BEC and superfluidity in ultracold Fermi gases

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


trapped atomsat T=0



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


Bosonsinteger spin

these twoworlds

are connected !

trapped atomsat T=0



two classes


Bosonsinteger spin

trapped atomsat T=0

„pairing“is the key



two classes


Bosonsinteger spin Feshbach

resonance

trapped atomsat T=0

interactioncontrol !!!



two classes


Bosonsinteger spin

superfluidity ?



two classes

Bosonsinteger spin


exotic statesof matter

neutron star



exploring the crossover

na3 = 0.04

molecularBEC


na3 = 0.04

na3 = 0.28

molecularBEC


na3 = 0.04

Bosons Fermions

na3,kF|a| = ∞

na3 = 0.28

molecularBEC


na3 = 0.04

na3 = 0.28

molecularBEC

kF|a| = 6

FermionsBosons

na3,kF|a| = ∞


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 ~


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




rf

~80MHz

breaking moleculescosts energy

→molecular signal

up-shifted


→molecular signal

up-shifted

mI=-10

1

high B-field




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)




rf

~80MHz


→molecular signal

up-shifted


→molecular signal

up-shifted

mI=-10

1 two-body physics

high B-field




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




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>


(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







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>


(b)

< 0.1 TF

≈ 0.22 TF

≈ 0.28 TF

T´ ≈ 0.3 TF

Kinnunen, Rodriguez, Törmä, Science 305, 1131 (2004)


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


TMR network cold moleculesfunding

conclusion


studies on the BEC-BCS crossover• cloud size• collective modes• pairing gap


studies on the BEC-BCS crossover• cloud size• collective modes• pairing gap

strongstrong casecase forforsuperfluiditysuperfluidity

TMR network cold moleculesfunding

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BEC and superfluidity in ultracold Fermi gases

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