Cold Molecules: Why? How? And Next?...•B. K. Stuhl, M. T. Hummon and J. Ye, Cold State‐Selected...
Transcript of Cold Molecules: Why? How? And Next?...•B. K. Stuhl, M. T. Hummon and J. Ye, Cold State‐Selected...
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Cold Molecules: Why? How? And Next?Modeling routes for their formation
Olivier Dulieu
Laboratoire Aimé Cotton, CNRS/ Université Paris‐Sud/ ENS Cachan Orsay, France
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Laboratoire Aimé Cotton in Orsay
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Staff:Nadia Bouloufa, Olivier Dulieu, Maxence Lepers , Goulven Quéméner, Maurice Raoult, Jacques RobertPhD:Dimitri Borsalino, Humberto daSilva JrPostdocs:Maykel Gonzalez-Martinez, Andrea Orban, Romain VexiauEmeritus:Anne Crubellier , Eliane Luc, Jean-François WyartThey left the group in 2013-2014:Mireille Aymar, Jesus Perez-Rios, GaorenWang
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ONGOING [email protected]
Structure of lanthanides (Er, Dy,…)and of small molecules
(A‐Sr), (A‐Sr) +, Rb‐(Ca+, Ba+, Yb+)…
Structure and dynamics of cold atoms
and molecules
Formation/ production of cold molecules
Long‐range interactions between atoms and
molecules
Dynamics of ultracold gases in external fieldsDynamics of cold
molecular ions
Collisional processes in the interstellar medium
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WHY?
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Adapted from Ye’s group; http://jila.colorado.edu/yelabs/research/ultracold‐molecules
Cold molecules
Translational kinetic energy
with high internal energy
BUT
Ultracold Chemistry?
How cold …?Looking at collision processes over
of kinetic energy/temperature
Ultracold molecules
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Cold Matter: Atoms, Ions, Molecules, Plasmas…almost 0 <T<<1K
• One of the main research topic in AMO physics for many years: full control of aquantum system at the single quantum level
• Connected to many areas: statistical physics, condensedmatter, optics, metrology,…• Boosted by the amazing success of laser cooling and evaporative cooling
Nowadays applied to many atomic species: Alkalis, alkaline‐earth, rare gas, lanthanides,…
Molecules are attractive for cold matter:•Additional degrees of freedom, offering new opportunities for manipulation and control• Pair of weakly interacting atoms for unprecedented precisionmeasurements•Reactivity and chemical reactions dominated by quantum effects (resonances, tunneling,...)•Ongoing efforts to create dense ensembles of cold molecules•Strong interplay between experiment and theory
•But direct laser cooling almost impossible!
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A brief guide to cold molecule formation methods…
• Assemble ultracold atoms: > >Ions welcome!
– Photoassociation > >Radiative association– Magnetoassociation > >
• Create stable molecules in (a single) excited level• Transfer to the absolute ground state: adiabatic transfer (STIRAP), shaped laser pulses,…
OR• Slow down preformedmolecules with external time varying electric or magnetic fields
through their intrinsic dipole moments, or via collisions with a buffer gasOR
• Let atoms stick together on/in helium nanodropletsOR
• Laser‐cool species with suitable properties (SrF, YO,…) >CaH+…OR…
T<<1mK
T>1mK
T~1K
T~1mK
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(mostly diatomics…)
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9
Cold Molecules: a hot topic indeed!
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Vol. 31, 2004Vol 392006
495 références!
