Weakly Bounds Systems in Atomic and Nuclear Physics March 8 12 2010 Institut für Experimentalphysik Universität Innsbruck Martin Berninger Francesca Ferlaino Alessandro Zenesini Walter Harm HannsChristoph Nägerl Rudi Grimm ID: 759806
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Slide1
The Efimov Effect
in Ultracold Gases
Weakly Bounds Systems in Atomic and Nuclear Physics
March 8 - 12, 2010
Institut für Experimentalphysik, Universität Innsbruck
Martin Berninger
, Francesca Ferlaino, Alessandro Zenesini,
Walter Harm, Hanns-Christoph Nägerl, Rudi Grimm
Slide2The Efimov Puzzle (an experimentalists view...)
Theory
Experiment
Efimov States in the molecules and nuclei, Rome 2009
Weakly-Bound Systems in Atomic and Nuclear Physics, Seattle 2010
Slide3Outline
Introduction atomic few-body physics
The Efimov scenarioExperimental Efimov physics with CsOverview experimental Efimov physicsNew results in caesium samples (preliminary)
Collisions in Dimer-Dimer samples
Ultracold exchange reactions
Slide4last bound level
y(
r
)
halo
dimer
kHz
2-body
Cs
Cs
4-body
Cs
2
Cs
2
Cs
2
Cs
Cs
Cs
3
Cs
Cs
Cs
Cs
Cs
Few-body physics
3-body
Cs
2
Cs
Cs
Cs
Cs
In general complex problem:
strong dependence on potential
many
vib.
levels
non-universal dimer
U(r)~1/r
6
r
U(r)
schematic drawing
THz
Universal regime
scattering length
a>>r
0
r
0
: range of the potential
r
0
~ l
vdW
~ 100a
0
for Cs
s
wave scattering length:
dimers
trimers
tetramers
Universal connection:
?
Halo
dimers
Efimov
trimers
Universal
tetramers
Slide5Ultracold atomic gases as a model system
Quantum gas
Classical gas
T ~ 1µK – 20nK
Temperature
Control knobs
Interactions
Interaction strength
a
crossed-beam trap
w
y
≈
w
z
≈
w
x
3D
2D
1D
Geometry
optical
lattice
„pancake“ trap
Mixtures
different interactions
different mass ratios
Bosonic / Fermionic systems
State
m
F
=3
F=3
m
F
=4
F=4
3
2
MW transfer
caesium
Slide6magnetic moment of bound state
differs from the magnetic moment
of the incident channel
B
a
a
bg
B
0
F=3+F=3
F=3+F=4
F=4+F=4
(example Cs)
r
U(r)
incident channel
bound state
Tunable interaction:
Feshbach resonance
Magnetic
tunability of the scattering length
Slide7energy
a
<
0
a
>
0
Two-particle picture
attractive
repulsive
halo
dimer
s-wave resonances for Cs in F
1
=3 F
2
=3 channel
50 G
100 G
-1000
1000
2000
-2000
3000
0
magnetic field (G)
scattering length (
a
0
)
0
150 G
s-wave + d-wave resonances in Cs
bound state in open channel:
E
B
~10kHz
background scattering length
a
bg
~2000a
0
E
b
B
44(6)
34(7)
34(6)
F1 F2
(F1+F2)
E. Tiesinga et al.
Slide8energy
a
<
0
a
>
0
The Efimov scenario
„Efimov – states“
halo
dimer
×
22.7
×
(22.7)
2
...there exists an infinite series of weakly
bound trimer states for resonant
two-body interaction...
V. Efimov, Phys. Lett. B
33
, 563-664 (1970)
weakly bound trimer
even more weakly
bound trimer
Slide9a
<
0
deeply bound dimer
Trap loss
energy
Slide103-atomic Efimov resonance
OFF resonance
ON resonance
new decay channel
Enhancement of losses
10nK
200nK
3-Atomic Efimov resonance
Kraemer et al., Nature 440, 315 (2006)
three-body recombination rate
a
4
recombination
length:
energy
Ultracold sample of
133
Cs atoms
in atomic ground state: F=3, m
F
=3
N ~ 10
5
atoms
T = 10/200nK
Slide113-atomic Efimov resonance
10nK
200nK
3-Atomic Efimov resonance
Kraemer et al., Nature 440, 315 (2006)
three-body recombination rate
a
4
recombination
length:
energy
for a<0,
a
:
C(a)=C(22.7a)
Braaten & Hammer
for a>0,
a
:
Atom-Dimer relaxation rate
:
s
0
=1.00624
Braaten-Hammer theory
a
AAA
=-850 a
0
a
min
=210 a
0
L
3
max
=5.7*10
-22
cm
6
/s
L
3
min
=1.33*10
-28
cm
6
/s
Slide123-atomic Efimov resonance
energy
E
for a<0,
a
:
C(a)=C(22.7a)
Braaten & Hammer
for a>0,
a
:
Atom-Dimer relaxation rate
:
s
0
=1.00624
a
>
0
halo
dimer
Slide13s-wave state
d-wave
state
# dimer: ~ 4000
# atoms: (3-6)x104 T = 30-300 nK
Separate atoms and dimers by magnetic gradient field before imaging
Measure the time-evolution & extract atom-dimer relaxation rate coefficient
b
Production
of 6s-molecules via
Feshbach association
Atom-dimer Efimov resonance
Slide14Atom-dimer resonance at
B
=25 G
a
AD
=+400
a
0
universality a>0 and
a<0 via a=0 ?
transition universal to non-universal ?
