Ultracold collisions in chromium:d-wave Feshbach resonance and rf-assisted molecule association
Q. Beaufils, T. Zanon, B. Laburthe, E. Maréchal, L. Vernac and Olivier GorceixLaboratoire de Physique des LasersUniversité Paris Nord
A. Crubellier (theory)Laboratoire Aimé-CottonUniversité Paris Sud - Orsay
CLEO/Europe-EQEC ConferenceMunich – 15 June 2009
Attractive interaction
Repulsive interaction
Dipolar effects in ultra-cold gases
Modified expansion and collapse dynamics (Pfau’s group)
Dipolar bosons in optical lattices (in our group and also in Stuttgart)
Dipolar relaxation (poster yesterday)
Feshbach resonance without hyperfine structure (this talk)
Magnetic dipole-dipole interaction :
long range and anisotropic
Chromium relevant properties:
Large dipolar effects in ultra-cold gases which stem from
the ground state electronic structure [Ar] 3d5 4s1 S=3
and magnetic moment of 6 µB
but also: Several metastable states Large inelastic Collision loss rates
new strategies to reach BEC
Chromium level scheme
7 S3
7 P4
425.
55 n
m
663-
654-
633
nm
Spontaneous decay
Rep
um
pers
= 5 MHz
7 P3
5D4,3
5S2
= 32 ns
[Ar] 3d5 4s
3d5 4p
3d4 4s2
6 µ B
6 µ B
~250 s-1
sat = 8.5 mW/cm2
427.
60 n
m
3d5 4s
Optical trapping of Cr atoms
We continuously accumulate Cr* atoms
in a mixed magnetic + optical trap
35W at 1075 nm with waist 50µm
Condensation of Cr is not possible in a magnetic trap (dipolar relaxation scales as µ3)
Sequence : MOT + OT Switch-off MOT beams and fieldRepump to ground state (ss<<dd)Spin polarization in lowest-energy sub-state m=-3“All-optical” evaporative coolingHold the sample for time tRelease then capture an absorption image to get T and N
time sequence for Cr-BEC and collision studies
Not to scaleNot to scale EvaporationEvaporation100 ms100 ms 16 s16 s
MOTMOT
Horizontal trapHorizontal trap
Vertical trapVertical trap
Repump Repump Spin polarizationSpin polarization
500 mW500 mW35 W35 W
Plate rotation 6sPlate rotation 6s
!!
Ninit = 6 106 At the ramp end, in this work, we get At the ramp end, in this work, we get
T between 2µK and 15µK and N between 3 10T between 2µK and 15µK and N between 3 1044 and 10 and 1055
Ramp end for Ramp end for collision studiescollision studies
Cr sample preparation : way down to Bose-Einstein Condensation
All-optical evaporation
After « dimple » formation, the trapping beam power is lowered from 35 W to 500 mW within 10 s.The complete cycle time is below 20 s.
Evaporation ramp can be stopped at will.
Temperature can be tuned from 15 µK to below 100 nK.The peak density is on the order of 1013 cm-3 .
BEC transition at ~~110 nK
t = 10 s – pure condensate t = 10 s – pure condensate
~20 000 atoms~20 000 atoms
t= 9.8 s - T = 80nKt= 9.8 s - T = 80nK
t=9.2 s - T = 200nKt=9.2 s - T = 200nK
Q. Beaufils, et al, Phys Rev 77, 061601 R (2008)
52Cr Feshbach resonances From Werner PhD dissertationat Stuttgart Uni
This workB close to 8.2 G
Pavlovic et al. PRA 69, 030701 (2004)
Cr2 molecular potential curves
0.4
0.3
0.2
0.1
0.0
-0.1
-0.2
4321
| 6; 6; 2; 1S lS m l m
| 6; 5; 0SS m l
Feshbach resonance in d-wave collisions at low field
• Several Feshbach resonances have been observed at Stuttgart Uni in Tilman Pfau’s group
J.Werner et al. Phys. Rev. Lett. 94, 183201 (2005)
Bg B
We work close to the Feshbach resonance at 8.2 G
Entrance channel : input : pair of free colliding atoms in d-wave
Closed channel : output s-wave excited bound molecule
Resonant coupling parameter
with
2/)12(22)( l
ddboundm V
Resonance in d-wave collisionsLoss mechanism
At ultra-low temperature scattering is inhibited in l>0, because atoms need to tunnel through a centrifugal barrier to collide. In our case, ie for a « d-wave entrance channel», tunneling is resonantly increased. by the presence of a bound molecular state. A third Cr atom triggers superelastic collisions, leading to three-body losses, as the kinetic energy gain greatly exceeds the trap depth.