Vol 11, 2009
Vol. 65, 2011
Vol. 13, 2011 Vol 1122011
Upcoming NJP issue in 2015…
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• J. Weiner, Experiments in cold and ultracold collisions, J. Opt. Soc. Am. B 6, 2270 (1989)• P. S. Julienne and F. H. Mies, Collisions of ultracold trapped atoms, J. Opt. Soc. Am. B 6, 2257 (1989)• P. D. Lett; P. S. Julienne, and W. D. Phillips, Photoassociative spectroscopy of laser cooled atoms, Ann. Rev. Phys. Chem., 46, 423 (1995).• P. S. Julienne, Cold Binary Atomic Collisions in a Light Field, J. Res. Natl. Inst. Stand. Technol. 101, 487 (1996)• J. Weiner, V. S. Bagnato, S. Zilio and P. S. Julienne, Experiments and theory in cold and ultracold collisions, Rev. Mod. Phys. 71, 1 (1999)• E. Timmermans, P. Tommasini, M. Hussein, and A. Kerman, Feshbach resonances in atomic Bose‐Einstein condensates, Phys. Reports 315, 199 (1999)• W. C. Stwalley and H. Wang, Photoassociation of ultracold atoms: a new spectroscopic technique, J. Molec. Spectrosc. 195, 194 (1999)• F. Masnou‐Seeuws and P. Pillet, Formation of ultracold molecules (T ≤ 200 μK) via photoassociation in a gas of laser‐cooled atoms, Adv. At. Mol. Opt.
Phys., 47, 53 (2001).• K. Burnett, P. S. Julienne, P. D. Lett, E. Tiesinga, and C. J. Williams, Quantum encounters of the cold kind, Nature, 416, 225 (2002)• O. Dulieu and F. Masnou‐Seeuws, Formation of ultracold molecules by photoassociation: theoretical developments, J. Opt. Soc. Am. B 20, 1083 (2003)• H. Bethlem and G. Meijer, Production and applications of translationally cold molecules, Int. J. Phys. Chem. 22, 73 (2003)• C. Chin, The Birth of Ultracold Molecules into the World of Quantum Gases, AAPS Bulletin 14, 14 (2004)• R. Krems, Molecules near absolute zero and external field control of atomic and molecular dynamics, Int. J. Phys. Chem. 24, 99 (2005)• M. Leduc and J. Vigué, Interplay between theoretical quantum chemistry and cold atom experiments, Theor, Chem, Acc. 116, 598 (2006) • B. Friedrich and G. Meijer, Molecules riding waves, Nature Phys. 2, 437 (2006)• K. Jones, E. Tiesinga, P. D. Lett, and P. S. Julienne, Ultracold photoassociation spectroscopy: Long‐range molecules and atomic scattering, Rev. Mod. Phys.
78, 483 (2006)• T. Köhler, K. Goral, and P. S. Julienne, Production of cold molecules via magnetically tunable Feshbach resonances, Rev. Mod. Phys. 78, 1311 (2006)• J. M. Hutson and P. Soldan, Molecule formation in ultracold atomic gases, Int. J. Phys. Chem. 25, 497 (2006)• E. Bodo and F. Gianturco, , Int. J. Phys. Chem. Collisional quenching of molecular ro‐vibrational energy by He buffer loading at ultralow energies, Int. J.
Phys. Chem. 25, 313 (2006)• P. F. Weck and N. Balakrishnan, Importance of long‐range interactions in chemical reactions at cold and ultracold temperatures, Int. J. Phys. Chem. 25, 283
(2006)• J. M. Hutson and P. Soldan, Molecular collisions in ultracold atomic gases, Int. J. Phys. Chem. 26, 1 (2007)• R. Krems,Cold controlled chemistry, Phys. Chem. Chem. Phys. 10, 4079 (2008)• I. Bloch, J. Dalibard, W. Zwerger, Many‐body physics with ultracold gases, Rev. Mod. Phys. 80, 885 (2008)• M. Bell and T. Softley, Ultracold molecules and ultracold chemistry, Mol. Phys. 107, 99 (2009)• O. Dulieu and C. Gabbanini, The formation and interactions of cold and ultracold molecules: new challenges for interdisciplinary physics, Rep. Prog. Phys.
72, 086401 (2009)• D. Chandler, Spotlight on orbiting resonances, J. Chem. Phys. 132, 110901 (2010)• C. Chin, R. Grimm, E. Tiesinga, and P. S. Julienne, Feshbach resonances in ultracold gases, Rev. Mod. Phys. 82, 1225 (2012)• D. Blume, Few‐body physics with ultracold atomic and molecular systems in traps, Rep. Prog. Phys. 75, 046401 (2012)• S. Willitsch, Coulomb‐crystallised molecular ions in traps: methods, applications, prospects, Int. J. Phys. Chem. (2012)• B. K. Stuhl, M. T. Hummon and J. Ye, Cold State‐Selected Molecular Collisions and Reactions, Ann. Rev. Phys. Chem. 65, 501 (2014)• …
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Outline
• (brief) Overview of methods and tools to describe an ultracold molecule
• Formation of ultracold ground state molecules via STIRAP
• Formation of ultracold molecular ions in merged atom/ion traps
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HOW…to describe a molecule
?
