Scientific Committe Organizing Committe - Harvard

Transcription

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Scientific Committe
Organizing Committe
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F.A. Gianturco
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C.H. Greene
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R. Grimm
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P. Villarreal
I. Baccarelli
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S. Bovino
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F.A. Gianturco
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Orlandini
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Foreword
Since the pioneering investigation by Efimov on weakly bound trimers, a
large number of studies have focussed on the peculiar behaviour exhibited
by the bound states of such systems. In spite of the fact that the so-called
Efimov effect was originally proposed within the context of nuclear physics,
molecular physicists promptly found several possible, and somewhat ideal
candidates among three-atom complexes that were fulfilling the necessary
requirements.
Thus, extensive theoretical studies on the He trimer and combinations of
He2 with weakly bound impurities such as Li have predicted that the corresponding first excited bound states could indeed display features of Efimov
behaviour. It has been however in the field of ultracold condensates where
Efimov’s predictions seemed to have been proved particularly fruitful and
more likely to produce firmer evidence of its existence.
Theoretical predictions for three-body recombination rates within BoseEinstein condensates have revealed, in fact, that the physics governing those
processes is clearly influenced by the presence of Efimov states. It has even
been suggested that the possibility should exist for experimentally created
trimer condensates with Efimov properties, while a very exciting breakthrough has been provided by the recent report on the first experimental
evidence of Efimov behaviour in an ultracold condensate formed with Cs
atoms.
In those experiments the existence of a Efimov trimer was inferred from
the presence of a giant three-body recombination loss in the range of large
negative scattering lengths, together with the presence of a local minimum
for the positive scattering length regime.
These exciting, and recent, developments in the context of the Efimov
Physics in cold atoms constitute a revival of the ideas developed about 30
years ago and a stimulus to the theoretical explorations done in the last 10-15
years.
The scope of the present Workshop, therefore, is that of bringing together
scientists which are already, albeit almost separately, directly involved in a
broad range of related investigations. We therefore are gathering in Rome
active researchers from both the nuclear and molecular fields of investigation, so that both communitites will share the most recent contributions to
this fascinating research topic, one which is currently undergoing an exciting
evolution, both with experiments and theories.
3
Our idea of holding an ITAMP Workshop somewhat ”extra moenia“ has
been positively received by the Institute’s Committee and has found all parties involved very interested in trying a new environment for the present
encounter: hence, the choice of the Eternal City!
We are thus grateful to the Interdisciplinary Center ”B. Segre“ of the
Lincei Academy for providing financial help, secretarial help and the splendid
environment of the Academy rooms in Palazzo Corsini.
The International Scientific Committee has also reacted with enthusiasm
to the idea of this Workshop and generously provided lots of options for
the collective initial input. We are all grateful to them for their positive
participation.
Our Local Organizing Committee in Rome has also tirelessly worked for
several months on many aspects of the Workshop, from web-page settings, to
logistics and correspondence with participants: our warm thanks go indeed
to all of them!
Finally, the hope is naturally that we will all have fun in presenting our
works, in discussing with one another all sorts of important points of physics
(the devil, in fact, is always in the details!) and even in exploring whatever
parts of Rome we will be able to see: enjoy and mingle!
Franco A. Gianturco
on behalf of the Scientific and
Local Organizing Committes
4
Logistics
The conference will be held in the ”Palazzo Corsini“ in Via della Lungara 10
(Academy in the map)
The conference dinner will be in the restaurant ”RESTAURANT“ on Tuesday
the 20th October at 8.30 pm.
The dinner on Monday 19th October is not included in the programme.
A possible choice of restaurants (also shown in the map) is the following:
• da Fabrizio (about 30 euro) Via di Santa Dorotea 15
• da Gildo (about 30 euro) Via della Scala 31/a
• da Romolo (about 50 euro) Via di Porta Settimiana 8
• Miraggio (about 40 euro) Via della Lungara 16
5
Conference Hotels
The three hotels where some rooms have been reserved for the participants
(Cisterna, La Rovere, Arenula) are indicated in the map.
6
Scientific programme
9
19th October 2009 Monday
08:30 - 09:15
Registration and Event information
09:15 - 09:30
Welcome to Participants and ITAMP Presentation
F.A. Gianturco - University of Rome Sapienza, Rome, Italy
H. Sadeghpour - ITAMP, Cambridge, MA
SESSION 1
09:30 - 10:00
10:00 - 10:40
10:40 - 11:00
11:00 - 11:40
11:40 - 12:20
12:20 - 13:00
13:00 - 14:30
SESSION 2
14:30 - 15:10
Chair R. Grimm, IQOQI - University of Innsbruck, Innsbruck, Austria
V. Efimov - University of Washington, Seattle, WA
Historical Remark
A. S. Jensen - Aarhus University, Aarhus, Denmark
Occurrence of the Efimov effect for three and more particles
Coffee Break
F. Minardi - CNR-INFM and LENS, Univesity of Florence, Italy
Observation of Efimov resonances in a heteronuclear atomic mixture
B. D. Esry - Kansas State University, Manhattan, KA
Three-body collisions that are not ultracold
K. M. O’Hara - The Pennsylvania State University, Philadelphia, PA
Efimov Trimers with Large but Unequal Scattering Lengths
Lunch Break
Chair M. Inguscio, LENS - University of Florence, Italy
S. Jochim - Max-Planck-Institute for Nuclear Physics, Heidelberg, Germany
A Universal Trimer in a Three-Component Fermi Gas
S. Knoop - Kirchhoff-Institut für Physik, Heidelberg, Germany
15:10 - 15:50
Observation of an Efimov resonance in an ultracold mixture of atoms and weakly
bound dimers
15:50 - 16:20
Coffee Break
16:20 - 17:00
17:00 - 19:00
P. Massignan - ICFO - The Institute of Photonic Sciences, Barcelona, Spain
Efimov states near a Feshbach resonance
Poster Session
11
20th October 2009 Tuesday
SESSION 3
09:00 - 09:40
09:40 - 10:20
10:20 - 10:50
Chair P. Villarreal, Instituto de Fisica Fundamental, CSIC, Madrid, Spain
T. González-Lezana - Instituto Fisica Fundamental, CSIC, Madrid, Spain
Rare gas molecular trimers: From Efimov scenarios to the study of thermal
properties
A. Kievsky - Istituto Nazionale di Fisica Nucleare, Pisa, Italy
Integral relations as a tool for describing scattering states
Coffee Break
S. Orlandini - CASPUR - University of Rome ”Sapienza“, Rome, Italy
10:50 - 11:30
11:30 - 12:10
12:10 - 12:50
13:00 - 14:30
SESSION 4
14:30 - 15:10
15:10 - 15:50
15:50 - 16:20
16:20 - 17:00
17:00 - 17:40
17:40 - 18:20
20:00 -
Spatial features and energetics of ultra weakly interacting three-particle systems:
do they hold Efimov states?
M. Jona-Lasinio - INFM-CNR, LENS - University of Florence, Italy
Realistic Low-energy Description of Ultracold Few-body Systems
E. Kolganova - BLTP JINR, Dubna, Russia
Efimov trimers in the framework of Faddeev approach
Lunch Break
Chair C. Greene, JILA, University of Colorado, Boulder, CO
S. Diehl - IQOQI, Austrian Academy of Sciences, Innsbruck, Austria
Atomic Three-Body Loss as a Dynamical Three-Body Interaction
H.-W. Hammer - HISKP and BCTP, University of Bonn, Bonn, Germany
Effective field theory for few-body systems with large scattering length
Coffee Break
Cheng Chin - James Franck and University of Chicago, Chicago, IL
Few-body universality of Ultracold Atomic Gases in the strong interaction regime
L. Platter - University of Washington, Seattle, WA
Finite Range Corrections in the Three-Body System with large Scattering Length
M. Zaccanti - LENS and University of Florence - INFM-CNR, Italy
Observation of an Efimov spectrum in an atomic system
Conference Dinner
12
21th October 2009 Wednesday
SESSION 5
09:00 - 09:40
09:40 - 10:20
10:20 - 10:50
Chair G. Modugno, LENS and University of Florence - INFM-CNR, Italy
J. M. Richard - LPSC, University of Grenoble, Grenoble, France
Unnatural parity states of three unit charges
J. von Stecher - JILA, University of Colorado, Boulder, CO
Numerical Studies of Universality in Few-Boson Systems
Coffee Break
L. Khaykovic - Bar Ilan University, Ramat Gan, Israel
10:50 - 11:30
11:30 - 12:10
Observation of universality in 7 Li three-body recombination across a Feshbach
resonance
D. Petrov - CNRS and LPTMS, University Paris-Sud, Orsay, France
Weakly bound heteronuclear dimers
12:10 - 13:00
Visit to Farnese Villa La Farnesina
13:00 - 14:20
Lunch Break
SESSION 6
14:20 - 15:00
15:00 - 15:40
Chair F. A. Gianturco, University of Rome Sapienza, Rome, Italy
R. Hulet - Rice University, Houston, TX (EPJD Lecturer)
Universal Scaling in the Recombination Rates of 7 Li
J. P. D’Incao - NIST and JILA, University of Colorado, Boulder, CO
Universal four-body resonances in ultracold atomic and molecular gases
F. Ferlaino - University of Innsbruck, Innsbruck, Austria
15:40 - 16:20
A step beyond the Efimov scenario: emergence of a pair of universal four-body
states
16:20 - 16:50
Coffee Break
S. Rittenhouse - ITAMP, Harvard-Smithsonian Center for Astrophysics,
16:50 - 17:30
17:30 - 18:10
Cambridge, MA
Semi-Classical Methods and N-Body Recombination
F. Werner - University of Massachusetts, Amherst , MA
Analytical results for resonantly interacting cold atoms
18:10 - 18:30
Final Discussion
18:30 -
End of Meeting
13
Invited Contributions
15
OCCURRENCE OF THE EFIMOV EFFECT FOR THREE
AND MORE PARTICLES
A.S. Jensen1 , D.V. Fedorov1 , M. Thogersen1
1
Department of Physics and Astronomy, Aarhus University, DK-8000 Aarhus C, Denmark
The Efimov effect can be investigated by use of coordinate space Faddeev equations for shortrange interactions[1]. Occurrence in halo nuclei[2] is limited to two neutrons and an ordinary
spin-zero nucleus because all other systems involve the long-range Coulomb interaction. Two
light and one heavier particle maximize the energy difference between neighbouring Efimov
states and the required size of scattering length. The occurrence conditions are at least
two large scattering lengths in the three.body system. Tuning is in principle possible for
polarizable spin-zero systems with electric field [3]. The effect is strengthened by three simultaneously large scattering lengths but much more decisively influenced by a large mass
ratio between two of the particles and the third [4]. It is important to estimate the influence
and necessary modifications due to finite scattering lengths and finite range potentials or
in general due to deviations from optimum theoretical conditions. Numerical computations
for identical bosons are used to parametrize range-corrections for both bound and unbound
two-body systems [5]. Next we derive an equation to determine the adiabatic potentials
for distances larger than the two-body range. Only phase shifts of a related scaled finite
range two-body potential enter this transcendental equations [6]. We show that effects of
the same order as the effective range are accompanied by a second order correction to the
scattering length. Combined with the non-adiabatic correction the Efimov effect the only
appears between effective range and scattering length. All three effects must be included
simultaneously. The generalization to N identical bosons is possible under restricted assumptions, i.e. only two-body correlations and the zero-range approximation [7]. Specific
scaling of the solution to the generalized transcendental equation is found. A class of solutions emerge with Efimov scaling properties of energies and radii of these states. They are
denoted many-body Efimov states [8,9] but appear as highly excited resonance states. Two
and three α-particle states appear with energies 0.091 MeV and 0.38 MeV, respectively. In
a dens and hot plasma of electrons and α-particles screening effectively reduce the Coulomb
repulsion [10]. The Efimov conditions are approached with tremendous consequence for the
astrophysically crucial triple α-reaction in such environment. We shall select from the above
menu and possibly add results obtained during the summer.
