Few-body physicswith ultracold fermions

Selim JochimPhysikalisches Institut Universität Heidelberg

The matter we deal with

• T=40nK … 1µK• Density n=109 … 1014cm-3

• Pressures as low as 10-17mbar• kBT ~ 5peV• Extremely dilute gases,

which can be strongly interacting!

Extreme matter!

Important length scales

• interparticle separation size of the atoms• de Broglie wavelength

size of the atoms • scattering length a , only one length

determines interaction strength

3 1 / n

2

2hmkT

→ Universal properties, independent of a particular system!→ We can tune all the above parameters in our experiments!

Few-body system: Tune the binding energy of a weakly bound molecule:

Tunability of ultracold systems

4

600 800 1000 1200-10

-5

0

5

10

Scat

terin

g le

ngth

(100

0 a 0)

Magnetic field (G)

Size (>> range of interaction):

Binding energy:

Feshbach resonance: Magnetic-field dependence of s-wave scattering length

/( ) r ar e 2

2BE ma

Ultracold Fermi gases

• At ultracold temperatures, a gas of identical fermions is noninteracting• Ideal Fermi gas

5

Ultracold Fermi gases

6

• Need mixtures to study interesting physics!• Simplest implementation: spin mixtures (↑,↓)

Ultracold Fermi gases

• Two (distinguishable) fermions form a boson ….. • … molecules can form a Bose condensate …

7

→ realize the BEC-BCS crossover!

Ultracold Fermi gases

• Two (distinguishable) fermions form a boson ….. • … molecules can form a Bose condensate …

• … tune from strongly bound molecules to weakly bound Cooper pairs

8

From A. Cho, Science 301, 751 (2003)

→ realize the BEC-BCS crossover!

A picture from the lab …

What’s going on in our lab

1. Universal three-body bound states

„Efimov“ trimers

T. Lompe et al., Science 330, 940 (2010)

2. Finite Fermi systems with controlled interactions

A new playground with control at the single atom level!

F. Serwane et al., Science 332, 336 (2011)

The Efimov effect

• An infinite number of 3-body bound states exists when the scattering length diverges: (3 identical bosons)

• At infinite scattering length: En=22.72En+1

• Scattering length values where Efimov trimers become unbound an+1=22.7an

E

1/a(strength of attraction)

Observing an Efimov Spectrum?

10nm(1st state) 5.2µm

(3rd state)227nm

(2nd state)

2.7mm(5th state)

0.12mm(4th state)

What is observed in experiments?

• three-body recombination

deeply bound molecule

Enhanced recombination

• With an (Efimov) trimer at threshold recombination is enhanced:

deeply bound molecule

E

1/a(strength of attraction)

What has been done in experiments?

• Observe and analyze collisional stability in ultracold gases

• seminal experiment with ultracold Cs atoms (Innsbruck):

T. Krämer et al., Nature 440, 315 (2006)

The 6Li atom

16

0 200 400 600 800 1000 1200-5

0

5

Scat

terin

g le

ngth

(100

0 a 0)

Magnetic field (G)

F=3/2

Ener

gy

magnetic field [G]

F=1/2

|2>|1>

mI= 0mI= 1

|1> |2>a12

Need three distinguishable fermions with(in general) different scattering lengths:

(S=1/2, I=1 -> half-integer total angular momentum)

The 6Li atom

17

0 200 400 600 800 1000 1200-5

0

5

Scat

terin

g le

ngth

(100

0 a 0)

Magnetic field (G)

F=3/2

Ener

gy

magnetic field [G]

F=1/2

|2>|1>

mI= 0mI= 1

|3> mI= -1

|1>

|3>

|2>

a13

a12

a23

Need three distinguishable fermions with(in general) different scattering lengths:

couple Zeeman sublevels using Radio-frequency B-fields: „Radio Ultracold“

2- and 3-body bound states ….

Binding energies of dimers and trimers:

• Three different universal dimers with binding energy

• Where are trimer states?

-5000

0

5000

600 650 700 750 800 850 900 950

100

10

1

0,1

0,01

1E-3

a12

a13

a23

Sca

tterin

g le

ngth

s (a

0)

A

B

|12> dimer |13> dimer |23> dimer

Bin

ding

ene

rgie

s / h

(MH

z)

Magnetic field (G)

2

2BE ma

E

1/a(strength of attraction)

Where are the trimer states?