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10 20 30interatomic distance (a
0)
-6000
-4000
-2000
0
ener
gy (c
m-1
) RbCs
KCs
NaCs
LiCs
ns+n’s
1Σ+
3Σ+
10 20 30interatomic distance (a
0)
-8000
-6000
-4000
-2000
0
ener
gy (c
m-1
)
RbCs (5s+6p)
KCs (4s+6p)
LiCs (2s+6p)
NaCs (3s+6p)
ns+6p
3Π
1Σ+
66
RC
33R
C
Ground state
Excited state
)(RDge
E
)(RD
Chemical bond
A diatomic molecule is…
or
66
RC
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The Born‐Oppenheimer approximation
Vm
Hn
iiR
1
22
22
22
Relative motion of the nuclei
Electronic Hamiltonian
2
22
2
22
2
222 RO
RR
RRR
2
2
2
2
22
2 RJLL
RJ
HeHv
Coriolis Rotation
);()();( RrRURrH iie
Total wave function
);()()()(iBO rRR
Adiabatic Potential Energy Curves:R: Separated atoms
Molecular symmetriesHund’s cases
,,,,,:12 SpS
,: p
,...,,,,,,, 53311312 gugugugg
,...1,1,0,0,0,0 uguugg
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Calculation of potential energy curves in the « chemical range »A tough many‐body problem! A scientific area in itself: Quantum Chemistry
Ex: Cs2: 2 nuclei and 110 electrons!
In the case of alkali atoms and alkaline‐earth atomic ions, a great simplification can be made: Atom/Ion treated asan effective one‐electron system: Use of ECP’s (Effective core potentials or pseudopotentials) with ℓ–dependentCPP’s (core‐polarization potentials) fitted on atomic energy spectra of the one‐electron system
[ECP+CPP+1e‐]+[ECP’+CPP’+1e‐]: exact energy at R=∞
Typical steps are (in an oversimplified way):
Choose a set of basis functions appropriate for numerical calculations: Gaussian orbitals
Determine one‐electron molecular orbitals through a self‐consistent field approach (Hartree‐Fock): describes themotion of one electron in the field of the cores and of the other electrons
Set up a configuration space with antisymmetrized spin‐orbital wave functions built on the HF orbitals
Diagonalize the Hamiltonian (Full Configuration Interaction (FCI)) to determine the structure of the dimer,considered as an effective two/three‐electron polarizable system
Convergence and accuracy checked against size of basis sets, and through detailed comparison with othermethods
Potential energy curves, permanent and transition dipole moments, static and dynamic dipole polarizabilities,…
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Calculation of potential energy curves in the « asymptotic range »
A well‐known “electrostatic” problem!