References
[1] D.V. Fedorov, A.S. Jensen, Phys. Rev. Lett. 71, 4103 (1993).
[2] D.V. Fedorov, A.S. Jensen, K. Riisager, Phys. Rev. Lett. 73, 2817 (1994).
[3] E. Nielsen, D.V. Fedorov, A.S. Jensen, Phys. Rev. Lett. 82, 2844 (1999).
[4] A.S. Jensen, D.V. Fedorov, Europhys. Lett. 62, 336 (2003).
[5] M. Thogersen, D.V. Fedorov, A.S. Jensen, Phys. Rev. A 78, R020501 (2008).
[6] M. Thogersen, D.V. Fedorov, A.S. Jensen, B.R. Esry, Y. Wang Phys. Rev. A (2009).
[7] T. Sogo, et al., Europhys. Lett. 69, 732 (2005); J. Phys. B 38, 1051 (2005).
[8] O. Sorensen, D.V. Fedorov, A.S. Jensen, Phys. Rev. Lett. 89, 173002 (2002).
[9] M. Thogersen, D.V. Fedorov, A.S. Jensen, Europhys. Lett. 83, 30012 (2008).
[10] A.S. Jensen, D.V. Fedorov, et al., ENAM 95, Edition Frontieres, 667 (1995).
17
OBSERVATION OF EFIMOV RESONANCES IN A
HETERONUCLEAR ATOMIC MIXTURE
F. Minardi1,2 , G. Barontini1 , J. Catani1,2 , F. Rabatti1,2 , G. Thalhammer1 ,
C. Weber1,3 , M. Inguscio1,2
1
LENS-European Laboratory for Nonlinear Spectroscopy and Università di Firenze, Via
Nello Carrara 1, I-50019 Sesto Fiorentino, Italy
2
CNR-INFM BEC Center, Via Giovanni Sansone 1, I-50019 Sesto Fiorentino, Italy
3
Institut für Angewandte Physik, Universität Bonn, Wegelerstrae 8, D-53115 Bonn,
Germany
We report on the experimental observation of Efimov resonances in a mixture of two atomic
species with different masses [1], namely 41 K and 87 Rb. We detect two narrow peaks in the
rate of three-body recombination collisions as we scan the KRb scattering length by means
of a broad Feshbach resonance. We attribute these peaks, occurring at negative scattering
length, to Efimov resonances arising from KKRb and KRbRb Efimov trimers. We integrate
a set of rate equations to describe the experimental data and we extract the position, widths
and amplitude of the resonances. We also observe a narrow peak at positive scattering length,
which might be an indication of an atom-dimer scattering resonance. These results represent
the first observation of Efimov physics with particles of different masses. Asymmetric systems
are relevant for other domains of Efimov physics, e.g. nuclear physics, and require further
analysis because several theoretical results are known only for the case of identical particles.
References
[1] G. Barontini, C. Weber, F. Rabatti, J. Catani, G. Thalhammer, M. Inguscio, F. Minardi,
Phys. Rev. Lett. in press, eprint arXiv:0901.4584.
18
THREE-BODY COLLISIONS THAT ARE NOT ULTRACOLD
B.D. Esry1 , Yujun Wang1 , J.P. D’Incao2
1
Department of Physics, Kansas State University, Manhattan, Kansas 66506 USA
2
JILA, University of Colorado and NIST, Boulder, Colorado 80309-0440, USA
I will present our recent work to understand collisions of three bodies at low, but not ultracold, energies when their interactions produce large two-body scattering lengths. At
ultracold energies, such systems display all of the behavior we have come to associate with
Efimov physics. The question we wanted to answer was whether those Efimov features persist to higher collision energies. We will show both numerically and analytically that they do
and under what conditions they do. In the process, we have obtained analytical expressions
for the various inelastic collision rates as a function of collision energy and scattering length
as well as for non-zero angular momentum. 1
This work was supported by the U.S. National Science Foundation and the U.S. Air Force Office of
Scientific Research.
1
19
EFIMOV TRIMERS WITH LARGE BUT UNEQUAL
SCATTERING LENGTHS
Efimov Trimers with Large but Unequal Scattering Lengths
K. M. O’Hara1 , J. R. Williams1 , J. H. Huckans1 , E. L. Hazlett1 , R. W.
1
1
K. M. O’Hara, J.Stites
R. Williams,
H. Huckans,
E. L. Hazlett,
, and Y.J. Zhang
R. W. Stites, and Y. Zhang
1
Dept. of Physics, The Pennsylvania State University, University Park, PA, 16802, USA
Dept. of Physics, The Pennsylvania State University, University Park, PA, 16802, USA
We have observed multiple three-body loss resonances in an ultracold three-component Fermi
gas that
when Efimov
trimer
statesloss
cross
the three-atom
scattering
threshold. The
We occur
have observed
multiple
three-body
resonances
in an ultracold
three-component
three-body
resonances
are located
in thestates
vicinity
ofthe
three
overlapping
two-body
Feshbach
Fermiloss
gas that
occur when
Efimov trimer
cross
three-atom
scattering
threshold.
resonances
where, depending
on theare
magnetic
0, of
1, three
2 or 3overlapping
of the scattering
lengths
The three-body
loss resonances
located field,
in theeither
vicinity
two-body
Feshbach
resonances
depending
on the of
magnetic
eithersuch
0, 1, as
2 or
3 of the
may be
positive.
In this where,
situation,
new effects
Efimovfield,
physics,
atom-molecule
scattering
lengths
be positive.AInqualitative
this situation,
new effects
Efimovspectrum
physics, such
interference
minima,
aremay
expected[1].
picture
of the of
Efimov
in shown
1
atom-molecule
interference
minima,
are expected
. Aand
qualitative
picture
of the
Efimov
in the as
figure
below. Loss
resonances
are observed
at 130
500 G[2,3]
where
corrections
to
2,3
spectrum
in
shown
in
the
figure
below.
Loss
resonances
are
observed
at
130
and
500
G
the zero range approximation may be required. We have recently observed an additional loss
where corrections to the zero range approximation may be required. We have recently obresonance at 895 G where the zero-range approximation provides an excellent description of
served an additional loss resonance at 895 G where the zero-range approximation provides
the data
an [4].
excellent description of the data4 .
0
-10
-10
4
n=1
6
1-2 dimer
2-3 dimer
1-3 dimer
T=
T=
Efimov trimer
K
n’ = 0
n=0
-10
8
Figure 1: Three-body recombination spectrum in an ultracold 6 Li gas with three equally6 Li gas with three equallypopulated
Figurepopulated
1: Three-body
recombination
spectrum
an ultracold
hyperfine
states |1!, |2!
and |3!.in The
scattering
lengths a13 , a23 and a12 are
hyperfine
states
1 !, | 2 ! and
| 3 !. The
scattering
,
a
and G
a12respectively.
are tuned by(left)
Feshbach
tuned
by |Feshbach
resonances
which
occur lengths
at 690, a811
and
13
23 834
Resonant
loss occurs
when
trimer states
cross
the three-atom
scattering
resonances
whichthree-body
occur at 690,
811 and
834Efimov
G respectively.
(left)
Resonant
three-body
loss occurs
threshold
(e.g. states
near 130,
895 G). The
grey-shaded
areas(e.g.
indicate
when Efimov
trimer
cross500
theand
three-atom
scattering
threshold
nearnon-universal
130, 500 and 895
regions.
(right) areas
A resonant
enhancement
of the
three-body
atom-loss
rate enhancement
constant K3 isof the
G). The
grey-shaded
indicate
non-universal
regions.
(right)
A resonant
observed
at
895
G.
three-body atom-loss rate constant K3 is observed at 895 G.
References
[1] J. P. DIncao and B. D. Esry, arXiv:0905.0772 (2009).
References
[2]D’Incao
E. Braaten,
D. Kang and L. (2009).
Platter, arXiv:0811.3578 (2008).
[1] J. P.
andH.-W.
B. D.Hammer,
Esry, arXiv:0905.0772
[3] T. B. Ottenstein, T. Lompe, M. Kohnen, A. N. Wenz and S. Jochim, Phys. Rev. Lett.
[2] E. Braaten, H.-W. Hammer, D. Kang and L. Platter, arXiv:0811.3578 (2008).
101, 203202 (2008).
[3] T. B. Ottenstein, T. Lompe, M. Kohnen, A. N. Wenz and S. Jochim, Phys. Rev. Lett.
[4] J. H. Huckans, J. R. Williams, E. L. Hazlett, R. W. Stites and K. M. O’Hara, Phys.
101, 203202
(2008).
Rev. Lett.
102, 165302 (2009).
[4] J. H. Huckans, J. R. Williams, E. L. Hazlett, R. W. Stites and K. M. O’Hara, Phys. Rev.
Lett. 102, 165302 (2009).
20
A UNIVERSAL TRIMER IN A THREE-COMPONENT FERMI
GAS
S. Jochim1,2 , A. N. Wenz1 , T. Lompe1 , T. B. Ottenstein1 , F. Serwane1 , G.
Zürn1
1
Max-Planck-Institute for Nuclear Physics, P.O. Box 103980, 69029 Heidelberg
2
Physics and Astronomy, Heidelberg University, 69120 Heidelberg
We will present our work on Efimov physics in a three-component Fermi gas of ultracold
6
Li atoms. We observed two three-body loss resonances [1] which indicate the presence of a
universal trimer state. For our description we adapt the theory of Braaten and Hammer [2]
for three identical bosons to the case of three distinguishable fermions by combining the three
scattering lengths a12 , a23 and a13 between the three components to an effective interaction
parameter am . Furthermore it is crucial to take into account a variation of the inelasticity
parameter η∗ , which is caused by a strong magnetic field dependence of the most weakly
bound deep dimer states. We find that the observed behavior of the three-body loss can
be quantitatively described by assuming the decay rate of the trimer state to be inversely
proportional to the binding energies of the dimer states [3].
References
[1] T.B. Ottenstein, T. Lompe, M. Kohnen, A.N. Wenz, S. Jochim, Phys. Rev. Lett. 101,
203202 (2008).
[2] E. Braaten, H.-W. Hammer, Physics Reports 428, 259 (2006).
[3] A.N. Wenz, T. Lompe, T.B. Ottenstein, F. Serwane, G. Zürn, S. Jochim, arXiv:0906.4378.
