideBCS side
TT//TTFF ≈ 0.0?≈ 0.0?
gapgap !!!!
gap vs. coupling strength
molecular lim
it
(two-body physics)
BEC
unitary
→ BCS
TF = 3.6µK1.2µK
gap vs. coupling strength
molecular lim
it
(two-body physics)
radial osc. frequency
collective oscillationcouples to pairs
→ explanation forabrupt change !!
TF = 3.6µK1.2µK
0,0
0,4
0,0
0,4
-20 0 20 400,0
0,4
0,0
0,4
(d)
(c)
(a)
fract
iona
l los
s in
|2>
RF frequency offset (kHz)
(b)
temperature dependence
< 0.2 TF
≈ 0.45 TF
≈ 0.75 TF
T´ ≈ 0.8 TF
temperature T´measured inBEC regime(1/kFa ≈ 3)
temperature T´measured inBEC regime(1/kFa ≈ 3)
measured@ 837 G
(unitarity)
controlledheating:
same TF, N
„thermodynamics ofinteracting fermions“
Chen et al.cond-mat/0411090
T´ → Ttrue temperature
„thermodynamics ofinteracting fermions“
Chen et al.cond-mat/0411090
T´ → Ttrue temperature
0,0
0,4
0,0
0,4
-20 0 20 400,0
0,4
0,0
0,4
(d)
(c)
(a)
fract
iona
l los
s in
|2>
RF frequency offset (kHz)
(b)
temperature dependence
< 0.1 TF
≈ 0.22 TF
≈ 0.28 TF
T´ ≈ 0.3 TF
temperature T´measured inBEC regime
temperature T´measured inBEC regime
„thermodynamics ofinteracting fermions“
Chen et al.cond-mat/0411090
T´ → Ttrue temperature
„thermodynamics ofinteracting fermions“
Chen et al.cond-mat/0411090
T´ → Ttrue temperature
measured@ 837 G
(unitarity)
controlledheating:
same TF, N
0,0
0,4
0,0
0,4
-20 0 20 400,0
0,4
0,0
0,4
(d)
(c)
(a)
fract
iona
l los
s in
|2>
RF frequency offset (kHz)
(b)
< 0.1 TF
≈ 0.22 TF
≈ 0.28 TF
T´ ≈ 0.3 TF
Kinnunen, Rodriguez, Törmä, Science 305, 1131 (2004)
comparison with theory
0.08
0.19
0.23
T/TF = 0.27K. Levin,
priv. comm.
phase diagram
0
0.4
1
0.2
0.8
0.6
0-1-2 1 2
BEC BCSsuperfluid
paired
molecules
Cooperpairs
6Li 6Li
6Li 6Li
T/TF
-1/kFa
Perali, Pieri, Pisani, StrinatiPRL 92, 220404 (2004)
harmonic trap (inhomog. system)
Perali, Pieri, Pisani, StrinatiPRL 92, 220404 (2004)
harmonic trap (inhomog. system)
6Li 6Li
TC
T *
conclusion
creation of a molecular BEC with 6Li2excellent starting point for further experiments
creation of a molecular BEC with 6Li2excellent starting point for further experiments
TMR network cold moleculesfunding
conclusion
creation of a molecular BEC with 6Li2excellent starting point for further experiments
studies on the BEC-BCS crossover• cloud size• collective modes• pairing gap
creation of a molecular BEC with 6Li2excellent starting point for further experiments
studies on the BEC-BCS crossover• cloud size• collective modes• pairing gap
strongstrong casecase forforsuperfluiditysuperfluidity
TMR network cold moleculesfunding
ultracold.atoms2D BEC in a surface trap
B. Engeser, K. Pilch, A. Jaakola, G.Hendl, H.-C. Nägerl
2D BEC in a surface trapB. Engeser, K. Pilch, A. Jaakola, G.Hendl, H.-C. Nägerl
fermionic Li-6 & molecular BECA. Altmeyer, S. Riedl, M. Bartenstein, R. GeursenS. Jochim, C. Chin, J. Hecker Denschlag
fermionic Li-6 & molecular BECA. Altmeyer, S. Riedl, M. Bartenstein, R. GeursenS. Jochim, C. Chin, J. Hecker Denschlag
BEC of cesium, ultracold moleculesT. Kraemer, M. Mark, P. Waldburger, J. Herbig C. Chin, H.-C. Nägerl
BEC of cesium, ultracold moleculesT. Kraemer, M. Mark, P. Waldburger, J. Herbig C. Chin, H.-C. Nägerl
Johannes Hecker Denschlag
quantum matter in optical latticesM. Theis, G. Thalhammer, K. Winkler, F. Lang, S. Schmid
Johannes Hecker Denschlag
quantum matter in optical latticesM. Theis, G. Thalhammer, K. Winkler, F. Lang, S. Schmid
Hanns-Christoph Nägerl START
2nd generation cesium BECM. Gustavsson, P. Unterwaditzer, A. Flir
Hanns-Christoph Nägerl START
2nd generation cesium BECM. Gustavsson, P. Unterwaditzer, A. Flir
Cheng ChinLise-Meitner fellow Li-K/Sr mixtures
E. Wille,G. Kerner, NN Florian Schreck
Li-K/Sr mixturesE. Wille,G. Kerner, NN Florian Schreck
Innsbruck
ultracold.atoms2D BEC in a surface trap
B. Engeser, K. Pilch, A. Jaakola, G.Hendl, H.-C. Nägerl
2D BEC in a surface trapB. Engeser, K. Pilch, A. Jaakola, G.Hendl, H.-C. Nägerl
fermionic Li-6 & molecular BECA. Altmeyer, S. Riedl, M. Bartenstein, R. GeursenS. Jochim, C. Chin, J. Hecker Denschlag
fermionic Li-6 & molecular BECA. Altmeyer, S. Riedl, M. Bartenstein, R. GeursenS. Jochim, C. Chin, J. Hecker Denschlag
BEC of cesium, ultracold moleculesT. Kraemer, M. Mark, P. Waldburger, J. Herbig C. Chin, H.-C. Nägerl
BEC of cesium, ultracold moleculesT. Kraemer, M. Mark, P. Waldburger, J. Herbig C. Chin, H.-C. Nägerl
Johannes Hecker Denschlag
quantum matter in optical latticesM. Theis, G. Thalhammer, K. Winkler, F. Lang, S. Schmid
Johannes Hecker Denschlag
quantum matter in optical latticesM. Theis, G. Thalhammer, K. Winkler, F. Lang, S. Schmid
Hanns-Christoph Nägerl START
2nd generation cesium BECM. Gustavsson, P. Unterwaditzer, A. Flir
Hanns-Christoph Nägerl START
2nd generation cesium BECM. Gustavsson, P. Unterwaditzer, A. Flir
Cheng ChinLise-Meitner fellow Li-K/Sr mixtures
E. Wille,G. Kerner, NN Florian Schreck
Li-K/Sr mixturesE. Wille,G. Kerner, NN Florian Schreck
Innsbruck
fermionsfermions