-5000

0

5000

600 650 700 750 800 850 900 950

100

10

1

0,1

0,01

1E-3

a12

a13

a23

Sca

tterin

g le

ngth

s (a

0)

A

B

|12> dimer |13> dimer |23> dimer

Bin

ding

ene

rgie

s / h

(MH

z)

Magnetic field (G)

first trimer second trimer

Observe crossings as inelastic collisions T. Ottenstein et al., PRL 101, 203202 (2008)T. Lompe et al., PRL 105, 103201 (2010)Also:Penn State:J. Huckans et al., PRL 102, 165302 (2009)J. Williams et al. PRL 103, 130404 (2009)University of Tokyo:Nakajima et al., PRL 105, 023201 (2010)

RG based theory: R. Schmidt, S. Flörchinger et al. Phys. Rev. A 79, 053633 (2009)Phys. Rev. A 79, 042705 (2009)Phys. Rev. A 79, 013603 (2009)

Can we also measure binding energies?

Theory data from: Braaten et al., PRA 81, 013605 (2010)

-5000

0

5000

600 650 700 750 800 850 900 950

100

10

1

0,1

0,01

1E-3

a12

a13

a23

Sca

tterin

g le

ngth

s (a

0)

A

B

|12> dimer |13> dimer |23> dimer

Bin

ding

ene

rgie

s / h

(MH

z)

Magnetic field (G)

first trimer second trimer

RF field

Attach a third atom to a dimer

Measure binding energiesusing RF spectroscopy

|2>

|2>

|2>|1>

|1> |3>

RF-association of trimers

dimer

trimer

T. Lompe et al., Science 330, 940 (2010)

radio frequency

radio frequency [MHz]

675 700 725 750

500

250

0

Bin

ding

ene

rgy

/ h (k

Hz)

Magnetic field (G)

RF-association of trimers

22

T. Lompe et al., Science 330, 940 (2010)T. Lompe et al., PRL 105, 103201 (2010)

• With our precision: theoretical prediction of the binding energy confirmed: Need to include finite range corrections for dimer binding energies

• Same results for two different initial systems

More recent results: Nakajima et al., PRL 106,143201 (2011)

An ultracold three-component Fermi gas

23

Fermionic trions, „Baryons“

An ultracold three-component Fermi gas

24

Color Superfluid

Starting grant

What’s going on in our la ｂ

1. Three component Fermi gases

RF-spectroscopy of Efimov trimers

T. Lompe et al., Science 330, 940 (2010)

2. Finite Fermi systems with controlled interactions

A new playground with control at the single atom level!

F. Serwane et al., Science 332, 336 (2011)

Our motivation

• Extreme repeatability and control over all degrees of freedom, but limited tunability

• Quantum dots, clusters …

• Wide tunability, but no „identical“ systems

• Atoms, nuclei …

Conventional traplike a soup plate!

Shot glass type trap

Creating a finite gas of fermions

Control the number of quantum states in the trap!

…small density of statesLarge density of states …

Transfer atoms to a microtrap …

Spill most of the atoms:

“laser culling of atoms”: M. Raizen et al., Phys. Rev. A 80, 030302(R)

Use a magnetic field gradient to spill:

Lower trap depth

µ x B~600 atoms ~2-10 atoms

Atoms in a microtrap

Transfer a few 100 atoms into a tightly focused trap (~1.8µm in size, 1.4kHz axial, 15kHz radial trap frequencies)

100µ

m

100µmTrap potential is proportional to intensity, good approximation: harmonic at the center

Single atom detection

CCD

distance between 2 neighboring atom numbers : ~ 6s1-10 atoms can be distinguished with high fidelity > 99%

one atom in a MOT1/e-lifetime: 250sExposure time 0.5s

Starting conditions

Reservoir temperature ~250nK

Depth of microtrap: ~3µK

Þ ExpectÞ Occupation probability of the

lowest energy state: > 0.9999100µ

m

100µm

0.08 FT T

L. Viverit et al. PRA 63, 033603 (2001)

1. Spill atoms in a controlled way

2. Recapture prepared atoms into magneto-optical trap

Preparation sequence

3,4 3,2 3,0 2,8 2,60

2

4

6

8

10

variance

mea

n at

om n

umbe

r

trap depth (relative scale)

0 0,5 1,0

Spilling the atoms ….