(r
0
~100a0) any relation to Efimov physics at different Feshbach resonances (@800G)?
Universal relation via pole:
for n=0, n‘=1
aAD/aAAA= 0.47
Knoop et. al., Nature Physics 5, 227 (2009)
1/
a
a
< 0
a
> 0
Atom-dimer Efimov resonance
Slide15energy
a
<
0
a
>
0
Tetra1
Tetra2
The extended Efimov scenario
Prediction of two
universal 4-body states
tied to each Efimov trimer!
H. Hammer and L. Platter, Eur. Phys. J. A
32
, 113 (2007)
J. von Stecher, J. P. D’Incao, and C. H. Greene, Nature Physics
5
, 417 - 421 (2009)
Slide16F. Ferlaino et. al., PRL
102
, 140401 (2009)
Tetra1
Tetra2
thold=250ms
thold=8ms
Four-body states - experimental results
Experiment
~ 0.47 a*T ~ 0.84 a*T
Position of theuniversal 4-body states Theorya*Tetra1 ~ 0.43 a*Ta*Tetra2 ~ 0.9 a*T
4-body
mixed
3-body
Fitting function
simple 3 body
simple 4 body
3 + 4 body
Slide17F. Ferlaino et. al., PRL
102
, 140401 (2009)
Tetra1
Tetra2
thold=250ms
thold=8ms
Four-body states - experimental results
Experiment
~ 0.47 a*
T
~ 0.84 a*
T
Position of the
universal 4-body states
Theory
a*
Tetra1
~ 0.43 a*
T
a*
Tetra2
~ 0.9 a*
T
Slide18Overview experimental Efimov physics
Barontini et al., Phys. Rev. Lett.
103, 043201 (2009)
Ottenstein et al., Phys. Rev. Lett. 101, 203202 (2008)Huckans et al., Phys. Rev. Lett. 102, 165302 (2009)Williams et al., Phys. Rev. Lett. 103, 130404 (2009)Wenz et al., Phys. Rev. A 80, 040702(R) (2009)
41
K + 87Rb
6Li
Fermionic systems
Bosonic mixtures
Bosonic systems
Zaccanti et al., Nature Physics 5, (2009)
Pollack et al., Science 326 (2009)
Gross et al., Phys. Rev. Lett 103, 163202 (2009)
Kraemer et al., Nature 440, 315 (2006)Knoop et. al., Nature Physics 5, 227 (2009)F. Ferlaino et. al., Phys. Rev. Lett. 102, 140401 (2009)
133Cs
39K
7Li
F=1, mF=1
F=1, mF=0
Slide19Successive Efimov Features – bosonic system (39K)
Zaccanti et al., Nature Physics, Vol. 5 (2009)
Florence-Group
Comparison with universal theory:
Valid only for |a|>>r
0
Model for finite-range interactions?
Res:
second order process: A+A+A D*+AaAD* losses in an atom sampledue to elastic scattering
Loss
a (a
0)a<03B Maxa1--15004B MaxaT*-650a>03B Mina1+224a2+5650AD Maxa1*30a2*930
Experiment with 39K atomic sampleacross Feshbach resonance, r0=64a0 atomic threshold
Slide20Usually, in the three-body process 3 particles are lost
Efimov physics in 39K: AD resonances
Thanks to M. Zaccanti & Co-Workers for the slides!
Slide21…but if AD cross section is large particle losses can be
>>3!!!
Efimov physics in 39K: AD resonances
Thanks to M. Zaccanti & Co-Workers for the slides!
Slide22Successive Efimov Features – bosonic system (7Li – F=1,mF=1)
Rice-Group
atomic sample 7Li (F=1,mF=1) across Feshbach resonance, r0=33a0
Pollack et al., Science 326 (2009)
Comparison universal theory
Valid only for each side,
systematic discrepancy (factor 2)
Variation in the short range phase across
the Feshbach resonance?
Lossa (a0)a (a0)a<03B Maxa1--298a2--63014B MaxaT1,1-120aT1,2-295aT2,1-2950aT2,2-6150a>03B Mina1+224a2+5650AD Maxindirecta2*608DD Maxdebatea*2,11470a*2,23910
Res:
a>0
a<0
a
Slide23Ottenstein et al., PRL
101, 203202 (2008)Huckans et al., PRL 102, 165302 (2009)Williams et al., PRL 103, 130404 (2009)Wenz et al., PRA 80, 040702(R) (2009)
Braaten et al., PRL
103
, 073202 (2009)
Naidon et al., PRL
103
, 073203 (2009)Floerchinger et al., PRA 79, 053633 (2009)Braaten et al., PRA 81, 013605 (2010)
Jochim & O‘Hara
6Li 3 componentFermi-Spin-mixture:
|3> mF= -3/2|2> mF= -1/2|1> mF= 1/2
Comparison with universal theoryUsing fit results for high field resonance (895G)reproduces low field resonances accurately: 125(3)G & 499(2)GNo change in the three body parameter for B ~ 750G? for aij ~ lvdw?