21
OBSERVATION OF AN EFIMOV RESONANCE IN AN
ULTRACOLD MIXTURE OF ATOMS AND WEAKLY BOUND
DIMERS
S. Knoop1,3 , F. Ferlaino1 , M. Berninger1 , M. Mark1,4 , H.-C. Nägerl1 , R.
Grimm1,2
1
2
Institut für Experimentalphysik and Zentrum für Quantenphysik,
Universität Innsbruck, 6020 Innsbruck, Austria
Institut für Quantenoptik und Quanteninformation, Osterreichische Akademie der
Wissenschaften, 6020 Innsbruck, Austria
An essential part of the Efimov scenario involves the interaction of the Efimov states near
the atom-dimer threshold. Resonant enhancement of inelastic relaxation has been predicted
at those values of the scattering length where the Efimov states merge into the atom-dimer
threshold. This can be directly probed by a trapped mixture of atoms and weakly bound
dimers. In this talk I will discuss our recent observation of an atom-dimer Efimov resonance in a mixture of Cs atoms and weakly bound Cs2 Feshbach molecules [1]. Our result
demonstrates that atom-dimer relaxation measurements provide complementary information
on Efimov physics to that obtained by three-body recombination in pure atomic gases. I
will review our experimental procedure, in particular, the technique of Feshbach association to create atom-dimer mixtures. Also the differences with three-body recombination
measurements in pure atomic sample will be discussed.
References
[1] S. Knoop, F. Ferlaino, M. Mark, M. Berninger, H. Schöbel, H.-C. Nägerl, R. Grimm,
Nature Phys. 5, 227-230 (2009).
3
4
Present address: Kirchhoff-Institut für Physik, Universität Heidelberg, Germany
Present address: Swinburne University of Technology, Melbourne, Australia
22
EFIMOV STATES NEAR A FESHBACH RESONANCE
Efimov states near a Feshbach resonance
2
Pietro Massignan11 and Henk T. C. Stoof
2
Pietro Massignan and Henk T. C. Stoof
1
2
ICFO - Institut
de Ciències Fotòniques, Parc Mediterrani de la Tecnologia, Castelldefels
1
ICFO - Institut de Ciències Fotòniques, Parc Mediterrani de la Tecnologia,
(Barcelona),
E-08860,
SpainSpain
Castelldefels
(Barcelona),
E-08860,
2
Institute
for Theoretical
Physics,
University
Utrecht,3584
3584 CE,
Institute
for Theoretical
Physics,
UniversityofofUtrecht,
Utrecht, Leuvenlaan
Leuvenlaan 4,4,Utrecht,
The
Netherlands
CE, The Netherlands
We study three-body collisions close to a Feshbach resonance by taking into account twoWe study three-body
close
to athe
Feshbach
resonance
by taking
into account
twobody scattering
processescollisions
involving
both
open and
the closed
channels
[1]. We
extract
1
body scattering processes involving both the open and the closed channels . We extract133
the atom-dimer scattering length and the three-body recombination rate in atomic
Cs,
the atom-dimer scattering length and the three-body recombination rate in atomic 133Cs,
obtaining a very good agreement with the experimental results of the Innsbruck group
[2].
obtaining a very good agreement with the experimental results of the Innsbruck group2 .
We predict
the
existence
at
negative
scattering
length
of
a
non-universal
sharp
minimum
We predict the existence at negative scattering length of a non-universal sharp minimum
in theinrecombination
losses
duedue
totothe
shallowbound
bound
level. In addition, we
the recombination
losses
thepresence
presence of
of aa shallow
level.
present
ab-initio
calculations
for
the
position
of
Efimov
features
in
a
gas
of 39 K atoms,
In addition, we present ab-initio calculations for the position of Efimov features
in a gaswhich
have been
recently
confirmed
experimentally
by theexperimentally
Florence group
[3]. Florence group3 .
of 39K
atoms, which
have been
recently confirmed
by the
2-body
3-body
10
9
10
6
-10
Re(aAD/a0)
Energy (µK)
0
-4
-10
-2
-1
-10
2
-10
4
-100
-12
B0
-11
0
100
+
Cs
Cs
+
K
0
-10
6
-10
9
-100 -30 -10
Magnetic field (G)
-1 -0.1
0
0.1 1
10 30 100
Detuning (G)
Figure 1: Left: Two and three-body energy levels as a function of magnetic field for 133 Cs.
FigureThe
2: cross
Left:shows
Two the
and position
three-body
energy
levels as aresonance
function of
magnetic
fieldInnsbruck
for 133 Cs. The
of the
recombination
observed
in the
cross shows
the position
the recombination
resonancescattering
observed length
in the Innsbruck
experiment
[2]
2
39
experiment
. Right:of Real
part of the atom-dimer
for 133 Cs and
K.
133 Cs and 39 K. Here + and - refer to
. Right:
Real
part
of
the
atom-dimer
scattering
length
for
Here + and - refer to collisions with the two shallow dimers. In both figures, the scales
1/5
collisions
withaxes
theare
two
shallowbydimers.
the
scales
on the
obtained
plottingIn
(Bboth
− B0figures,
)1/5 , E 1/10
, and
aADon
. the axes are obtained by
1/5
1/5
1/10
plotting (B − B0 )
,E
, and aAD .
References
[1] P. Massignan and H. T. C. Stoof, Phys. Rev. A 78, 030701(R) (2008).
[2]
T. Kraemer, M. Mark, P. Waldburger, J. G. Danzl, C. Chin, B. Engeser, A. D. Lange,
References
K.
Pilch, A. and
Jaakkola,
H.-C.
Nägerl,
andRev.
R. Grimm,
440, 315
(2006).
[1] P. Massignan
H.T.C.
Stoof,
Phys.
A 78,Nature
030701(R)
(2008).
[3] M. Zaccanti, B. Deissler, C. D’Errico, M. Fattori, M. Jona-Lasinio, S. Müller, G. Roati,
[2] T. Kraemer, M. Mark, P. Waldburger, J.G. Danzl, C. Chin, B. Engeser, A.D. Lange, K.
M. Inguscio, and G. Modugno, arXiv:0904.4453v1 (2009).
Pilch, A. Jaakkola, H.-C. Nägerl, and R. Grimm, Nature 440, 315 (2006).
[3] M.Zaccanti, B.Deissler, C.D’Errico, M.Fattori, M.Jona-Lasinio, S.Müller, G.Roati, M.Inguscio,
and G.Modugno, arXiv:0904.4453v1 (2009).
23
RARE GAS MOLECULAR TRIMERS: FROM EFIMOV
SCENARIOS TO THE STUDY OF THERMAL PROPERTIES
Tomás González-Lezana1
1
Instituto de Fı́sica Fundamental, CSIC, c/ Serrano 123, 28006 Madrid, Spain
Molecular clusters formed by rare gas atoms exhibit a rich variety of properties which have
led many authors in the past to focuss their efforts on these systems. In particular, few body
molecules have been ideal prototypes to probe the possible occurence of effects observed in
larger aggregates such as molecular superfluidity or phase transitions. In addition, the trimer
formed with the lightest rare gas, helium, as He3 [1,2], have been found to manifest the socalled Efimov effect[3]. Thus, by conveniently enlarging the corresponding pair interactions,
it is possible to observe that the first excited state becomes energetically less stable than the
energy of the He2 bound state. These bound states, on the other hand, are characterised by a
extreme spatial delocation, in clear contrast with the case observed for heavier systems such
as Ar3 or Ne3 . The energetics and geometries of the bound states found for these systems
have been studied by means of a variational quantum mechanical approach based in the use
of distributed Gaussian functions to describe interparticle distances [4,5]. The rovibrational
spectra for the case of a nonzero total angular momentum, J #= 0, can be analysed with
a recently proposed method in which the eigenstates of the purely vibrational problem are
used as radial functions in the basis set for the total Hamiltonian [6,7] . An example of
the application for Ar3 will be presented in the conference. Finally, recent results of the
investigation of some properties of the Ar trimer as a function of the temperature will be
also discussed.
References
[1] T. González-Lezana, J. Rubayo-Soneira et al. Phys. Rev. Lett. 82, 1648 (1999).
[2] T. González-Lezana, J. Rubayo-Soneira et al. J. Chem. Phys. 110, 9000 (1999).
[3] V. Efimov, Phys. Lett. 33B, 563 (1970); Nucl. Phys. A210, 157 (1973).
[4] T. González-Lezana et al., Comp. Phys. Comm. 145, 156 (2002).
[5] I. Baccarelli et al., Phys. Rep. 452, 1 (2007).
[6] M. Márquez-Mijares et al., Chem. Phys. Lett. 460, 417 (2008)
[7]. M. Márquez-Mijares et al., J. Chem. Phys. 130, 154301 (2009).
24
INTEGRAL RELATIONS AS A TOOL FOR DESCRIBING
SCATTERING STATES
A. Kievsky1
1
Istituto Nazionale di Fisica Nucleare, Largo Pontecorvo 3, 56100 Pisa, Italy
Recently, two integral relations have been derived from the KVP in order to obtain the
scattering matrix [1]. The integral relations depend on the wave function in the interaction
region and, therefore, it is possible to determine the scattering matrix even if the asymptotic
part of the wave function is not explicitely known. A particular well suited example for the
applicability of these relations if the Hyperspherical Adiabatic (HA) expansion. For bound
states the convergence of the HA expansion has been proved to be very fast. However the
convergence of the expansion slows down significantly in the case of low energy scattering
states [2]. Configurations in which the system clusters in two or more structures are very
dicult to describe using hyperspherical variables. These configurations are not separable
in the hyperspherical variables and a huge number of HA basis elements are necessary to
describe the process. This unpleasant behavior is independent of the interaction, and shows
the close relation that can appear between the pattern of convergence of the expansion and
the boundary conditions to be imposed to the wave function. In this talk it will be shown
how the HA expansion method can be used to describe elastic scattering with a pattern of
convergence similar to a bound state calculation. The number of HA terms needed to obtain
completely stable results depends very little on the structure of the potential, exactly as
for bound state calculations. The integral relations are governed by the wave function in
the interaction region. Therefore the stability of the results with a low number of HA basis
elements is a clear indication that inclusion of more terms in the expansion only modifies
the wave function outside the interaction range. This method will be particularly efficient
in the description of few-atom collisions by means of HA expansion. Different examples will
be given.
References
[1] P. Barletta, C. Romero-Redondo, A. Kievsky, M. Viviani and E. Garrido, arXiv/nuclth/0905.2052.
[2] P. Barletta and A. Kievsky, Few-Body Syst. 45, 25 (2009).
25
SPATIAL FEATURES AND ENERGETICS OF ULTRA
WEAKLY INTERACTING THREE-PARTICLE SYSTEMS:
DO THEY HOLD EFIMOV STATES?
S. Orlandini1,2 , I. Baccarelli1 , F. A. Gianturco2
1
CASPUR, Consortium for Supercomputing in Research,
Via dei Tizii 6, 00185 Rome, Italy
2
Chemistry Department, University of Rome ‘Sapienza’,
P.le A. Moro 5, 00185 Rome, Italy
A variational method based on the use of bond coordinates and of a basis set expansion
described by distributed Gaussian functions (DGF) [1] is reviewed in its most recent implementation [2]. The method takes advantage of the Jacobi-Davidson filtering procedure
[2] to better apply to the study of ultra weakly bound triatomic clusters. The theoretical
and computational study of these systems constitute indeed a very challenging task and, in
its current implementation, the present method has been shown to be a reliable and robust
procedure for characterizing very diffuse states [2-5]. A particularly interesting capability
of the DGF method is given by its natural ability to describe the spatial features of these
unusual systems by means of several statistical properties such as radial distributions, sizes
and dominance of triangular configurations for the corresponding bound states [1].