•We can control the atom number with exceptional precision!•Note aspect ratio 1:10: 1-D situation

1kHz~400feV

0 1 2 3 40

102030405060708090

100

2% 2%

coun

ts

fluorescence signal

96%

5 6 7 8 9 100

20

40

60

80

100

120

140

6.5%5%

88.5%

coun

ts

fluorescence signal

A green laser pointer trap

• Output power:• Total output ~70mW• Most of it green, 532nm• About 10mW at 1064nm,• Some pump light at 808nm.

At suitable pump current:• It emits a single longitudinal mode (single frequency)• Has very low noise: RIN < -110dB/Hz

• We have decent control over the motional degrees of freedom!

• What about interactions?

The 6Li atom

37

0 200 400 600 800 1000 1200-5

0

5

Scat

terin

g le

ngth

(100

0 a 0)

Magnetic field (G)

F=3/2

Ener

gy

magnetic field [G]

F=1/2

|2>|1>

mI= 0mI= 1

|1> |2>a12

(S=1/2, I=1 -> half-integer total angular momentum)

First few-body interactions …

0 20 40 60 80 100

1

2

mea

n at

om n

umbe

r

holdtime [ms]

523 Gauss

Interaction-induced spilling!

0 20 40 60 80 100

1

2

mea

n at

om n

umbe

r

holdtime [ms]

760 Gauss 523 Gauss

F. Serwane et al., Science 332, 336 (2011)

First few-body interactions

• What happens if we bring the two atoms in the ground state across the Feshbach resonance

• One atom is observed in n=2

a~0 a>0

a

Interactions in 1D

23

1D 23

2 1g = 1 /

D

D

ama Ca a

Feshbach resonance

Confinement induced resonance

(for radial harmonic confinement)

M. Olshanii, PRL 81, 938 (1998).

-1

0

1

g 1D [1

0 a pe

rp ħ

pe

rp]

750 800 850 900

-20

-10

0

10

20

a 3D [1

03 a0]

magnetic field [G]

1D

3D

Trap has aspect ratio 1:10

0

-4

-2

0

2

4

6

E [ħ

a]

1/g1D

Energy of 2 atoms in the trap

Relative kinetic energy of two interacting atoms (exact solution!)

x2-x1(relative coordinate)

T. Busch et al., Foundations of Physics 28, 549 (1998)

2 distinguishable vs. 2 identical fermions

-1

0

1

g 1D [1

0 a pe

rpħ

perp]

Tunneling time equal to case of two identical fermions: the system is „fermionized“

2 distinguishable fermions

2 identical fermions 750 800 850 900

10

100

1000

distiguishable fermions identical fermions linear fit identical fermions

tunn

elin

g tim

e [m

s]

magnetic field [G]

Tunneling dynamics

0 250 500

1,00

1,25

1,50

1,75

2,00

Mea

n at

om n

umbe

r

Hold time [ms]

Fermionization

relative wave function

2 distinguishable fermions

2 identical fermions

(2-particle limit of a Tonks-Girardeau gas)

ground state

Wave function square, and energy are identical!

Conclusion

• We detect and count single atoms with very high fidelity

• We prepare few-fermion systems with unprecedented control

• We control the interactions in the few-fermion system

A toolbox for the study of few-body systems0 1 2 3 4

0

25

50

75

100

2% 2%

coun

ts

fluorescence signal

96%

750 800 850 900

10

100

1000

distiguishable fermions identical fermions linear fit identical fermions

tunn

elin

g tim

e [m

s]

magnetic field [G]

The future

• Investigate interacting few-body systems in the ground state: Few-body „quantum simulator“

• Realize multiple interacting wells

Measure pairing in a finite system

Study dynamics of few-fermion systems: How many atoms do we need to have a thermal ensemble?

Thank you very muchfor your attention!

André Wenz

Martin Ries Gerhard Zürn

Selim Jochim Thomas Lompe

Johanna BohnFriedhelm Serwane