In a cold atom gas, the kinetic energy of the atoms is much smaller than any other characteristic energy(electronic, vibrational, rotational…), thus they feel each other at very large distances, well beyond the range ofchemical interaction (exchange forces)
Vo overlap between the electronic wave functions of each atom
Potential energy determined by atomic properties
Multipolar expansion of the electrostatic interaction:
Interaction of two charge distributions at large distances
Calculation of potential energy curves in the asymptotic range
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0,1
041
BABA
BA
LLLL
LLel R
VV
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1. Electrostatic potential generated by A in a remote point O’
2. Potential energy felt by B due to the slowly‐varying field created by A
3. Potential energy between A and BO
qi
R
ir
A O’
qj
jrB
Z
Rrr ji ,
(LA,LB) : rank of multipolar moments of A et B• (0,0) : charge‐charge interaction 1/R• (1,0) : dipole‐charge interaction 1/R²• (1,1) : dipole‐dipole interaction 1/R3
• (0,2) : charge‐quadrupole interaction 1/R3 …
MULTIPOLAR EXPANSION
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BALL
ML
ML
L
LMLL
MLLel LLL
Rf
VBA
BABA
BA ;min with QQ4
10,
10
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• 1st order : permanent multipoles
Ex : 2 neutral non‐S atoms => dominant term = Vqq ~ 1/R5
Ex : 2 neutral S atoms => p1 = 0
• 2nd order : induced multipoles
Ex : dipolar interaction = Vdd ~ 1/R6 (van der Waals)(2)
0,1
0
001 Q̂Q̂4
1ˆBA
BABA
BA
LLB
MLBA
MLA
L
LMLL
MLLpelpp R
fV
BbAa
baelBA
BAbap EEEE
V
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),(),(
2ˆ
0,
10
Q̂Q̂4
1ˆBA
BABA
BA
LL
ML
ML
L
LMLL
MLLel R
fV
MULTIPOLAR EXPANSION
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Example: structure of alkali dimers
Na2
Adapted from Jones et al,RMP 2006, Weiner et al, RMP 1999
Observation of Pure Long‐Range MoleculesPredicted by Uang et al, PRL 1978
Hyperfine structure
Fine structure
Aldegunde et al PRA 79, 013401 (2009)
Rb2, v=0
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Features of the radial motion
From J. M. Hutson, Theory of atomic and molecular collisions, in Cold Molecules: Theory, Experiment, Applications, CRC Press, 2009
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Scattering length
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HOW…to create a cold molecule
?
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Laser Cooling of Molecules…not so cool!
« ground‐breaking » idea: photoassociation of cold atoms…
F=3
F=4
23
45
Cs Cs2
v
v’
A novel scheme is proposed for sequential cooling of rotation, translation, andvibration of molecules. More generally, this scheme manipulates and controls thestates and energies of molecules. The scheme, while somewhat complex, is simplerand more feasible than simply providing a large number of synchronously butindependently tunable lasers. The key component is a multiple single frequency laserin which a single narrow band pump laser generates an ensemble of resonant‘‘stimulated Raman’’ sidebands subsequently amplified and selected in a sample ofthe molecules to be cooled….Only this specific order of rotation–translation–vibration appears feasible (using molecules produced by photoassociation of ultracoldatoms avoids the requirement for translational cooling). Each step employs truedissipative cooling … by spontaneous emission and should yield a largetranslationally cold sample of molecules in the lowest v=0, J=0 level of the groundelectronic state…
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Photoassociation of cold atoms+radiative stabilization
0 50 100 150 200R (a.u.)
−5000
0
5000
10000
15000
Ener
gy
hν
s+s
s+p
0 50 100 150 200R (a.u.)
−5000
0
5000
10000
15000
Ener
gy
s+s
s+p
0 50 100 150 200R (a.u.)
−5000
0
5000
10000
15000
En
erg
y
hν
s+s
s+p
First obersvations of ultracold moleculesCs2: Orsay, PRL, 80, 4402 (1998);Rb2: Pisa, PRL, 84, 2814 (2000)…
to produce (deeply‐bound) ultracold molecules
Collision froide
Photo-association
Formation d’une molécule Froide et stable
Désexcitation
Dissociation
Photon 1
Photon 2
Photon 2’
Seminal papers on cold atom PA:Thorsheim, H.R., Weiner, J., and Julienne, P.S., Laser‐induced photoassociation of ultracold sodium atoms, Phys. Rev. Lett., 58, 2420, 1987.Lett, P.D., Helmerson, K., Phillips, W.D., Ratliff, L.P., Rolston, S.L., and Wagshul, M.E., Spectroscopy of Na2 by photo‐association of laser‐cooled Na, Phys. Rev. Lett., 71, 2200, 1993.Miller, J.D., Cline, R.A., and Heinzen, D.J., Photoassociation spectrum of ultracold Rb atoms, Phys. Rev. Lett., 71, 2204, 1993.
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transfer density of probability inwards…
But not selective in the final states…
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Cold molecule formation: Feshbach resonances, Magnetoassociation
•Atoms with electronic AND nuclear magnetic moments (alkalis, lanthanides,…)•First pointed out by Stwalley (PRL 37, 1628, 1976) and Tiesinga et al (PRA 47, 4147, 1993)•The magnetic moment of a molecular complex and of an atom pair are different, so that their energy vary differently with magnetic field•= Change of the dissociation energy of a high‐lying molecular bound state• Very powerful method for creating (weakly‐bound) ultracold molecules!
