Pairing Gaps in the BEC-BCS crossover regime

15/06/2005, Strong correlations in Fermi systems

Cheng Chin JFI and Physics, University of Chicago

Exp.: Rudolf Grimm’s group, Innsbruck University, Austria

BEC BCSa=±

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Content

• How do we distinguish two-body pairing and many-body pairing?

• Peculiar system 6Li– Why do we have 300G Feshbach resonance?

• Pairing gap and collective modes in the crossover…– Breakdown of the smooth crossover?

• What is the experimental gap δ?– BEC limit– BCS limit– In general

Phase diagram of a two-component Fermi gas

10-5

100

10510

-6

100

106

Binding energy (EF )

Te

mp

. (T

F )

Thermal Fermi gas

Thermal bosons

Deg.Fermigas Bose-Einstein

condensationCooperpairing

chemistry

Superconductor

AMOHigh-Tc

He-3

6Li

M. Holland

The Magnetic handle: Feshbach resonance

700 800 900

-50

0

50

-1000

0

1000

ener

gy/h

(K

Hz)

magnetic field (G)

scat

terin

g le

ngth

(nm

)

Scattering between |1> and |2>

BEC regime BCS regime

834G

a>0 a<0

mol. state

300G wide Feshbach resonnace

No interaction

Tunable interaction

Feshbach resonance: tuning the scattering length

2/

||||0

iEE

VVTT

if

fifi

atomic separation

potential

-B

Transition matrix

)BB

ΔB( aa

resbg

1

Scattering length

Nice picture, but also wrong!-- Fano profile

6Li2 molecular energy (ab channel)

Bare state

0

00

2/11 r

rara bg

Δ~40,000 EF

R0=30 a0

Δ=detuningΓ=Feshbach coupling

The Magnetic handle: Feshbach resonance

700 800 900

-50

0

50

-1000

0

1000

ener

gy/h

(K

Hz)

magnetic field (G)

scat

terin

g le

ngth

(nm

)

Scattering between |1> and |2>

BEC regime BCS regime

834G

a>0 a<0

mol. state

300G wide Feshbach resonnaceTunable interaction

Tunable and stable, (Petrov et al., 2004)

Innsbruck: 6Li BEC-BCS crossoverna3 = 0.001 kFa = - 0.5a = ±

densityprofile

Bartenstein et al., PRL 04

RadialCompressionMode

AxialBreathingMode

1/kFa

Bartenstein et al., PRL 04

gapChin et al.,Science 04

δ

rf

In the molecule picture

Pairing gap measurement: RF excitation

State 3 is initially unpopulated

f atom= E23

fmolecule = E23+Eb+2EK

atoms molecules

Eb

Ex

cita

tio

n r

ate

Pairing in the BEC regime

T´ >> TF

T´ ~ TF

T´ < 0.2 TF

RF offset (kHz)

molecules only

atoms only

mixtureEb

exc

itatio

n r

ate

(a

.u.)

BEC limit 720G a=2180a0 kFa=0.4

Also by JILA group

Excellent agreement

ExperimentBartenstein et al., PRL 05TheoryChin and Julienne, PRA 05

)(

)(~)(

32

2/1

EEEE

EEEP

b

b

Radio-frequency spectroscopy on molecules

m

Bound-free transitions

2* )()(

2

drrrh

mKf

600 700 800 900

-1

0

82

83

bound-bound

(1,3)

en

erg

y / h

(M

Hz)

magnetic field (G)

(1,2)

bound-free

Bound-free transitions

2*

' )()(2

drrrh

mmb

EXPERIMENT:Bound-free transitions 720.13(4)G RF:82.593(2)MHz 694.83(4)G RF:82.944(2)MHzBound-bound transitions 676.09(3)G RF:83.2966(5)MHz 661.44(2)G RF:83.6645(3)MHz

THEORY (Simoni, Tiesinga, Julienne)

as=45.167(8)a0, aT=-2140(18)a0Feshbach resonance positions

|1>+|2>: 834.11.5 GResonance width: 300G

Exp: M. Bartenstein et al, PRL 94, 103201Theo: C. Chin and P. Julienne, PRA 71, 012713

k

RF offset (kHz)

0.00 0.25

RF offset (EF)

exci

tatio

n ra

te

(875 G ka=-3)

T´ >> TF

0.5 TF

< 0.2 TF

Creation of a hole in state 2 and then a particle in state 3 with zero momentum transfer.

Energy cost: 222 /~)()( Fkk EEE

0.06 EF

RF excitation (BCS regime)

Pairing gap vs. Temperature (psuedo gap?)

0.0

0.4

(d)

(c)

(a)

0.0

0.4

-20 0 20 40

0.0

0.4

frac

tiona

l los

s in

|2>

RF frequency offset (kHz)

0.0

0.4(b)

0.36

0.3

0.25

<< 0.1

T/TF

0.38TF

0.26TF ~ Tc

0.18TF

0.10TF

TTheory

C. Chin et al., Science 04 J. Kinnunen et al., Science 04

Calibrated by K. Levin

Other theory: H. Heiselberg: supergap A. Griffin: Andreev states Yu and Baym: SU(2) symmetry breaking

Last evidence: Pairing gaps vs. Fermi energies

Two-bodycalculation

gap

TF = 3 Kdense clould

TF = 1 Kdilute cloud

BEC regime BCS regime

RF pairing gap δ approaches Eb in the BEC limit

Δ2/EF in the BCS limit.

Conjecture: δ=

Conclusion and Future

)()( 22kk EE

RF pairing gap δ vanish due to dimensionality?

Others:A unified theory for RF with the right limit? Broadening of the narrow featurePseudo gapLack of mean-field shift??