The method also allows us to look for the possible existence of Efimov or Halo states by the
analysis of the changes in the energetics of the trimers and their subsystems as a consequence
of potential-tuning [4].
A selection of representative results obtained in the past will be presented and discussed into
details together with our preliminary results on the 4 He72 Li system.
References
[1] T. González-Lezana, et al., Comput. Phys.
al., Phys. Rep. 452, 1 (2007).
[2] S. Orlandini, I. Baccarelli, F.A. Gianturco,
[5] S. Orlandini, et al., in preparation.
Comm. 145, 156 (2002) and I. Baccarelli, et
Comp. Phys. Comm. 180, 384 (2009).
J. Chem. Phys. 125, 234307 (2006).
Mol. Phys. 106, 573 (2008).
26
REALISTIC LOW-ENERGY DESCRIPTION OF ULTRACOLD
FEW-BODY SYSTEMS
Mattia Jona-Lasinio1 , Ludovic Pricoupenko2 , Yvan Castin3
1
3
LENS and Dipartimento di Fisica, Universitá di Firenze,
Via Nello Carrara 1, 50019 Sesto Fiorentino, Italy
2
Laboratoire de Physique Théorique de la Matiére Condensée,
Université Pierre et Marie Curie,
case courier 121 4 place Jussieu, 75252 Paris Cedex 05, France
Laboratoire Kastler Brossel, École Mormale Supérieure UPMC, CNRS,
24 rue Lhomond, 75231 Paris Cedex 05, France
The collisional properties of ultracold atomic systems in the resonant regime acquire a universal character: the microscopic details of the interaction potential become irrelevant and the
scattering properties of the system are well described by a zero-range (contact) interaction
parameterized by the scattering length. Real life is much more complex as in experiments
one can never really reach the full universality of the system because of the high atomic loss
rate close to resonance due to recombination events towards weakly and deeply bound states.
Furthermore, as soon as we leave the resonant regime the off-resonant interaction as well as
the finite range of the real interatomic potential start to play a role. We propose a simple
two-channel model with finite-range interaction that takes into account all the low-energy
physical parameters of the system and describes three-body interactions for an atomic system close to resonance. Our model includes both Feshbach and shape resonances. We study
the problem of three identical bosons [1] interacting via an S-wave interaction, and the more
complex problem of three polarized identical fermions [2] interacting in the P-wave channel
close to a Feshbach resonance. Our approach quantifies non universal effects appearing for finite magnetic field detuning. We obtain analytical and numerical predictions for most of the
physical quantities relevant in present experiments: atom-dimer scattering length, existence
and lifetime of trimers, recombination rate for three colliding atoms towards weakly and
deeply bound states. We exclude an Efimov effect for three polarized fermions interacting in
the P-wave channel. We obtain important insights in the description of seminal experiments
performed with Sodium [3] and Caesium [4,5].
References
[1] M. Jona-Lasinio and L. Pricoupenko, arXiv:0903.3808 (submitted), (2009).
[2] M. Jona-Lasinio, L. Pricoupenko and Y. Castin, Phys. Rev. A 77, 043611 (2008).
[3] J. Stenger, S. Inouye, M. R. Andrews, H.-J. Miesner, D. M. Stamper-Kurn, and W.
Ketterle, Phys. Rev. Lett. 82, 2422 (1999)
[4] T. Kraemer, M. Mark, P. Waldburger, J. G. Danzl, C. Chin, B. Engeser, A. D. Lange,
K. Pilch, A. Jaakkola, H.-C. Nägerl and R. Grimm , Nature 440, 315 (2006)
[5] M. Mark, F. Ferlaino, S. Knoop, J. G. Danzl, T. Kraemer, C. Chin, H.-C. Nägerl, and
R. Grimm, Phys. Rev. A 76, 042514 (2007)
27
EFIMOV TRIMERS IN THE FRAMEWORK OF FADDEEV
APPROACH
E.A. Kolganova1
1
Joint Institute for Nuclear Research, Dubna, Moscow reg. 141980 Russia
Method of scattering calculations using differential Faddeev equations with a hard-core interactions is discussed. Numerical results on binding energies of the helium trimers and
ultra-cold collisions of 4 He atom on 4 He dimer are reviewed [1].
References
[1] E. A. Kolganova, A. K. Motovilov, and W. Sandhas, Physics of Particles and Nuclei 40,
206 (2009).
28
ATOMIC THREE-BODY LOSS AS A DYNAMICAL
THREE-BODY INTERACTION
Sebastian Diehl1 , Andrew J. Daley1 , Peter Zoller1 et al.
1
Institute for Quantum Optics and Quantum Information
of the Austrian Academy of Sciences,
Otto-Hittmair-Platz 1, A-6020 Innsbruck, Austria
We discuss how large three-body loss of atoms can give rise to effective hard-core threebody interactions for a system on the optical lattice. In a bosonic system, the hard-core
constraint stabilizes attractive two-body interactions. In this regime, an Ising-type phase
transition separates the conventional atomic superfluid from a dimer superfluid. Increasing
the attraction further, for unit filling the system then approaches a supersolid state. Via
numerical simulations of the many-body dynamics in one-dimensional systems, we identify
schemes to prepare these phases [1]. Further applications are discussed for fermions: In a
three-component attractive Fermi gas, we nd evidence for atomic color superfluidity, which
in a system without hard-core constraint is preempted by trion formation [2].
References
[1] A.J. Daley, J.M. Taylor, S. Diehl, M. Baranov, P. Zoller, Phys. Rev. Lett. 102, 040402
(2009); S. Diehl, A.J. Daley, M. Baranov, P. Zoller, in preparation (2009).
[2] A. Kantian, M. Dalmonte, A.J. Daley, S. Diehl, P. Zoller, in preparation (2009).
29
EFFECTIVE FIELD THEORY FOR FEW-BODY SYSTEMS
WITH LARGE SCATTERING LENGTH
H.-W. Hammer1
1
Helmholtz-Institut für Strahlen- und Kernphysik (Theorie) and Bethe Center for
Theoretical Physics, Universität Bonn, 53115 Bonn, Germany
Effective field theories provide a powerful framework to exploit a separation of scales in
physical systems. I will discuss the application of this method to few-body systems with
short-range interactions and large scattering length[1]. Such systems show universal behavior
and can display the Efimov effect [2]. Finally, I will discuss some applications in nuclear
physics and the physics of ultracold atoms [3,4,5,6].
References
[1] E. Braaten and H.-W. Hammer, Phys. Rept. 428, 259 (2006).
[2] V. Efimov, Phys. Lett. 33B, 563 (1970).
[3] D.L. Canham, H.-W. Hammer, Eur. Phys. J. A 37, 367 (2008).
[4] K. Helfrich, H.-W. Hammer, EPL 86, 53003 (2009).
[5] E. Braaten, H.-W. Hammer, D. Kang, L. Platter, arXiv:0811.3578v1.
[6] H.-W. Hammer, L. Platter, Eur. Phys. J. A 32, 113 (2007).
30
FEW-BODY UNIVERSALITY OF ULTRACOLD ATOMIC
GASES IN THE STRONG INTERACTION REGIME
Cheng Chin1
1
James Franck Institute and Department of Physics,
929 E. 57th St.,Chicago, IL 60637, USA
Recent research on ultracold atoms entered a new era in which atomic interactions can be
fully controlled and engineered to simulate a broad range of new many-body and few-body
phenomena in condensed matter, nuclear physics or even cosmology. An excellent example is
the Observation of three-body Efimov states. Efimov states, first conjectured in 1970 in the
context of nuclear physics, were observed in recent experiments based on various ultracold
bosonic and fermionic gases. In this talk, I will summarize the brief history of Efimov
physics research in cold atom community, observations in various cold atoms systems and
the ramifications or outstanding issues in the search of universality in few-body physics.
31
FINITE RANGE CORRECTIONS IN THE THREE-BODY
SYSTEM WITH LARGE SCATTERING LENGTH
Lucas Platter1
1
Institute for Nuclear Theory, University of Washington, Seattle, WA 98195, USA
Effective Field Theories (EFTs) facilitate a straightforward analysis of corrections to universal properties of few-body systems due to finite range corrections. I will discuss how these
corrections are impacted by the discrete scale invariance exhibited by three-body observables in the zero-range limit and will explain the implications of these results for atomic and
nuclear systems.
References
[1] C. Ji, D.R. Phillips and L. Platter, Phys. Rev. A 79, 022702, 2009.
[2] C. Ji, D. .R. Phillips and L. Platter, in preparation.
32
OBSERVATION OF AN EFIMOV SPECTRUM IN AN
ATOMIC SYSTEM
M. Zaccanti1 , B. Deissler1 , C. D’ Errico1 M. Fattori1,2 , M. Jona-Lasinio1
S. Müller3 , G. Roati1 M. Inguscio1 , and G. Modugno1
1
LENS and Physics Department,Università di Firenze, and
INFM-CNR, Via Nello Carrara 1, 50019 Sesto Fiorentino, Italy
2
Museo Storico della Fisica e Centro Studi e Ricerche E. Fermi, Roma, Italy
3
Physikalisches Institut, Universität Stuttgart, 70550 Stuttgart, Germany
In 1970 the Russian physicist V. Efimov predicted a puzzling quantum-mechanical effect that
is still of great interest today. He found that three particles subjected to a resonant pairwise
interaction can join into an infinite number of loosely bound states even though each particle
pair cannot bind. Interestingly, the properties of these aggregates, such as the peculiar
geometric scaling of their energy spectrum, are universal, i.e. independent of the microscopic
details of their components. Despite an extensive search in many different physical systems,
including nuclei, atoms and molecules, Efimov spectra still elude observation. Here we report
on the discovery of two bound trimer states of potassium atoms very close to the Efimov
scenario, which we reveal by studying three-particle collisions in an ultracold gas with tunable
interaction. Our observation provides the first evidence of an Efimov spectrum and allows a
direct test of its scaling behaviour, shedding new light onto the physics of few-body universal
systems.
33
UNNATURAL PARITY STATES OF THREE UNIT CHARGES
Jean-Marc Richard1,2
1
Laboratoire de Physique Subatomique et Cosmologie, IN2P3-CNRS, Université Joseph
Fourier, INPG, 53, avenue des Martyrs, 38026 Grenoble, France,
2
Institut de Physique Nucléaire de Lyon, Université de Lyon, IN2P3-CNRS-UCBL, 4, rue
Enrico Fermi, 69622 Villeurbanne, France
The ground-state of hydrogen ion, H− = (p, e− , e− ) is known to be rather weakly bound,
and demonstrating its stability [1] requires a wave function beyond the simple Hartree–Fock
approximation f (r1 )f (r2 ). It is the only state below the threshold H(1s) + e− made of a
hydrogen atom and an isolated electron [2].
