cold atoms experiments - yale university · atoms in optical lattices strongly interacting becs + _...

1

D. Jin

JILA, NIST and the University of Colorado

$ NSF, NIST

Cold Atoms Experiments

Investigate many-body quantum physics with a model system

Why study atomic gases?

- low density, low temperature- well understood microscopics

- unique experimental tools - controllable interactions

n ~ 1013 cm-3, T ~ 100 nK

2

* Fermi gas and BCS-BEC crossover

Lots of exciting experiments:

Rapidly rotating BECs

Atoms in optical latticesStrongly interacting BECs

+

_

+

_Cold molecules

1d and 2d gases

I. Introduction

II. Controlling Interactions

III. BCS-BEC Crossover

IV. Recent Experiments at JILA

Outline:

3

Some NumbersNumbers:

atoms electronsn = 1013 1023 cm-3

d = 10-7 10-10 mN = 105 ∞

m = 7x10-26 9x10-31 kg

TF=10-6 105 KvF = 10-2 106 m/s

T/TF=0.05 <0.001

Trap inhomogeneous density

x

n

1. Meta-stable.True ground state is a solid.

2. Spin degree of freedom is frozen out.

3. Contact interactions (collisions) are s-wave.

Important propertiesUltracold (100 nK!) gas :

spin ↑

spin ↓kT

4

Contact InteractionsCollisions/interactions are only s-wave.

non-s-wave

kT

Spin-polarized fermions stop colliding.

R

s-wave

V(R)

centrifugal barrier

R

V(R)

Techniques1. Laser cooling and trapping

2. Magnetic trapping & evaporative cooling

3. Optical trapping & evaporative cooling

spin 1spin 2

can confine any spin-statecan apply arbitrary B-field

5

Time-of-flight absorption imaging

• Probing the atoms

Probing the ultracold gas

1999: 40K JILAmany experimental groups: 40K, 6Li, 173Yb,3He*

Fermi gas of atoms

T ~ 0.05 TF

Fermi sea of atoms

EF = kBTF

EF = hftrap(6N)1/3

6

Quantum degeneracyGet T from the measuredvelocity distribution.

reach T/TFermi ~ 0.05

N = 4 ·105 , T = 16 nKT/TFermi = 0.05

0.01 0.1 10

10

20

μ/k bT

T/TF

Apparatus

7

II. Controlling Interactions

Interactionss-wave scattering length, a

a > 0 repulsive, a < 0 attractiveLarge |a| → strong interactions

V(R)

R

a

8

Controlling interactions

0 ¶

scattering length, a

a > 0 repulsive, a < 0 attractiveLarge |a| → strong interactions

40K

A magnetic-field tunable atomic scattering resonance

Channels are coupled by the hyperfine interaction.

Magnetic-field Feshbach resonance

→←colliding atoms in channel 1

molecule state in channel 2

9

Ebinding

molecules

→←

attractive

repulsive

ΔB>


repulsive

free atoms


molecules

→←

attractive

repulsive

ΔB>

free atoms

s-wave scattering length, a

Ebinding

10

215 220 225 230-3000

-2000

-1000

0

1000

2000

3000

sc

atte

ring

leng

th (a

o)

B (gauss)


C. A. Regal and D. S. Jin, PRL 90, 230404 (2003)

repulsive

attractive

spectroscopic measurement of the mean-field energy shift

Turning atoms into molecules

Ramp across Feshbach resonance from high to low B

215 220 225 230-3000

-2000

-1000

0

1000

2000

0

5.0x105

1.0x106

1.5x106

scat

terin

g le

ngth

(ao)

B (G)

atom

num

ber

ener

gy

B

The atoms reappear if we sweep back to high B.

