few-body physics with ultracold fermions
DESCRIPTION
Few-body physics with ultracold fermions Selim Jochim Physikalisches Institut Universität Heidelberg. The matter we deal with. T =40nK … 1µK Density n =10 9 … 10 14 cm -3 Pressures as low as 10 -17 mbar k B T ~ 5peV Extremely dilute gases , which can be strongly interacting !. - PowerPoint PPT PresentationTRANSCRIPT
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