However, in the sector with unnatural parity, the effective threshold is H(2p) + e− , with an
excited hydrogen atom, as long as spin effects and radiative corrections are neglected. This
threshold energy is Eth = −0.125 in natural units. The lowest state is found very weakly
bound [3], at E $ −0.1253. Not surprisingly, there is no excitation below this threshold [4].
In this talk, we discuss how this state survives when the masses of the constituents are varied.
The result by Mills [5] is recovered, that there is no bound state of unnatural parity for the
positronium ion Ps− = (e+ , e− , e− ). When the electrons become different, a very small mass
difference suffices to break this fragile binding [6].
References
[1] See, for instance, S. Chandrasekhar, Astrophyical J. 100, 176 (1944)
[2] R.N. Hill, J. Math. Phys. 18, 2316 (1977).
[3] E. Wold, Phys. Math. Univ. Oslo, Vol. 13 (1962); J. Midtdal, ibidem Vol. 21 (1964);
G.W.F. Drake, Phys. Rev. Lett. 24, 126 (1970); R. Jàuregui and C. F. Bunge, J. Chem.
Phys. 71, 4611 (1979).
[4] H. Grosse and L. Pittner, J. Math. Phys. 24, 1142 (1983).
[5] A.P. Mills, Phys. Rev. A 24, 3242 (1981).
[6] J.-M. Richard, arXiv:0907.2592 [physics.atom-ph].
34
NUMERICAL STUDIES OF UNIVERSALITY IN FEW-BOSON
SYSTEMS
Javier von Stecher1 , Jose P. D’Incao1 , Chris H. Greene1
1
JILA and Department of Physics, University of Colorado, Boulder, Colorado 80309-0440,
USA
This presentation will focus on recent developments in the description of the few-boson
system. The combination of different numerical techniques, such as correlated Gaussian
calculations and a hyperspherical treatment, leads to an accurate description of the fourboson system[1]. These numerical methods are used to analyze the universal aspects of such
system and their relation with Efimov physics [2]. Finally, the possibility of extending these
studies to larger systems will be discussed.
References
[1] Javier von Stecher and Chris H. Greene (arXiv:0904.1405) to appear in Phys. Rev. A.
[2] J. von Stecher, J. P. D’Incao and Chris H. Greene, Nat. Phys. 5, 417 (2009).
35
OBSERVATION OF UNIVERSALITY IN 7 Li THREE-BODY
RECOMBINATION ACROSS A FESHBACH RESONANCE
Lev Khaykovich1 , Noam Gross1 , Zav Shotan1 , Servaas Kokkelmans2
1
2
Department of Physics, Bar-Ilan University, Ramat-Gan, 52900 Israel
Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
Since the pioneering experimental evidences of Efimov states in an ultracold gas of Cs atoms
[1], their signatures have been found in other atomic systems such as 39 K2 , mixture of 41 K
and 87 Rb3 and a three-component 6 Li [4,5]. Here we discuss our recent experimental study
of three-body recombination in a gas of ultracold and optically trapped 7 Li atoms in the
vicinity of a Feshbach resonance. In particular we report on evidence of universality in this
three-body observable across the resonance [6]. We find a recombination minimum and an
Efimov resonance in regions of positive and negative scattering lengths, respectively. Both
observed features lie deeply within the range of validity of the universal theory and the
relations between their properties, i.e. widths and locations, are in an excellent agreement
with the theoretical predictions [7].
References
[1] T. Kraemer et. al., Nature, 440, 315 (2006); S. Knoop et. al., Nature Phys. 5, 227
(2009).
[2] M. Zaccanti et. al., Nature Phys. 5, 586 (2009).
[3] G. Barontini et. al., Phys. Rev. Lett. 103, 043201 (2009).
[4] T.B. Ottenstein et. al., Phys. Rev. Lett. 101, 203202 (2008); A.N. Wenz et. al.,
arXiv:0906.4378.
[5] J.H. Huckans et. al., Phys. Rev. Lett. 102, 165302 (2009); J.R. Williams et. al.,
arXiv:0908.0789.
[6] N. Gross, Z. Shotan, S. Kokkelmans and L. Khaykovich, arXiv:0906.4378.
[7] E. Braaten, H.-W. Hammer, Ann. Phys. 322, 120 (2007).
36
WEAKLY BOUND HETERONUCLEAR DIMERS
D.S. Petrov1 , B. Marcelis2 , S.J.J.M.F. Kokkelmans2 G.V. Shlyapnikov1
1
2
Laboratoire Physique Théorique et Modéles Statistique, Université Paris Sud, CNRS,
91405 Orsay, France
Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
We consider collisional properties of weakly bound heteronuclear molecules (dimers) formed
in a two-species mixture of atoms with a large mass difference. We focus on dimers containing light fermionic atoms as they manifest collisional stability due to an effective dimer-dimer
repulsion originating from the exchange of the light atoms. In order to solve the dimer-dimer
scattering problem we develop a new theoretical approach, which provides a physically transparent and quantitative description of this four-atom system in terms of three- and two-body
observables. We calculate the elastic scattering amplitude and the rates of inelastic processes
such as the trimer formation and the relaxation of dimers into deeply bound molecular states.
Irrespective of whether the heavy atoms are bosons or fermions, the inelastic rate can be significantly lower than the rate of elastic collisions. Moreover, the measurement of the inelastic
rate which is a four-body observable, can be an efficient and precise tool for determining
three-body observables such as the three-body parameter, positions of Efimov states and
their lifetimes.
37
UNIVERSAL SCALING IN THE RECOMBINATION RATES
OF 7 Li
Randall G. Hulet1 , Scott E. Pollack1 , D. Dries1 , Evan Olson1
1
Department of Physics and Astronomy, and Rice Quantum Institute,
Rice University, Houston, TX 77005, USA
The Feshbach resonance for 7 Li in the F = 1, mF = 1 state is one of the broadest known
for bosonic atoms. The large width facilitates precise tuning of the s-wave scattering length
a. We previously showed that a could be tuned over a range of at least seven decades, from
0.01 ao to 105 ao , where ao is the Bohr radius[1]. We now report measurements of the 3-body
recombination rate coefficient K3 in a Bose-Einstein condensate. For a > 0, we measure K3
for a as low as 100 ao , and as large as 104 ao . We find that K3 fits the universal expression
given in ref. 2 for a > 0 remarkably well, with just two fitted parameters. Two minima
in K3 occur at values of a whose ratio is the universal value of 22.7. In addition, we find
a maximum in K3 between the two minima, where the ratio of a at the maximum to the
minimum is 4.5. Such maxima have been previously observed and attributed to the effect of
an atom-dimer resonance that increases the number of atoms lost per recombination event
[3].
References
[1] S.E. Pollack, D. Dries, M. Junker, Y. P. Chen, T. A. Corcovilos, and R. G. Hulet, Phys.
Rev. Lett. 102, 090402 (2009).
[2] E. Braaten, H.-W. Hammer, Annals of Physics 322, 120-163 (2007).
[3] M. Zaccanti et al., arXiv:0904.4453 (2009).
38
UNIVERSAL FOUR-BODY RESONANCES IN ULTRACOLD
ATOMIC AND MOLECULAR GASES
José P. D’Incao1 , Javier von Stecher1 , Chris H. Greene1
1
Department of Physics and JILA, University of Colorado, Boulder, CO 80309, USA
We study the manifestations of universal four-body physics in ultracold, strongly interacting,
atomic and molecular gases. We find that ultracold scattering observables such as fourbody recombination [1] and dimer-dimer relaxation [2], display resonant structure caused
by the emergence of universal four-boson states [1,3,4]. Such resonant effects enable the
control of few-body interactions and potentially enrich the range of experimentally accessible
phenomena. We also demonstrate the close relationship between universal four-body physics
with Efimov physics. Our analysis [2] shows that B2 + B2 → B3 + B rearrangement
reactions offers a path for an efficient trimer formation, building the bridge between threeand four-body universal physics. Our analysis of the temperature dependence of this reaction
provides an interpretation of the available experimental data and sheds light on the possible
experimental realization of rearrangement processes in ultracold gases.
References
[1] J. von Stecher, J. P. D’Incao, and C. H. Greene, Nature Phys. 5, 417 (2009).
[2] J. P. D’Incao, J. von Stecher, and C. H. Greene, Phys. Rev. Lett. 103, 033004 (2009).
[3] H. W. Hammer and L. Platter, Eur. Phys. J. A 32, 113 (2007).
[4] F. Ferlaino, et. al, Phys. Rev. Lett. 102, 140401 (2009).
39
A STEP BEYOND THE EFIMOV SCENARIO: EMERGENCE
OF A PAIR OF UNIVERSAL FOUR-BODY STATES
F. Ferlaino1 , S. Knoop1 , M. Berninger1 , W. Harm1 , J. P. D’Incao2,3 ,
H. -C. Nägerl1 , R. Grimm 1,3
1
Institut für Experimentalphysik, Universität Innsbruck, 6020 Innsbruck, Austria
Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der
2
3
Ultracold cesium atoms and Feshbach molecules provide unique model systems to explore
universal few-body phenomena. In previous experiments, we have obtained clear evidence for
Efimov three-body states by studying atomic three-body recombination [1] and atom-dimer
relaxation in ultracold atomic and molecular samples [2]. Here, we report on a fundamental
step beyond the Efimov scenario by investigating universal four-body processes. We measure
the four-body recombination rate coefficients in an atomic gas at large negative scattering
lengths and we observe two resonant enhancements of losses[3]. This provides strong evidence for the existence of a pair of four-body states, which is strictly connected to Efimov
trimers via universal relations. Our findings confirm recent theoretical predictions [4,5] and
demonstrate the enrichment of the Efimov scenario when a fourth particle is added to the
generic three-body problem.
References
[1] T. Kraemer, M. Mark, P. Waldburger, J. G. Danzl, C. Chin, B. Engeser, A. D. Lange, K. Pilch,
A. Jaakkola, H. -C. Nägerl, and R. Grimm, Nature 440, 315 (2006).
[2] S. Knoop, F. Ferlaino, M. Mark, M. Berninger, H. Schöbel, H. -C. Nägerl, and R. Grimm,
Nature Phys. 5, 227 (2009).
[3] F. Ferlaino, S. Knoop, M. Berninger, W. Harm, J. P. D’Incao, H. -C. Nägerl, and R.
Grimm, Phys. Rev. Lett. 102, 140401 (2009).
[4] H. Hammer and L. Platter, Eur. Phys. J. A 32, 113 (2007).
[5] J. von Stecher, J. P. D’Incao, and C. H. Greene, Nature Phys. 5, 417 (2009).
40
SEMI-CLASSICAL METHODS AND N-BODY
RECOMBINATION
Seth T. Rittenhouse1,2 , N. P. Mehta2,3 , J. P. D’Incao2 , J. von Stecher2
and Chris H. Greene2
1
ITAMP, Harvar-Smithsonian Center for Astrophysics, Cambridge, Massachusettes 02138
2
Department of Physics and JILA, University of Colorado, Boulder, Colorado 80309
3
Department of Physics, Grinnell College, Grinnell, Iowa 50112
Loss rates in ultracold gases have proven to be a powerfull probe for the exploration of basic
few-body physics. For this tool to be effective, the rate constant for various processes must
be understood theoretically. We develop the formula for the cross section and rate constant
of N-body recombination. Using this formula, and making basic assumptions about the
behavior of the S-matrix, the scaling behavior with respect to the scattering length of N
boson recombination can be extracted. Further, by employing semi-classical methods to
four-boson hyperradial potentials, we nd that recombination into an Efimov state can be
resonantly enhanced by the presence of a four-body state. This research was supported by
funding from the National Science Foundation.