→←

11

Molecule binding energy

220 221 222 223 224

-500

-400

-300

-200

-100

0

atoms molecules binding energy theory

(Ticknor, Bohn)

Δν (k

Hz)

B (gauss) C. Regal et al.Nature 424, 47 (2003)

extremely weakly bound !long lifetime

III. BCS-BEC crossover

12

Making condensates with fermionsmolecules

BEC

Cooper pairs

BCS

kF

BCS-BEC crossover theory (partial list):Eagles, Leggett, Nozieres and Schmitt-Rink, Randeria, Strinati, Haussman, Holland, Timmermans, Griffin, Levin …

BCS – BEC crossover

generalized Cooper pairs

spin ↑spin ↓

10510-5 1010

100

10-2

10-4

10-6

2 /Δ k TB F

T/T

c F

BCS-BEC landscape

energy to break fermion pair

trans

ition

tem

pera

ture

BEC

superfluid 4He

alkali atom BEC

high Tc superconductors

superfluid 3He

superconductors

M. Holland et al.,PRL 87, 120406 (2001)

13

2 1 0 -1 -2-6

-4

-2

0

2

2 1 0 -1 -20

0.5

1.0

1.5

2.0

μ/E

F

BEC limit BCS limit

1/kFa

Δ/E

F

1/kFa

BCS-BEC Crossover

← BEC BCS →

M. Marini, F. Pistolesi, and G.C. Strinati, Europhys. J. B 1, 151 (1998)

1/kFa characterizes interactions in BCS-BEC crossover

Gap Chemical potential


molecules

→←

attractive

repulsive

ΔB>

free atoms

s-wave scattering length, a

Ebinding

14

Changing the interaction strength in real time

molecules

attractive

repulsive

ΔB>

EF

2 μs/G

: FAST

Changing the interaction strength in real time: SLOW

molecules

attractive

ΔB>

EF

40 μs/G

15

Changing the interaction strength in real time: SLOWER

molecules

attractive

ΔB>

EF

4000 μs/G

Cubizolles et al., PRL 91, 240401 (2003); L. Carr et al., PRL 92, 150404 (2004)

Molecular Condensate

M. Greiner, C.A. Regal, and D.S. Jin, Nature 426, 537 (2003).

Time of flightabsorption image

initial T/TF: 0.19 0.06

16

40 μs/G

Observing a Fermi condensate

attractive

repulsive

ΔB>

EF?4000 μs/G

?

-0.5 0.0 0.5

0

1x105

2x105

3x105

N m

olec

ules

Condensates without a two-body bound state

C. Regal, M. Greiner, and D. S. Jin, PRL 92, 040403 (2004)

Dissociation of moleculesat low density

ΔB = 0.12 G ΔB = 0.25 G ΔB=0.55 G

T/TF=0.08

ΔB (gauss)

17

Fermi Condensate2004

strongerattractive interactions

Imaging atom pairs

Bose-Einstein Condensate

C. A. Regal, M. Greiner, and D. S. Jin, PRL 92, 040403 (2004)

40 μs/G

Mapping out a phase diagram

molecules

attractive

repulsive

ΔB>

EF

4000 μs/G

T/TF

a

18

BCS-BEC Crossover

1 0 -10

0.1

0.2

Interaction strength 1/kFa

Ent

ropy

T/T

F-0.0200.0100.0250.0500.0750.1000.1250.1500.175

condensate fraction

00.01

0.05

0.1

0.15

C.A. Regal, M. Greiner, and D. S. Jin, PRL 92, 040403 (2004)

Initi

al

← BEC BCS →

1 0 -10

0.1

0.2


Ent

ropy

T/T

F

-0.0200.0100.0250.0500.0750.1000.1250.1500.175

BCS-BEC Crossovercondensate

fraction0

a BCS-BEC crossover theory

Q. Chen, C.A. Regal, M. Greiner, D.S. Jin & K. Levin, PRA 73, 041601 (2006).

Initi

al

C.A. Regal, M. Greiner, and D. S. Jin, PRL 92, 040403 (2004)

