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Understanding Feshbach molecules

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Joint Quantum Institute, NIST and The University of Maryland ... J. K. Freericks (Georgetown U.), M. Maska (U. Silesia), R. Lemanski (Wroclaw) Outline ... – PowerPoint PPT presentation

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Title: Understanding Feshbach molecules


1
EuroQUAM satellite meeting, University of Durham,
April 18, 2009
Understanding Feshbach molecules with long range
quantum defect theory Paul S. Julienne Joint
Quantum Institute, NIST and The University of
Maryland
Collaborators (theory) Tom Hanna, Eite Tiesinga
(NIST) Thanks also to Bo Gao (U. of Toledo) and
Cheng Chin (U. Chicago) J. K. Freericks
(Georgetown U.), M. Maska (U. Silesia), R.
Lemanski (Wroclaw)
2
Outline
  • Sone general considerations

2. The significance of the long-range
potential 0812.1486, Feshbach review
0902.1727, Book chapter 0903.0884, MQDT
treatment LiK, KRb
3. Long-range potential quantum defect theory
for atom-atom collisions Can we get simple,
practical models?
3
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4
Ultracold polar molecules are now with us
1. Atom preparation
100 kHz
100 THz
5
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7
Resonance scattering S-matrix theory of molecular
collisions
F. H. Mies, J. Chem. Phys. 51, 787, 798 (1969)
8
Bound states from van der Waals theory
9
Spectrum of van der Waals potential
40K87Rb
Blue lines a 8
Adapted from Fig. 8 Chin, Grimm,
Julienne, Tiesinga, Feshbach Resonances in
Ultracold Gases, submitted to Rev. Mod.
Phys. arXiv0813.1496
10
-10.56 GHz
-3.17 GHz
-0.41 GHz
11
-3.17 GHz
-3.00 GHz
12
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13
Goal Simple, reliable model for classification
and calculation
Now Full quantum dynamics with CC
calculations All degrees of freedom with real
potentials Exact, but not simple
  • vdW-MQDT Reduction to a simpler representation
  • Parameterized by
  • C6 van der Waals coefficient
  • ? reduced mass
  • abg background scattering length
  • resonance width
  • B0 singularity in a(B)
  • ??????magnetic moment difference

14
Analytic properties of ?(R,E) across thresholds
(E) and between short and long range (R)
Generalized Multichannel Quantum Defect Theory
(MQDT) F. H. Mies, J. Chem. Phys. 80, 2514
(1984) F. H. Mies and P. S. Julienne, J. Chem.
Phys. 80, 2526 (1984) Ultracold Eindhoven
(Verhaar group), JILA (Greene, Bohn) P. S.
Julienne and F. H. Mies, J. Opt. Soc. Am. B 6,
2257 (1989) F. H. Mies and M. Raoult, Phys. Rev.
A 62, 012708 (2000) P. S. Julienne and B. Gao, in
Atomic Physics 20, ed. by C. Roos, H. Haffner,
and R. Blatt (2006) (physics/0609013)
Analytic solutions for -C6/R6 van der Waals
potential B. Gao, Phys. Rev. A 58, 1728, 4222
(1998) Also 1999, 2000, 2001, 2004, 2005 Solely a
function of C6, reduced mass ?, and scattering
length a
15
For coupled channels case
Given the reference the single-channel
functions for scattering (Egt0) ?(E), C(E), tan
?(E) and bound states (Elt0) ?(E)
From vdW theory, given C6, ?, a
MQDT theory (1984) gives coupled channels
S-matrix and bound states.
Assume a single isolated resonance weakly coupled
to the continuum Yc,bg ltlt1, Ycc -Ybg,bg 0
16
Van der Waals MQDT bound state equation
Use
Solution as kb --gt 0
with
17
Classification of resonances by strength,
arXiv0812.1496
18
Closed channel dominated
Entrance channel dominated
Broad
Narrow
19
Closed channel dominated
Entrance channel dominated
Color sin2?(E)
20
Two-channel box model
with
21
Bound state E and Z for selected
resonances Points coupled channels Lines box
model
Closed-channel character
Energy
22
Can we get simple models for bound and scattering
states?
Use vdW solutions for MQDT treatment
Ingredients Atomic hyperfine/Zeeman
properties Atomic-molecule basis set frame
transformation Van der Waals coefficient C6 S,
T scattering lengths
23
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26
40K87Rb aa resonances
27
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29
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31
n -3
A(-1)
B(-2)
D(-3)
32
Ion-atom MQDT elastic and radiative charge
transfer Na Ca
Model calculation only (no real Potentials)
Ion-atom -C4/R4 Idziaszek, et al., Phys. Rev.
A 79, 010702 (2009)
33
Universal van der Waals inelasticity
Long range
Chemistry
Asymptotic
AB
Cold species prepared
Scatter off long-range potential
Assume unit probability of inelastic event at
small R
34
Universal van der Waals model
Applied to RbCs molecular quenching by Hudson,
Gilfoy, Kotochigova, Sage, and De Mille, Phys.
Rev. Lett. 100, 203201 (2008)
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