41
ANALYTICAL RESULTS FOR RESONANTLY INTERACTING
COLD ATOMS
Félix Werner1 , Yvan Castin2
1
2
Department of Physics, University of Massachusetts, Amherst, MA 01003, USA
Laboratoire Kastler Brossel, École Normale Supŕieure, 24 rue Lhomond, 75005 Paris,
France
For an infinite scattering length, we generalize Efimov’s Ansatz to several experimentally
relevant situations:
• For 3 particles in an isotropic harmonic trap, we obtain the spectrum and wavefunctions, and deduce that the three-body loss rate is small not only for fermionic
states, but also for bosonic universal states [1].
• In free space, we determine how Efimov trimers are modified by three-body losses, and
we find a regime where the decay rates vanish [2].
• For N particles in an isotropic harmonic trap, the hyperradius (a collective degree of
freedom describing the global size of the gas) is separable, and the hyperradial problem
is solvable [3].
We also obtain exact results for an arbitrary scattering length and trapping potential, such
as virial theorems [4].
References
[1] F. Werner and Y. Castin, Phys. Rev. Lett. 97, 150401 (2006).
[2] F. Werner, Europhys. Lett. 86, 66006 (2009).
[3] F. Werner and Y. Castin, Phys. Rev. A 74, 053604 (2006).
[4] F. Werner, Phys. Rev. A 78, 025601 (2008).
42
Posters
43
Posters
P01
EXCITED ROVIBRONIC STATES OF H+
3
Alexander Alijah1
1
Departamento de Fı́sica, Universidade Federal de Minas Gerais, Av. Antônio Carlos
6627, 31270-901 Belo Horizonte, Brazil
H+
3 , the simplest triatomic, has been studied intensely due to its important role in chemistry,
physics and astronomy [1]. Actual research deals with the rovibrational states in the ground
and excited electronic states [2]. We will focus on the lowest electronic triplet state, 3 E’. Its
potential energy surface is double-valued, but the two sheets are degenerate at equilateral
triangular nuclear configurations where they suffer a conical intersection. The rovibronic
states on the upper sheet [3,4] are thus resonances, known as Slonzewski resonances. They
are of particular interest here and will be presented at the conference, as J.H.Macek has
pointed out in a recent paper [5] that for some of those states, namely those with both the
electronic and nuclear spins aligned, the Efimov effect may play a role.
References
[1] See papers of a discussion meeting on the subject organized and edited by T. R. Geballe,
D. Gerlich, J. Tennyson and T. Oka, Philos. Trans. R. Soc. London A 364, 2847 (2006)
[2] A. Alijah, Recent progress on small hydrogen molecular ions, in: Proceedings of the
NATO Advanced Research Workshop Molecular Self-Organization in Micro-, Nano-, and
Macro-Dimensions: From Molecules to Water, to Nanoparticles, DNA and Proteins, Kiev
2008, in press
[3] L. P. Viegas, M. Cernei, A. Alijah, A. J. C. Varandas, J. Chem. Phys. 120, 253 (2004)
[4] L. P. Viegas, A. Alijah, A. J. C. Varandas, J. Phys. Chem. A 109, 3307 (2005)
[5] J. H. Macek, Phys. Scr. 76, C3 (2007)
45
Posters
P02
UNIVERSAL FEW-BODY PHYSICS IN ULTRACOLD Cs:
EFIMOV STATES AND BEYOND
M. Berninger1 , A. Zenesini2 , F. Ferlaino1 , S. Knoop3 , W. Harm1 , J.P.
D’Incao4 H.-C. Nägerl1 , R. Grimm1,2
1
Institut für Experimentalphysik and Zentrum für Quantenphysik, Universität Innsbruck,
6020 Innsbruck, Austria
2
3
Kirchhoff-Institut für Physik, Ruprecht-Karls-Universität Heidelberg, 69120 Heidelberg,
Germany
4
Despite considerable experimental efforts, the detection of Efimov states has remained an
elusive goal for over 35 years. The first system to reveal an evidence for the existence of
these states was an ultracold gas of cesium atoms. The particular tunability of its scattering
length from large negative to larger positive values is the key feature making cesium a firstclass model system to study universal physics. At negative scattering length, we measured
a loss resonance in a pure atom sample indicating the presence of an Efimov state coupling
to the free atom threshold. At positive scattering lengths, the Efimov state merges into the
atom-dimer treshold resulting in an experimentally observable increase of the relaxation rate.
By producing a sample of atoms and halo dimers we could observe this feature, completing
therefore the first chapter of the Efimov scenario. Motivated by theoretical predictions by
Stecher et al. and Hammer et al., we have recently investigated four body processes in
recombination experiments. These measurements revealed the existence of two loss features
which could be attributed to the existence of universal four body states tied to an Efimov
trimer, confirming the theoretical results.
46
Posters
P03
COLLISIONAL COOLING AND ROTATIONAL QUENCHING
AT ULTRALOW ENERGIES OF A WEAKLY BOUND
TRIPLET MOLECULE: Cs2 WITH HE AS A BUFFER GAS
D. Caruso1 , M. Tacconi1 , F.A. Gianturco1 , E. Yurtsever2
1
2
Department of Chemistry and CNISM, University of Rome La Sapienza, Piazzale A.
Moro 5, 00185 Rome, Italy
Department of Chemistry, Koç University, Rumelifeneriyolu, 34450 Sariyer, Istanbul,
Turkey
Over the last decades there has been quite an impressive growth, both on the theory and
on the experiment, of the study of atomic and molecular processes at low and ultralow
temperatures [1-2], a field of research which has remarkably increased our knowledge on a
very broad variety of topics, from atomic physics [3] to molecular properties [4] and even
astrophysics [5]. In this study quantum scattering calculations at ultralow collision energies
(close to 10−8 cm−1 ) are carried out for the Cs2 (a3 Σ+
u ) state in interaction with helium. The
above system is considered to be in its vibrational ground state, while several excitated
initial rotational states are considered. In order to give a quantitative description of the
collisional quantum dynamics, we have computed the potential energy surface (PES) for the
Cs2 -He complex at the CCSD(T) level of theory by using aug-ccpVQZ basis set. Analytical
representation of the ab initio PES have been obtained and then have been used to evaluate
the scattering observables within the Coupled Channel framework as implemented in our
inelastic scattering code ASPIN [6].
References
[1] S. Haroche, Phys. Rev. Lett. 101, 160001 (2008).
[2] W. Ketterle, Chem. Phys. Chem. 3, 736 (2002).
[3] D. De Mille, Phys. Rev. Lett. 88, 067901 (2002).
[4] D. Herschbach, Rev. Mod. Phys. 71, S411 (1999).
[5] C.A.R. Sa De Melo, Phys. Today 61, 45 (2008).
[6] D. Lopéz-Durán, E. Bodo, F.A. Gianturco, Comput. Phys. Comm. 179, 821 (2008).
47
Posters
P04
THE He-Cs2 (3 ΣU ) COMPLEX AS A WEAKLY BOUND
SPECIES
Rita Prosmiti1 , Gerardo Delgado-Barrio1 and Pablo Villarreal1
Ersin Yurtsever2
Emanuele Coccia3 and F. A. Gianturco3
1 Instituto de Fisica Fundamental, C.S.I.C., Serrano 123, 28006 Madrid, Spain
2 Department of Chemistry, Koç University, Rumeligeneri Yolu, 34450 Sariyer, Istanbul,
Turkey
3 Department of Chemistry and CNISM, University of Rome ”Sapienza“, Piazzale A. Moro
5, 00185 Rome, Italy
The structure and energetics of the 3,4 He-Cs2 (3 Σu ) molecule is analyzed from first principles.
With the cesium dimer at its equilibrium distance, the electronic structure was determined
through ab initio methods at the CCSD(T) level of theory, using a large basis set to compute
the interaction energies. At the T-shaped geometry there is a shallow well with a depth of
∼ 2 cm−1 placed at R ∼ 6.75 Å, R being the distance from the center of mass of Cs2 to He.
That depth gradually decreases to ∼ 0.75 cm−1 , while R increases to about 11.5 Å at linear
arrangements.
A simple model of adding atom-atom Lennard-Jones potentials, with well-depth and equilibrium distance parameters depending on the angular orientation, was found to accurately
reproduce the ab initio points. Using this analytical form, variational calculations [1] at
zero total angular momentum are performed, predicting a single bound level at ∼ −0.106
(∼ −0.042) cm−1 for the boson (fermion) species.
Further calculations using Quantum Monte Carlo methods [2] are carried out and found to
be in good agreement with the variational ones. Based on the present results, we can also
argue that possible modifications of such ultraweak forces could give us further insight on
the role of Efimov states [3,4] in realistic molecular systems.
References
[1] O. Roncero, M. P. de Lara-Castells, G. Delgado-Barrio, P. Villarreal, T. Stoecklin, A.
Voronin and J. C. Rayez, J. Chem. Phys. 128, 164313 (2008).
[2] E. Bodo, E. Coccia, D. Lopez-Duran and F. A. Gianturco, Phys. Scripta 76, C104 (2007).
[3] V. Efimov, Phys. Lett. B 33, 563 (1970).
[4] V. Efimov, Soviet J. Nucl. Phys. 12, 589 (1971).
48
Posters
P05
ATTRACTIVE LATTICE BOSE GAS WITH THREE-BODY
HARDCORE CONSTRAINT
Sebastian Diehl1 , Andrew J. Daley1 , Peter Zoller1 et al.
1
Institute for Quantum Optics and Quantum Information
of the Austrian Academy of Sciences,
Otto-Hittmair-Platz 1, A-6020 Innsbruck, Austria
We discuss how large three-body loss of atoms can give rise to effective hard-core threebody interactions for a system on the optical lattice. In a bosonic system, the hard-core
constraint stabilizes attractive two-body interactions. In this regime, an Ising-type phase
transition separates the conventional atomic superfluid from a dimer superfluid. Increasing
the attraction further, for unit filling the system then approaches a supersolid state. Via
numerical simulations of the many-body dynamics in one-dimensional systems, we identify
schemes to prepare these phases [1]. Further applications are discussed for fermions: In a
three-component attractive Fermi gas, we nd evidence for atomic color superfluidity, which
in a system without hard-core constraint is preempted by trion formation [2].
References
[1] A.J. Daley, J.M. Taylor, S. Diehl, M. Baranov, P. Zoller, Phys. Rev. Lett. 102, 040402
(2009); S. Diehl, A.J. Daley, M. Baranov, P. Zoller, in preparation (2009).
[2] A. Kantian, M. Dalmonte, A.J. Daley, S. Diehl, P. Zoller, in preparation (2009).