19

Probing the BCS-BEC crossover

Thermodynamic measurements

Vortices

Collective excitations

Probes ofpairing

Condensate fractionUnbalanced

spin population

1 0 -10

0.1

0.2


Entro

py T

/TF

Unitarity andUniversality

Correlations inatom shot noise

Initi

al

Probing the BCS-BEC crossover

Increasing interactions

0 0.5 1.0 1.5 2.0 2.50

0.20.40.60.81.01.2

OD

k/kF0

1/(kFa) = -80-10

+1

(Ketterle, MIT)

20

IV. Recent experiments at JILA1. Photoemission spectroscopy

for ultracold atoms

2. Exploring a p-wave Feshbachresonance

Photoemission spectroscopy for ultracold atoms

Look at the BCS-BEC crossover (s-wave)

Like ARPES

21

The gap and the pseudogap

BCS superconductivity

2Δ is the energy to break a pair

BCS-BEC crossover

rf spectroscopy: A brief history

220 221 222 223 224

-500

-400

-300

-200

-100

0

atoms molecules binding energy theory

(Ticknor, Bohn)

Δν (k

Hz)

B (gauss) C. Regal et al.Nature 424, 47 (2003)

22

50.7 50.4 50.1 49.8

0.2

0.4

0.6

0.8

1.0

trans

fer (

arb.

)

0

radio frequency (MHz)

rf spectroscopy: A brief history

2ΔMolecule dissociation

C.A. Regal, C. Ticknor, J. L. Bohn, & D.S. Jin, Nature 424, 48 (2003)

Ene

rgy

40K

Measuring the gap?BEC side On resonance

Coexistence Coexistence

C. Chin et al., Science 305, 1128 (2004)

2Δ Δ?

Transfer

J. Kinnunen, M. Rodrıguez,& P. Torma, Science 305, 1131 (2004)

0 0

6Li

rf offset

EF

23

Controversy…

Fermi sea

T=0 FE

C. H. Schunck et al.,Science 316, 867 (2007)

6Li

Theory papers

Trap inhomogeneity:

Issues

•Torma, Science 2004•Levin, PRA 2005•Griffin, PRA 2005•Stoof, PRA 2008•Levin, PRA 2008•Mueller, preprint 2007•…

x

n

24

•Chin & Julienne, PRA 2005•Yu & Baym, PRA 2006•Baym, PRL 2007•Perali & Strinati, PRL 2008•Punk & Zwerger, PRL 2007•Basu & Mueller, preprint 2007•Veillette et al., preprint 2008•Levin, preprint 2008•…

Theory papersIssues

Final‐state effects:

6Li

RF spectroscopy without final-state effects

0 20 40 60rf offset (kHz)

Num

ber (

arb.

)

our 40K data

C. H. Schunck et al., arXiv:0802.0341v1

6LiEF

EF

25

RF offset

Final-state effectsC. H. Schunck et al., arXiv:0802.0341v2

6Li

Momentum-resolved rfspectroscopy

PES for atoms

Conservation of energy

26

Photoemission spectroscopy for atom gases

Conservation of energy

Zeemansplitting

rf freq

0νh

1. Apply rf pulse.2. Turn off trap.3. Selectively image transferred atoms after expansion.4. Perform an inverse Abel transform to get N(k) from the image.5. Repeat for a different rf frequencies.

Momentum-resolved rfspectroscopy

a b

10 20 30

5

10

15

20

25

30

35

40

4510 20 30 40

5

10

15

20

25

30

35

40

4510

20

30

40

50

60

70

80

90

100

27

Weakly-interacting Fermi gas

0

10

20

0 5 10 15k ( m )μ -1

Sing

le-p

artic

le e

nerg

y (k

Hz)

T/TF = 0.18

0

20155 100

-10

-30

-50

-70

k ( m )μ -1

-20

-40

-60

Sing

le-p

artic

le e

nerg

y (k

Hz)

0

20155 100

10

-10

-30

-50

-70

k ( m )μ -1

20

-20

-40

-60

MoleculesSimulation:

28

Strongly interacting Fermi gas (cusp of BCS-BEC crossover)

-20

-10

0

10

20

0 5 10 15

Sing

le-p

artic

le e

nerg

y (k

Hz)

k ( m )μ -1

-30

0

10

20

0 5 10 15k ( m )μ -1

Weakly interacting Fermi gas:

