Ultra-cold Molecules: Formation, Trapping and Prospects

1
Ultra-cold MoleculesFormation, Trapping and
Prospects

• Pierre Pillet
• Laboratoire Aimé Cotton, CNRS Bât. 505, Campus
  dOrsay,
• 91405 Orsay cedex, France
• pierre.pillet_at_lac.u-psud.fr
• http//www.lac.u-psud.fr

____________________________________________
34th EGAS SOFIA 9th 12th July 2002
2
OUTLINE

• Control of a pair of colliding atoms through
  photoassociation
• Schemes for formation of cold ground-state
  molecules, temperature and formation rate
• Trapping and accumulation
• Photoassociative spectroscopy
• Two-color photoassociation
• Feshbach resonance
• Conclusion

3
L A S E R C O O L I N G
4
Laser cooling for molecules
In molecular systems, lack of closed two-level
scheme
Laser cooling scheme for Cs atom and Cs2 dimer
Because of the large number of ro-vibrational
levels, to add repuming lasers is not a
reasonable solution. If to extend laser cooling
techniques to molecules is not totally
impossible, it seems to be actually difficult!
5
COLD MOLECULES
Sympathetic cooling with a He buffer gas in a
magnetic trap CaH, 400 mK, 108 molecules J.
Doyle, B. Friedrich, et al., (Harvard), Nature
395, 148 (1998))
Decelerator of polar molecules in a supersonic
beam (ND3 , 106 cm-3, 350 mK) G. Meijer et al.
(FOM), Nature 406, 491 (2000)
6
At the frontier of atomic and molecular
physicsUse of cold atoms to form cold molecules
7
Control of a Pair of Colliding Cold Atoms via
PhotoassociationCs(6s,F4)Cs(6s,F4)hnL
Cs2(Wu,g(6s6p3/2(or 1/2)v,J)
level f
continuum a

• To form an electronically excited molecule in a
  selected ro-vibrational level
• These excited molecules are cold but have a very
  short life ( 30 ns)
• Mostly they dissociate the channel to form
  ground-state molecules is negligible

8
Theory Fermi golden rule PA rate
Properties of photoassociation of cold atoms
(case of a MOT)

• COLD ATOMS
• Resonant process Ef(v,J)-2Ei-hnLkBTa few MHz
• FRANCK-CONDON FACTOR
• Excitation at the classical outer turning point
  (R0) The intensities are proportionnal to
  (modulation of the intensities of the
  spectral lines)
• Excitation of long-range molecules Efficiency
  decrease with v
• DETECTION (trap-losses)
• The photoassociated molecules dissociate by
  giving two  hot  atoms which escape outside the
  cold atomic cloud

9
Energy (cm-1)
10
SET-UP
11
Absolute calibration 150 MHz
12
Photoassociation Spectra below the 6s6p3/2
limit Notice the modulation of the line
intenities The low v correspond to shortest
range excitation at the classical turning point
13
All the vibrational progressions are observed in
the fluorescence spectrum Only the 0g- and 1u are
observed in the ion spectrum below the 6s6p3/2
limit Proof for formation of translationally cold
ground-state molecules
Delay of the pulsed laser Td10msgtgtTsp30ns
Ballistic expansion and time-of-flight of the
falling molecular cloud
TmolTat
Tmol20-515µK
14
0g- and 1u states present Condon points at
intermediate distance suitable for bound-bound
transition toward the singlet ground-state or the
lowest triplet state
0g- excitation leads to the formation of cold
molecules in a3Su state in vibrational levels in
the  middle  of the well. 1u one leads to cold
molecules in X1Sg state, in levels very close
to the dissociation limit.
These cases are quite optimum for the formation
of cold molecules via photoassociation
15
Photoassociation Spectra below the 6s6p1/2
dissociation limit All the vibrationnal
progressions are observed The excitation of 0u
(6s 6p1/2) permits the formation of cold
molecules
16
Schemes of formation of cold molecules via
photoassociationPhotoassociation
Cs(6s,F4)Cs(6s,F4)hnL-gtCs2(Wu,g(6s6p3/2(or
1/2)v,J) Spontaneous emission and formation of
cold molecules Cs2(Wu,g(6s1/26p3/2v,J)) -gtCs2
(X1Sg or a3Su v,J) hnSP
0g- and 1u (6s 6p3/2) also Rb2 (Pisa)
0u (6s 6p1/2) internal coupling between
two states 0u (6s6p1/2 ) and 0u (6s6p3/2 )
with the same symmetry
17
TRAPPING COLD MOLECULES DIPOLE TRAP - NdYAG
laser does not work for the considered
molecules. - CO2 laser is more promising (T.
Takekoshi et al. PRL 81, 5105 (1999)Trapping of
the cold molecules, present in the MOT.
  MAGNETIC QUADRUPOLAR TRAPWe can trap the cold
molecules in the triplet state with the good
magnetic momentum the momenta of the two atoms
are parallel
The magnetic field gradient for trapping is
comparable for atoms and molecules 3 mT/cm.
18
Accumulation and trapping in a mixed atomic MOT
and molecular quadrupolar trap (magnetic field
gradient 6mT/cm)
(a)   Scheme  a3Su (b)   Trapping in the MOT
zone, (b) all the lasers (MOT and PA) off, (b)
only PA laser off (c)    Lifetime 0.5
s (d)    Accumulation at 60ms
19
Spatial analyzis
200 000 molecules at 40 µK
20
DETECTION The photoionisation is a two-photon
resonant process via the (2)3Pg vibrational
levels correlated to the dissociation limit 6s5d
(REMPI)
21
Rate for photoassociation (case 0u)
Dynamic trap eq.
Measured photoassociation rates bPAnat 0.1 5
s-1/atom The number of cold molecules is given
by the branching ratio between bound-bound and
bound-free molecular transition
22
Rate for formation of cold molecules (case 0g-)
Direct measurement
The branching ratio for bound-bound transitions
towards the ground state is 0.9
RATECM (v6, 140 W/cm2, nat 5 1010) 0,06
s-1/atom 106 molecules/s with 5 107 atoms
23
Formation rate of cold molecules (a) Calculated
branching ratios 0g- (6s6p3/2), 0g-
(6s6p1/2) (b) Expected formation rates T 140
µK, n 1011 cm-3, I 55 W.cm-2 0.1 molecule per
atom and per second  Rate a few 106 molecules
per second
Computed phototoassossiated rates
(a) 0g-, (b) 0u (6s6p3/2), (6s6p1/2) T
140 µK, n 1011 cm-3, I 55 W.cm-2
24