49
Posters
P06
FEW-BODY PHYSICS WITH ULTRACOLD Cs
W. Harm1 , M. Berninger1 , A. Zenesini2 , F. Ferlaino1 , H.-C. Nägerl1 ,
R.Grimm1,2
1
Institut für Experimentalphysik and Zentrum für Quantenphysik, Universität Innsbruck,
6020 Innsbruck, Austria
2
The successful production of weakly bound molecules in dilute quantum gases enriched the
link between ultracold physics and few body physics. Besides the production of atomic
and molecular Bose-Einstein Condensates (BEC), ultracold gases can be used to investigate
collisions and chemistry of molecules and the formation of Efimov states. We present our
work on ultracold cesium atoms and molecules confined in an optical dipole trap at temperatures down to 30nK. Due to the heavy mass of 133 Cs, relativistic spin-spin dipole and
second-order spin-orbit interactions lead to a rich internal structure, resulting in a broad
variety of molecular states. Our full control over external and internal degrees of freedom
and the magnetic tunability of the scattering properties enables us to selectively populate
cesium molecules in various s-, d-, g-, and even l-wave states using Feshbach resonances,
while investigations on single atoms, in regions of resonant two-body interactions, have lead
to the first experimental evidence for the existence of Efimov states. Our technical efforts,
to explore further Efimov features and molecular states, are now heading towards regions of
larger tunability of the scattering length at magnetic fields of 550G and 800G, where two
broad Feshbach resonances are theoretically predicted by the NIST model.
50
Posters
P07
THE HETERONUCLEAR EFIMOV EFFECT
K. Helfrich1,2 , H.-W. Hammer1
1
Helmholtz-Institut für Strahlen- und Kernphysik and Bethe-Center for Theoretical
Physics, Universität Bonn, Nussallee 14-16, 53115 Bonn, Germany
2
[email protected]
An effective field theory approach is used to calculate loss rates connected to the Efimov effect
in ultracold heteronuclear quantum gases. We generalize our theory for the homonuclear case
[1] which has already been successfully used to describe recent experiments in ultracold 133 Cs
[2] and 6 Li [3]. Thus, we make it applicable to new experiments conducted, e.g., in Florence
with a mixture of 87 Rb and 41 K [4] and in Tübingen with 87 Rb and 7 Li [5]. We show various
three-body recombination rates in dependence of the scattering length and of the mass ratio
of the involved particles. Besides, we calculate the ratio of scattering lengths for which
Efimov resonances are expected for positive and negative scattering length.
References
[1] E. Braaten and H.-W. Hammer, Phys. Rept. 428, 259 (2006).
[2] T. Kraemer et al. Nature 440, 315 (2006).
[3] T.B. Ottenstein et al. Phys. Rev. Lett. 101, 203202 (2008) and
J.H. Huckans et al. Phys. Rev. Lett. 102, 165302 (2009).
[4] G. Barontini et al. arXiv:0901.4584 [cond-mat.other].
[5] C. Marzok et al. Phys. Rev. A 79, 012717 (2009).
51
Posters
P08
ULTRACOLD THREE-COMPONENT FERMI GASES: GOING
FROM FEW-BODY TO MANY-BODY PHYSICS
Thomas Lompe1 , Timo Ottenstein1 , Friedhelm Serwane1 , Andre Wenz1 ,
Gerhard Zürn1 , Selim Jochim1,2
1
MPI for Nuclear Physics, Saupfercheckweg 1, 69117 Heidelberg, Germany
2
Ruprecht-Karls-Universität, Heidelberg
Ultracold Fermi gases consisting of three distinguishable particles are expected to exhibit
fascinating many-body physics as for example pairing competition and color superfluidity.
The 6 Li system is especially well suited for such experiments, as it allows to prepare a threecomponent Fermi gas where all interparticle scattering lengths can be tuned to large values
simultaneously due to broad and overlapping Feshbach resonances. This should make it
possible to study a system which has a SU(3) symmetry just like colors in QCD, yet has
much simpler and tunable interactions. With the recent success in creating such gases this
physics now seems to be within experimental reach [1]. However, the observation of Efimov
states in this system has also made it clear that one needs a better understanding of the
few-body physics of this system before one can attempt to probe its many-body behavior.
One open question which will need to be adressed is the how the rates of elastic and inelastic
collisions between dimers and a third atom and between two dimers consisting of different
combinations of atoms scale with the scattering lengths. Here we will discuss experimental
approaches to measuring these effects in order to find a regime favorable for studying manybody physics of three-component Fermi gases.
References
[1] T.B. Ottenstein et. al., Phys. Rev. Lett. 101, 203202 (2008).
52
Posters
P09
w-body universality
of Ultracold
Atomic Gases
in the stron
FEW-BODY UNIVERSALITY
OF ULTRACOLD
ATOMIC
GASES IN THE
STRONG INTERACTION
interaction
regime REGIME
1
1,2
1,2
PascalPascal
Naidon
Masahito
Naidon1,, Masahito
UedaUeda
1
1
ERATO Macroscopic Quantum Project, JST Tokyo, 113-8656, Japan
2
ERATO
Macroscopic
Project,
JST Bunkyo-ku
Tokyo, 113-0033,
113-8656,
Department
of Physics, Quantum
University of Tokyo,
7-3-1 Hongo,
JapanJapan
epartment of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku 113-0033, Ja
We consider the Efimov trimer theory as a possible framework to explain losses by inelastic
three-body collisions observed [1,2] in a three-hyperfine-component ultracold mixture of
(fermionic) lithium 6. Our results [3] show that such a trimer state is indeed possible given
theEfimov
two-body trimer
scattering theory
lengths inasthe
lithium mixture,
and giveslosses
rise by inela
consider the
a three-component
possible framework
to explain
to an enhancement of inelastic three-body collisions which is qualitatively consistent with
e-body collisions
observed1,2 in a three-hyperfine-component ultracold mixture
the observed losses. If confirmed, this would be the first instance of an Efimov trimer of
mionic) lithium
6. Our
results5 show that such a trimer state is indeed possible gi
distinguishable
fermions.
two-body scattering lengths in the three-component lithium mixture, and gives
References
n enhancement
of inelastic three-body collisions which is qualitatively consistent w
[1] T. B. Ottenstein et al., Phys. Rev. Lett. 101, 203202 (2008).
observed losses.
If confirmed,
would
the(2009).
first instance of an Efimov trime
[2] J. H. Huckans
et al., Phys. this
Rev. Lett.
102,be
165302
P. Naidon and M. Ueda, arXiv:0811.4086.
nguishable[3]fermions.
53
Posters
P10
EFIMOV PHYSICS OF FERMIONS IN MIXED DIMENSIONS
Yusuke Nishida1
1
Center for Theoretical Physics, Massachusetts Institute of Technology, 77 Massachusetts
Avenue, Cambridge, Massachusetts 02139, USA
The Efimov effect in ultracold atoms has been observed in Bose gases, Bose-Bose mixtures,
and three-component Fermi gases. However, the Efimov effect in Fermi-Fermi mixtures
has not been observed so far because a large mass ratio ¿ 13.6 is needed to overcome the
centrifugal barrier. Therefore it has been considered that the currently available Fermi-Fermi
mixture of 40 K and 6 Li can not be used to create a novel type of Efimov trimers involving
two identical fermions. In this presentation, I will show that the above critical mass ratio
can be decreased to 6.35 or 2.06 by confining only heavier atoms in 2D or 1D and thus the
40
K-6 Li mixture indeed exhibits the Efimov effect when 40 K is confined in 1D with keeping
6
Li in 3D [1]. The three-body recombination rate in such a system in the dilute limit has
a characteristic log-periodic dependence on the effective scattering length with the scaling
factor 22.0[2]. Therefore the ultracold mixture of 40 K and 6 Li in the 1D-3D mixed dimensions
is a promising candidate to observe the Efimov physics for the first time in fermions. The
idea of mixed dimensions in Fermi-Fermi mixtures also offers the novel possibility of creating
a gas of stable trimers. When one species (A atoms) is confined in a multilayer geometry
by an optical lattice and resonantly interacts with the other species (B atoms) in 3D, two
A atoms confined in different layers and one B atom always form an Efimov-like three-body
bound state[3]. In contrast to Efimov trimers in a free space, such trimers are stable against
the three-body recombination because two A atoms are spatially separated. The trimer gas
phase will appear as a ground state of the system when the layer separation is smaller than
the effective scattering length and the mean interparticle distance of the system. Finally,
from the renormalization group analysis and finding the limit cycle behavior, I will point it
out that resonantly interacting anyons in 2D can exhibit the Efimov-like geometric spectrum
in its four-body sector when the statistics is close to fermion[4]. This is in contrast to bosons
that never exhibits the Efimov effect in 2D.
References
[1] Y. Nishida and S. Tan, Phys. Rev. Lett. 101, 170401, (2008).
[2] Y. Nishida and S. Tan, Phys. Rev. A 79, 060701(R) (2009).
[3] Y. Nishida, arXiv:0906.4584.
[4] Y. Nishida, Phys. Rev. D 77, 061703 (2008).
54
Posters
P11
SPATIAL FEATURES AND ENERGETICS OF ULTRA
WEAKLY INTERACTING THREE-PARTICLE SYSTEMS:
DO THEY HOLD EFIMOV STATES?
S. Orlandini1,2 , I. Baccarelli1 , F. A. Gianturco2
1
CASPUR, Consortium for Supercomputing in Research,
Via dei Tizii 6, 00185 Rome, Italy
2
Chemistry Department, University of Rome ‘Sapienza’,
P.le A. Moro 5, 00185 Rome, Italy
A variational method based on the use of bond coordinates and of a basis set expansion
described by distributed Gaussian functions (DGF) [1] is reviewed in its most recent implementation [2]. The method takes advantage of the Jacobi-Davidson filtering procedure
[2] to better apply to the study of ultra weakly bound triatomic clusters. The theoretical
and computational study of these systems constitute indeed a very challenging task and, in
its current implementation, the present method has been shown to be a reliable and robust
procedure for characterizing very diffuse states [2-5]. A particularly interesting capability
of the DGF method is given by its natural ability to describe the spatial features of these
unusual systems by means of several statistical properties such as radial distributions, sizes
and dominance of triangular configurations for the corresponding bound states [1].
The method also allows us to look for the possible existence of Efimov or Halo states by the
analysis of the changes in the energetics of the trimers and their subsystems as a consequence
of potential-tuning [4].
A selection of representative results obtained in the past will be presented and discussed into
details together with our preliminary results on the 4 He72 Li system.
References
[1] T. González-Lezana, et al., Comput. Phys.
al., Phys. Rep. 452, 1 (2007).
[5] S. Orlandini, et al., in preparation.
Comm. 145, 156 (2002) and I. Baccarelli, et
Comp. Phys. Comm. 180, 384 (2009).
J. Chem. Phys. 125, 234307 (2006).
Mol. Phys. 106, 573 (2008).
55
Posters
P12
COLD AND ULTRACOLD QUENCHING QUANTUM
DYNAMICS FOR MOLECULAR ANIONS
Mario Tacconi1 , Franco A. Gianturco2 , David Lopéz-Durán3
1,2
Dept. of Chemistry, University of Rome Sapienza, P.le Aldo Moro 5, Rome, 00185, Italy
3
Instituto de Fı́sica Fundamental, C.S.I.C., Serrano 123, Madrid, 28006, Spain.