Cr2* excited molecules decay to more deeply bound states
while three atoms are lost
Su
pere
last
ic c
olli
sion
KTTkBm [email protected])( 5
KTTkBm [email protected])( 5
Theory
Experiment
Q. Beaufils et al., PRA 79, 032706 (2009)
Atom losses near resonance
We have monitored losses vs the magnetic field We have monitored losses vs the magnetic field strength at various temperatures well below the strength at various temperatures well below the Wigner threshold for d-wave collisions but above Wigner threshold for d-wave collisions but above BEC transition. BEC transition.
3
4
5
6
789
104
2
3
4
5
Ato
mN
umb
er
252015105Time (s)
Typical decay curve – 3-body loss mechanism
2.5
2.0
1.5
1.0
0.5
0.0
25.525.024.524.023.523.022.5
14
Th
ree-
body
los
s pa
ram
eter
(m
s )
Magnetic field (MHz)
6-1
3-body loss parameter strongly depends on TWidth and max of resonant loss signal strongly depend on T. B is known with B about 2mG
Fit with
where 0= M g µB (B-Bres)
Unusual T dependence
Loss signal width vs B strongly depends on T
3-body loss parameter strongly depends on T
Cr2 rf-association
Bg B
Rf photon
0.4
0.3
0.2
0.1
0.0
-0.1
-0.2
4321
We set the magnetic field close to 8 G (sligthly below the Feshbach resonance) and we add an rf-field. The colliding pair of atoms emits an rf-photon while it is colliding, and is transfered into the Cr2* bound molecular state when a resonance occurs. The loss mechanism then follows the same path as before.
30x103
25
20
15
10
5
0
Ato
m n
umbe
r af
ter
8s
2625242322
Magnetic field (MHz)
rf-peak Bare Feshbach resonance
Cr2 rf-spectroscopy
The rf peak shifts with B. This allows for precise determination of the Feshbach resonance position at 8.157 Gie for molecular spectroscopy.
9000
8000
7000
6000
Ato
m N
umbe
r
5004003002001000rf frequency (kHz)
-1000
-800
-600
-400
-200
rf r
eson
ance
(kH
z)
25.0x103
24.524.023.523.022.522.0 Magnetic field (kHz)
25x103
20
15
10
5
0
Atom
Num
ber after 7s (no rf)
rf peaks for two values of B
rf at max verifies the energy conservation equation
signal without rf
Cr2 rf-association at high power
0.4
0.3
0.2
0.1
0.0
K2/
K2(
0)
543210
kHz kHz kHz kHz kHz kHz kHz
/
1050 kHz900 kHz700 kHz500 kHz400 kHz400 kHz300 kHz
Q. Beaufils et al., arXiv:0812.4355
Association rf of molecules as a Feshbach resonance between dressed states
2
122 0,
JKK
Finally, we study how the peak intensity varies vs rf-power in the strong field regimeExperimental outcomes are best described in a dressed molecule approach:
The rf assisted loss parameter only depends on the ratio of the Rabi frequency to the rf frequency .A four-body process (three atoms and a photon) is described by a simple analytical Bessel function !
Acknowledgements
Financial support:•Conseil Régional d’Ile de France (Contrat Sésame)•Ministère de l’Enseignement Supérieur et de la Recherche (CPER, FNS and ANR)•European Union (FEDER)•IFRAF•CNRS•Université Paris Nord
Publications related to this talk:Q. Beaufils et al., PRA 77, 061601® (2008)
•Q. Beaufils et al., PRA 79, 032706 (2009)
•Q. Beaufils et al., arXiv:0812.4355
Ph.D students:Ph.D students:
Quentin Beaufils
Gabriel Bismut
Benjamin Pasquiou www-lpl.univ-paris13.frPost-docs:Post-docs:
Paolo Pedri
Thomas Zanon (now at LNE-CNAM)
Permanent staff:Permanent staff:
Bruno Laburthe-Tolra, Etienne Maréchal, Laurent Vernac and O. G.
Former membersArnaud Pouderous (industrial property specialist, Hirsch & Partners), Radu Chicireanu (now at NIST) Jean-Claude Keller (retired)
Group members : The Cold Atom Group in Paris Nord
THANKS!
From left to right: Laurent Vernac, Etienne Maréchal, Thomas Zanon, Jean-Claude Keller, Bruno Laburthe, Quentin Beaufils, OGAND Anne Crubellier (not shown on photo)
Interpretation4/))(()(
)()(
220
2dm
dm
kk
dd n
TkBdm )( 0Thermal averaging, when
TkhQ
lTK
Bm
T
002 exp)(
)12(2)(
Feshbach coupling Superelastic rate
F. H. Mies et al., PRA, 61, 022721 (2000)P. S. Julienne and F. H. Mies, J. Opt. Soc. Am. B. 6, 2257 (1989).
Calculation with no adjustable parameter (adiabatic elimination of d) (Anne Crubellier LAC)
2/)12(22)( l
ddboundm V
)(m psd
nnn dBm 3
Losses = Rate of coupling to the molecular bound state
= Rate of association through the barrier