Efimov features in fermionic spin mixtures (6Li)
LossstateB(G)a<03B Maxn=0127n=0500n‘=1895
Res:
Slide24Gross et al., PRL
103
, 163202 (2009)
Khaykovich-Group
atomic sample 7Li (F=1,mF=0)across Feshbach resonance
Comparison with universal theory:a+/|a-| = 0.92(14) (Theory=0.96(3)) Why does 7Li agree so nicely in (F=1,mF=0) and not in (F=1,mF=1)?
Bosonic system showing universality (7Li – F=1,mF=0)
Lossa (a0)a<03B Maxa--264a>03B Mina+1160
Results:
Slide25Barontini et al., Phys. Rev. Lett.
103
, 043201 (2009)
Efimov Resonances – Heteronuclear systems (41K + 87Rb)
Florence-Group
System composed of distinguishable particles with different massesExperiment with bosonic mixture of 41K and 87Rbat a interspecies Feshbach resonance Two resonantly interacting pairs are sufficient for Efimov physics Existence of two Efimov series:KRbRb: exp(/s0) = 131KKRb: exp(/s0) = 3.51105
Results:
KKRb-resonance
Loss
a (a
0
)
a<0
3B Max
KRbRb-2463B MaxKKRb-22000a>0AD Maxindirecta*667
No oscillations for a>0 observed
Slide266d6
B (Gauss)
preliminary
K3
preliminary
Lifetime measurements @ high magnetic fields
Recombination rate @
6s6 resonance ~ 800G, width ~ 90G
T~200nK
Resonance!
Unitarity
limit:
Another piece to the puzzle!
L
3
L
3
f l m
f
Slide27nD= -L2 nD 2
Measuring relaxation rate L2:
Ferlaino et al., PRL 101, 023201 (2008)
Experimental results: dimer-dimer collisions
s-wave state
d-wave
state
2 atoms in F=3, mF=3
microwave
Sample of universal dimers in 6s-state:
crossed dipole trap (1060nm)
N
D
~ 4000
T ~ 40 – 350 nK
k
B
T << EB ~ h50kHz << EvdW ~ h2.7MHz
105 ultracold 133Cs atoms (40nK) Feshbach association Removal of atoms with microwave Sample of ultracold dimers
scattering length (a
0
)
2-body reaction cross section (Wigner 1948)
energy
a
<
0
a
>
0
Tetra1
Tetra2
?
Slide28Exchange reactions with distinguishable particles
B
+ A
2
F=4, m
F
=2, 3 or 4
Feshbach molecule / halo dimer
2x (F=3, m
F
=3)
m
F
=3
F=3
F=4
2
m
F
=4
3
MW transfer
A + A
2
F=3, m
F
=3
?
Slide29total loss
exchange
T=50 nK
b
: atom-dimer loss
rate coefficient
Exchange reactions loss rates
Knoop et al., Phys. Rev. Lett.
104
, 053201 (2010)
Theory:
Jose D’Incao & Brett Esry
B
E
A+A+B
A
2
+B
A+A
B
D
E
new decay channel
m
F
=4
m
F
=3
m
F
=2
resonance @ 35 G:
opening exchange channel
B
E
A+B
A+A
AB
A
2
Slide30A
2(v=-1)+B → A+AB(v=-1)
Closer look around 35 G
appearance of trapped atoms in state A!
Ultracold exchange reaction
controlled by magnetic field
T=100 nK, t
hold
=22ms
m
F
=4
m
F=3
mF=2
Slide31Role of the large scattering length
A
2
(v=-1)
+B
A+A
B
(v’<v)
A+A
B
(v=-1)
A
2
(v’<v)
+B
A+A
A+B(
m
F
=2)
A+B(
m
F
=3)
A+B(
m
F
=4)
y(
r
)
Slide32Theory
Experiment
Experimentalists wish list for Theory
Is there any relation for Efimov physics at different Feshbach resonances
(
133
Cs low fields and Feshbach resonance @ 800G)?
Model for finite-range interactions, transition universal to non-universal (
39
K &
133
Cs)?
Variation in the short range phase across the Feshbach resonance (
7
Li)
– Factor 2?
Why does
7
Li agree so nicely in (F=1,m
F
=0) and not in (F=1,m
F
=1)?
Why there is no change in the three body parameter in
6
Li spin mixture for
B ~ 750G and/or
for a
ij
~ l
vdw
?
Coming soon:
Cs data for
800G resonance
Any connection of Efimov physics from
a>0 to
a<0 via a=0 (
133
Cs)?
– Factor 1/2?
Temperature dependence in
133
Cs halo molecules?
a <<
a
Slide33The Caesium-Efimov-Team
M.B.
Rudi
Grimm
Francesca
Ferlaino
Alessandro
Zenessini
Hanns-Christoph Nägerl
Walter
Harm