T/Tc ≈ 0.9

-20

-10

0

10

20

0 5 10 15

Sing

le-p

artic

le e

nerg

y (k

Hz)

k ( m )μ -1

-30

-30 -20 -10 0 10 20Single-particle energy (kHz)

Inte

nsity

(arb

.)

k ( m )μ -1

7.69.812.014.216.4

Curves at fixed k

29

A. Perali, P. Peiri, G. C. Strinati, & C. Castellani, PRB 66, 024510 (2002)

BCS‐like dispersion

Theory: The Spectral Functionpseudogap

Renormalized μT/Tc=1.001

Theory: Randeria, Levin, Yanase & Yamada, Strinati, Bruun & Baym, Bulgac, Barnea,…

-20

-10

0

10

20

0 5 10 15

Sin

gle-

parti

cle

ener

gy (k

Hz)

k ( m )μ -1

-30

Evidence of a pseudogap

22)( Δ+−−= μεμ ksE

Fit centers to

6.05.97.06.12

±=Δ±=μ kHz

kHz

EF0 = 10.4 kHz

But the ramp to resonance increases the density

30

Next?Probe the BCS-BEC crossover

TemperatureInteraction strengthSpin-imbalance

This technique could be used more generally.

P-wave Pairing?Fermi condensates with non-s-wave pairing?

• Examples: • superfluid 3He (p-wave)• high Tc superconductors (d-wave)

• Novel features:• anistropic gap• multiple superfluid phases,• narrow resonance

s-waveL=0

p-waveL=1

m l= -1,0,+1

31

P-wave resonance

0

V(R)

R

centrifugal barrier

S

0

V(R)

R

300 K

300 μK

0.5 μK

P-wave resonance

0

V(R)

R

centrifugal barrier

300 K

300 μK

0.5 μK

32

p-wave resonance

180 200 22010-13

10-12

10-11

10-10

10-9

σ (c

m2 )

B (gauss)

C.A. Regal, C. Ticknor, J.L. Bohn, & D.S. Jin, PRL 90, 053201 (2003)

40K

spin-polarized gas|f=9/2, mf=-7/2>

elas

tic c

ollis

ion

cros

s se

ctio

n

198 199 2000

2x105

4x105

6x105

8x105

Num

ber

B (Gauss)

Multiplet structure

ml = ±1 ml = 0B0 = 198.3 G B0 = 198.8 G

C. Ticknor, C.A. Regal, D.S. Jin, and J.L. Bohn, PRA 69, 042712 (2004).

ml = ±1ml = 0 B

33

-1.0 -0.5 0 0.5 1.0 1.5-300

-200

-100

0

100

200

Ene

rgy

(kH

z)

ΔB (Gauss)

P-wave molecule energy

ml = ±1

ml = 0

B

J.P. Gaebler, J.T. Stewart, J.L. Bohn, & D.S. Jin, PRL 98, 200403 (2007)

A way to “see” molecules

0

V(R)

R

Create molecules

Look for energetic atoms created by tunneling

34

P-wave Feshbach molecules

ml = 0ml = ±1

B


40K

0 0.5 1.0 1.5 2.00

1x104

2x104

Mol

ecul

e N

umbe

r

Hold time (ms)

Molecule lifetime

ml = ±1

B

time

resonance

τ =1.2 ms

hold time

molecule creation

35

Quasi-bound molecule lifetime

B

time

resonance

hold time

molecule creation

-200 -100 010-3

10-2

10-1

100

10 100

Energy (kHz)

Life

time

(ms)

P-wave molecule lifetimes

E−3ê2


ml = 0ml = ±1

36

Ultracold atoms gases provide a unique model system for exploring quantum, many-body phenomena.

Conclusion:

PeopleJayson Stewart, John Gaebler

Markus Greiner

Brian DeMarco

Cindy Regal

cold atoms experiments - yale university · atoms in optical lattices strongly interacting becs + _...

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