• FIRST CONCLUSION
• A way for formation of ultra-cold ground-state
  molecules a rate of 0.2 molecules per atom and
  per second, at 10-100 µK. For increasing the
  rate, increase the atomic density.
• Others ways sympathetic cooling, Stark
  decelerator.
• Trapping 104-6 molecules at a temperature of a
  few 10 µK.
• The use of a dipole CO2 laser trap is promising.
• Role of the sensitivity of the REMPI detection
  (photoionization time-of-flight).
• FEW MORE WORDS
• Photoassociative spectroscopy
• Two color photoassociation
• Use of Feshbach resonance

25
1u long-range molecules at the frontier of
atomic and molecular physics
Adiabatic asymptotic potential including fine et
hyperfine structure
The exchange terms are negligible
V1
With the rotation s, p, d and f-waves Eur. Phys.
J. D11, 59 (2000).
26
The long-range spectroscopy permits to determine
asymptotic long-range coefficients C3
(proportional to the atomic dipole) of the
potential curves The case of the 0g- (6s6p3/2)
has so permitted to give a value for the atomic
lifetime Cs(6p3/2) t30.462/-0.003 ns (R.
Gutteres, C. Amiot, O. Dulieu, F.
Masnou-Seeuws) to compare with experimental
values t30.41(10) ns (Young et al) and
t30.50(7) ns (Rafac et al) At the frontier of
the atomic and molecular physics we use
cold atoms to do molecular spectroscopy and then
to determine atomic parameters
27
TWO-COLOR PHOTOASSOCIATION
J0 2 4
Frustration of PA dark resonances
Stimulated Raman PA Preparation of cold molecules
in a well-defined level? Lifetime of 2
t2t1(D/W122) Fano profiles (interference) G
-L1-gt1 -SP-gt F G -L1-gt 1 -L2-gt 2 -L1-gt 1 -SP-gt F
28
CONTROL OF THE FORMATION OF MOLECULES THROUGH A
FESCHBACH RESONANCE   Cs(6s,F3,m3)Cs(6s,F3,m3
)hnLCs2(0g-(6s6p3/2)v,J)
v6, J0 and 2
Due to the Feshbach resonance, we observe an
increasing of the PA rate for vlt30, corresponding
to an excitation at the external turning point
R0lt 38 a0.
29
CONCLUSION

• Applications Molecule optics and molecule
  interferometry, molecule lithography, metrology,
  high precision measurement
• Bose-Einstein condensation of a molecular gas,
  molecule laser, ensemble of ultacold dipoles,
  BCS
• Starting with an atomic condensate Interest for
  Stimulated Raman Phototassociation (Rb2, Li2) and
  for Feshbach Resonance (Rb2)
• Case of Cs BEC Mixed magnetic and dipolar trap
  for F3, m3 level LAC and Innsbruck
• (R. Grimm) in progress
• - Ultra-cold photochemistry to form more complex
  cold molecules? (heteronuclear dimers of
  alkalines, trimers)

30
LAC Team

• Experiments Daniel Comparat, Samuel Guibal,
  P.P., Christian Lisdat, Nicolas Vanhaecke, Salah
  Boussen, Nathalie Hoang, Wilson de Melo Souza,
  Andrea Fioretti (Pisa), Cyril Drag (2000), Bruno
  Laburthe Tolra (2001)
• Theory Françoise Masnou-Seeuws, Olivier Dulieu,
  Anne Crubellier, Claude Amiot, Philippe
  Pellegrini, Benoît T Jampens, Kai Willner,
  Pascal Naidon, Claude Dion, Ricardo Gutteres,
  Mihaëla Vatacescu (1999), Viatcheslav Kokoouline
  (1999)