From www.uibk.ac.at Chin et al, RMP 2012
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Cold molecule formation: energy relaxation toward the absolute ground level
STIRAP : STImulated Raman Adiabatic Passage (Bergman 1990)
Determine the most efficient STIRAP scheme in order to create ultracold molecules in their absolute ground state
Efficiency: strongly depends on the detailed characteristics of the system AND of the lasers available in the lab
Achieved in a optical lattice to avoid atomic and molecular collisions
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Full modeling of STIRAP in KRb
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PRA 90, 033413 (2014)
See experiments by J. Ye and D. Jin at JILA
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Full modeling of STIRAP in KRb
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PRA 90, 033413 (2014)
Assuming pump = dump
Ipump = Idump
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Full modeling of STIRAP in KRb
Thé m l
PRA 90, 033413 (2014)
Assuming pump = dump
Ipump = Idump
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Full modeling of STIRAP in KCs
Thé m l
New J. Phys 2015 (in press)
Assuming pump = dump
Ipump = Idump
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Full modeling of STIRAP in KCs
Thé m l
New J. Phys 2015 (in press)
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R. Vexiau, N. Bouloufa, M.Aymar, J. G. Danzl, M. J. Mark, H.‐C. Nägerl, and O. Dulieu , Eur. Phys. J. D, special issue on Cold Molecules, 65, 243 (2011)
Off‐resonant regime: smooth variation
Resonant regime
Suppression of resonantregime due to unfavorable FC
Cs2 v=0 of the ground stateKnowledge of molecular data
Strongly resonant patterns
isotropic dynamical polarizabilities in real frequency
Optical trapping of ultracold molecules
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Magic wavelengths for atom and molecule trapping
ULM & LAC, NJP, special issue on Cold Molecules,(2015)
Rb2 v=0 of the lowest triplet state
Cs2 v=0 of the ground stateR. Vexiau, et al , Eur. Phys. J. D, 65, 243 (2011)
Identical trapping conditions (same polarizability) for initial and final statesGood matching of the motional states in the lattice
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And NEXT…?
Thé m l
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Merging laser‐cooled atoms and ions: hybrid traps
Cold Rb trap
Ion cristal
Resonant‐excitation mass spectrometryDrewsen et al PRL 93, 240201 (2014)
Ca+
fluor
esce
nce
The hybrid trap at University of Basel (Willlitsch’ group)
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Cold molecular ion formation by radiative association
H. Da Silva Jr, M. Aymar, M. Raoult, O. Dulieu, New J. Phys., in press (2015)
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Cold molecular ion formation by radiative association
H. Da Silva Jr, M. Aymar, M. Raoult, O. Dulieu, New J. Phys., in press (2015)
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Cold molecular ion formation by radiative association
H. Da Silva Jr, M. Aymar, M. Raoult, O. Dulieu, New J. Phys., in press (2015)
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Strongly (polar) magnetic molecules made of Erbium
arXiv:1504.04578
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Merci, Thank you
COLUM2012 Nov. 18-23
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Anistropic effect in collisions of ultracold polar molecules
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Full quantum treatment of atom‐molecule collisions…
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Laser‐cooling of molecules…finally!
YO molecule
SrF molecule
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Molecules and ultracold matter« The field of cold and ultracold molecules has recently witnessed a number of spectacular advancesreliant upon the high quality of our knowledge of molecular structure at a very fundamental level.This lecture will illustrate this premise, highlighting the characteristics of molecules that we all careabout. »
Phase space density
binding energy (Hz)
10-6
106
109
1012
X(0,0) molecules
QUANT.
DEGEN.
Atomic properties
Molecular dynamics
Cold Chemistry
Thé m l
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Scattering length: a crucial parameter for cold collisions
Scattering amplitude in elastic collisions
Asymptotic wave function:
Elastic cross section
Scattering length Cold collisions
The dynamics is fully determined by a global parameter for the interaction: a
This has important consequences for achievement of quantum degeneracy of ultracold gases