Aim of the present work is to use the predictive power of the modern ab initio and the
full quantum dynamic computational techniques to investigate the efficiency of the cooling
of molecular systems by thermal contact with a cold or ultracold heavy alkali atoms gas,
namely Rb or cold Helium buffer gas. Recently, we have focused our attention on two anionic
molecular system: OH− (X1 Σ+ ) [1,2] and LiH− (X2 Σ+ ) [3] interacting with Rb(2 S) and He
respectively. An anion basically can offer a variety of advantages over the neutral counter
part. Among the others: (i) an ion can be trapped
localization (Coulomb Crystal) of the ions can be obtained; (iii) the presence of an extra
electron on the molecular target can mitigate the probability of unwanted charge exchange
processes in which an electron is transfered from the Alkali atom to the diatomic molecule
[1,2]. In order to give a quantitative description of the collisional quantum dynamics, we
have computed the potential energy surfaces (PES) for the electronic ground states of the
LiH− -He and OH− -Rb anionic complexes [1-3] at the CCSD(T) [4] level of theory by using
large (up to the quintuple zeta) gaussian basis sets. For the Rb atom the Effective Core
Potential ECP28MDF along with the companion basis set [8s7p5d3f] has been used [5] .
Analytical representation of the ab initio PESs have obtained and then have been used to
evaluate the scattering observables within the Coupled Channel framework as implemented
in our inelastic scattering code ASPIN [6]. In the particular case of OH− (X1 Σ+ )-Rb both
rotational [1] and vibrational [2] quenching dynamics have been studied in details in the
ultralow collisional energy regime. In the case of LiH− (X2 Σ+ )-He we have focused on the
rotational quenching dynamics and on the role played by the fine structure of the rotaional
levels [3].
References
[1] L. Gonzalez-Sanchez, M. Tacconi, E. Bodo, F.A. Gianturco, Eur. Phys. J. D, 49, 85
(2008).
[2] M. Tacconi, F.A. Gianturco, J. Phys. Chem, in press, (2009).
[3] D. Lopéz-Durán, M. Tacconi, F.A. Gianturco, Eur. Phys. J. D, submitted, (2009).
[4] C. Hampel, K. Peterson, and H.-J. Werner, Chem. Phys. Lett. 190, 1 (1992).
[5] I.S. Lim, P. Schwerdtfeger, B. Metz, H. Stoll, J. Chem. Phys. 122, 104103 (2005).
[6] D. Lopéz-Durán, E. Bodo, F.A. Gianturco, Comput. Phys. Comm. 179, 821 (2008).
56
Posters
P13
THE DEPENDENCE OF POTENTIAL ENERGY SURFACE IN
THE STUDIES OF SILVER TETRAMER FORMATION
Lichang Wang1 , Zhe Xu2 , Jianbo Li1 , Susan Lu2
1
2
Department of Chemistry and Biochemistry, Southern Illinois University, Carbondale, IL
62901, U. S. A.
Department of Systems Science and Industrial Engineering, State University of New York
at Binghamton, Binghamton, NY13902, U. S. A.
One of the most important areas in computational chemistry is to unravel the formation
mechanism of transition metal clusters and nanoparticles using dynamics simulations. To
acheive an accurate description of the formation process, one needs to examine the dependence of the formation mechanism on the potential energy surface (PES) that is employed
in the dynamics simulations. Here, we studied the formation of silver tetramers from two
silver dimers as an example to investigate such a PES dependence using three PESs: the
bulk Sutton-Chen potential [1], the cluster Sutton-Chen potential [2,3], and the artificial
neural network potential [4]. We will present the results on the PES dependence of final
products, namely structures of tetramer and rovibrational states of dimers after nonreactive
scattering.
References
[1] A. P. Sutton, J. Chen, Philos. Mag. Lett. 64, 139 (1990).
[2] T. Pawluk, L. Xiao, J. Yukna, L. Wang, J. Chem. Theory Comput. 3, 328 (2007).
[3] J. Yukna, L. Wang, J. Phys. Chem. C 111, 13337 (2007).
[4] Z. Xu, X. Shi, J. Li, S. Lu, L. Wang, IEEE Proceeding of the 5th International Conference
on Nature Computing (in press, 2009).
57
Posters
P14
OBSERVATION OF AN EFIMOV SPECTRUM IN AN
ATOMIC SYSTEM
M. Zaccanti1 , B. Deissler1 , C. D’ Errico1 M. Fattori1,2 , M. Jona-Lasinio1
S. Müller3, G. Roati1 M. Inguscio1 , and G. Modugno1
1
LENS and Physics Department,Universitá di Firenze, and
INFM-CNR, Via Nello Carrara 1, 50019 Sesto Fiorentino, Italy
2
Museo Storico della Fisica e Centro Studi e Ricerche E. Fermi, Roma, Italy
3
Physikalisches Institut, Universität Stuttgart, 70550 Stuttgart, Germany
In 1970 the Russian physicist V. Efimov predicted a puzzling quantum-mechanical effect that
is still of great interest today. He found that three particles subjected to a resonant pairwise
interaction can join into an infinite number of loosely bound states even though each particle
pair cannot bind. Interestingly, the properties of these aggregates, such as the peculiar
geometric scaling of their energy spectrum, are universal, i.e. independent of the microscopic
details of their components. Despite an extensive search in many different physical systems,
including nuclei, atoms and molecules, Efimov spectra still elude observation. Here we report
on the discovery of two bound trimer states of potassium atoms very close to the Efimov
scenario, which we reveal by studying three-particle collisions in an ultracold gas with tunable
interaction. Our observation provides the first evidence of an Efimov spectrum and allows a
direct test of its scaling behaviour, shedding new light onto the physics of few-body universal
systems.
58
Partecipants
59
Alexander Alijah
[email protected]
Departamento de Fı́sica, Universidade Federal de Minas Gerais, Belo Horizonte, Brazil
Isabella Baccarelli
[email protected]
CASPUR, Rome, Italy
Martin Berninger
[email protected]
Institute for Experimental Physics and Centrum for Quantum Physics, University of Innsbruck,
Innsbruck, Austria
Stefano Bovino
[email protected]
Department of Chemistry, University of Rome ”Sapienza“, Rome, Italy
Domenico Caruso
[email protected]
Cheng Chin
[email protected]
James Franck Institute and Department of Physics, University of Chicago, Chicago, IL
Emanuele Coccia
[email protected]
Gerardo Delgado-Barrio
[email protected]
Instituto de Fisica Fundamental, CSIC, Madrid, Spain
Sebastian Diehl
[email protected]
IQOQI, Austrian Academy of Sciences, Innsbruck, Austria
José P. D’Incao
[email protected]
Department of Physics and JILA - NIST , University of Colorado, Boulder, CO
Vitaly Efimov
[email protected]
Department of Physics, University of Washington, Seattle, WA
Brett D. Esry
[email protected]
Department of Physics, Kansas State University, Manhattan, KA
Dario De Fazio
[email protected]
IMIP CNR, Rome, Italy
Francesca Ferlaino
[email protected]
Institute for Experimental Physics, University of Innsbruck, Innsbruck, Austria
61
Franco A. Gianturco
[email protected]
Tomás González-Lezana
[email protected]
Instituto de Fı́sica Fundamental, CSIC, Madrid, Spain
Chris H. Greene
[email protected]
Department of Physics and JILA, University of Colorado, Boulder, CO
Rudolf Grimm
[email protected]
IQOQI - Institute for Experimental Physics, University of Innsbruck and Austrian Academy of
Sciences, Innsbruck, Austria
Hans-Werner Hammer
[email protected]
Helmholtz-Institut für Strahlen und Kernphysik (Theorie) and Bethe Center for Theoretical
Physics, Universität Bonn, Bonn, Germany
Walter Harm
[email protected]
Institute for Experimental Physics and Centrum for Quantum Physics, University of Innsbruck,
Innsbruck, Austria
Kerstin Helfrich
[email protected]
Helmholtz-Institut für Strahlen und Kernphysik and Bethe-Center for Theoretical Physics, Universität Bonn, Bonn, Germany
Randall G. Hulet
[email protected]
Dept. of Physics and Astronomy, and Rice Quantum Institute, Rice University, Houston, TX
M. Inguscio
LENS and Physics Department, Università di Firenze and INFM-CNR, Sesto Fiorentino, Italy
Aksel S. Jensen
[email protected]
Departement of Physics and Astronomy, Aarhus University, Aarhus, Denmark
Selim Jochim
[email protected]
Max-Planck-Institute for Nuclear Physics, Heidelberg, Germany
Mattia Jona-Lasinio
[email protected]
LENS and Department of Physics, University of Florence - INFM-CNR, Sesto Fiorentino, Italy
Lev Khaykovich
[email protected]
Department of Physics, Bar-Ilan University, Ramat-Gan, Israel
Alejandro Kievsky
[email protected]
Istituto Nazionale di Fisica Nucleare, Pisa, Italy
62
Steven Knoop
[email protected]
Kirchhoff-Institut für Physik, University of Heidelberg, Heidelberg, Germany
Elena A. Kolganova
[email protected]
Joint Institute for Nuclear Research, Dubna, Russia
Thomas Lompe
[email protected]
Max-Planck-Institute for Nuclear Physics, Heidelberg, Germany
Pietro Massignan
[email protected]
ICFO - Institut de Ciències Fotòniques, Barcelona, Spain
Francesco Minardi
[email protected]
LENS and CNR-INFM, Università di Firenze, Sesto Fiorentino, Italy
Salvador Miret-Artés
[email protected]
Giovanni Modugno
[email protected]
LENS, Università di Firenze, Sesto Fiorentino, Italy
Pascal Naidon
[email protected]
ERATO Macroscopic Quantum Project, JST Tokyo, Tokyo, Japan
Yusuke Nishida
[email protected]
Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA
Ken M. O’Hara
[email protected]
Department of Physics, The Pennsylvania State University, Philadelphia, PA
Sergio Orlandini
[email protected]
CASPUR - Department of Chemistry, University of Rome ”Sapienza“, Rome, Italy
Dmitry S. Petrov
[email protected]
CNRS and LPTMS, Université Paris Sud, Orsay, France
Lucas Platter
[email protected]
Institute for Nuclear Theory, University of Washington, Seattle, WA
Jean-Marc Richard
[email protected]
LPSC, IN2P3-CNRS, Université Joseph Fourier, Grenoble, France
Seth T. Rittenhouse
[email protected]
ITAMP, Harvar-Smithsonian Center for Astrophysics, Cambridge, MA
63
Hossein Sadeghpour
[email protected]
ITAMP, Harvar-Smithsonian Center for Astrophysics, Cambridge, MA
Mario Tacconi
[email protected]
Pablo Villarreal
[email protected]
Javier von Stecher
[email protected]
JILA and Department of Physics, University of Colorado, Boulder, CO
Lichang Wang
[email protected]
Department of Chemistry and Biochemistry, Southern Illinois University, Carbondale, IL
Félix Werner
[email protected]
Departement of Physics, University of Massachusetts, Amherst, MA
Matteo Zaccanti
[email protected]
LENS and Physics Department, Università di Firenze and INFM-CNR, Sesto Fiorentino, Italy
Alessandro Zenesini
[email protected]
IQOQI, Austrian Academy of Sciences, Innsbruck, Austria
64
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