CLEO/Europe-EQEC Conference Munich – 15 June 2009. 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 Gorceix. Laboratoire de Physique des Lasers Université Paris Nord
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Munich – 15 June 2009
Ultracold collisions in chromium:d-wave Feshbach resonance and rf-assisted molecule association
T. Zanon, B. Laburthe,
E. Maréchal, L. Vernac and Olivier Gorceix
Laboratoire de Physique des Lasers
Université Paris Nord
A. Crubellier (theory)
Université Paris Sud - Orsay
Magnetic dipole-dipole interaction :
long range and anisotropic
the ground state electronic structure [Ar] 3d5 4s1 S=3
and magnetic moment of 6 µB
new strategies to reach BEC
Chromium level scheme
Isat = 8.5 mW/cm2
G / 2p = 5 MHz
t = 32 ns
6 µ B
[Ar] 3d5 4s
6 µ B
Condensation of Cr is not possible in a magnetic trap (dipolar relaxation scales as µ3)
We continuously accumulate Cr* atoms
in a mixed magnetic + optical trap
35W at 1075 nm with waist 50µm
MOT + OT
Switch-off MOT beams and field
Repump to ground state (bss<<bdd)
Spin polarization in lowest-energy sub-state m=-3
“All-optical” evaporative cooling
Hold the sample for time t
Release then capture an absorption image to get T and N
Ninit = 6 106
At the ramp end, in this work, we get
T between 2µK and 15µK and N between 3 104 and 105
Ramp end for collision studies
Not to scale
Plate rotation 6s
Cr sample preparation : way down to Bose-Einstein Condensation
BEC transition at ~110 nK
t=9.2 s - T = 200nK
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 .
t= 9.8 s - T = 80nK
t = 10 s – pure condensate
~20 000 atoms
Q. Beaufils, et al, Phys Rev 77, 061601 R (2008)
B close to 8.2 G
52Cr Feshbach resonances
at Stuttgart Uni
Cr2 molecular potential curves
Pavlovic et al. PRA 69, 030701 (2004)
J.Werner et al. Phys. Rev. Lett. 94, 183201 (2005)
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
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
Q. Beaufils et al., PRA 79, 032706 (2009)
We have monitored losses vs the magnetic field strength at various temperatures well below the Wigner threshold for d-wave collisions but above BEC transition.
where e0= DM g µB (B-Bres)
Typical decay curve – 3-body loss mechanism
3-body loss parameter strongly depends on T
Width and max of resonant loss signal strongly depend on T. B is known with dB about 2mG
Loss signal width vs B strongly depends on T
3-body loss parameter strongly depends on T
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.
The rf peak shifts with B. This allows for precise determination of the Feshbach resonance position
at 8.157 G
ie for molecular spectroscopy.
rf peaks for two values of B
signal without rf
nrf at max verifies the energy conservation equation
Finally, we study how the peak intensity varies vs rf-power in the strong field regime
Experimental outcomes are best described in a dressed molecule approach:
The rf assisted loss parameter only depends on the ratio of the Rabi frequency W to the rf frequencyw.
A four-body process (three atoms and a photon) is described by a simple analytical Bessel function !
Q. Beaufils et al., arXiv:0812.4355
Association rf of molecules as a Feshbach resonance between dressed states
Group members : The Cold Atom Group in Paris Nord
Thomas Zanon (now at LNE-CNAM)
Bruno Laburthe-Tolra, Etienne Maréchal, Laurent Vernac and O. G.
Arnaud Pouderous (industrial property specialist, Hirsch & Partners),
Radu Chicireanu (now at NIST)
Jean-Claude Keller (retired)
From left to right: Laurent Vernac, Etienne Maréchal, Thomas Zanon,
Jean-Claude Keller, Bruno Laburthe, Quentin Beaufils, OG
AND Anne Crubellier(not shown on photo)
F. H. Mies et al., PRA, 61, 022721 (2000)
P. S. Julienne and F. H. Mies, J. Opt. Soc. Am. B. 6, 2257 (1989).
Thermal averaging, when
Calculation with no adjustable parameter (adiabatic elimination of Gd) (Anne Crubellier LAC)
Losses = Rate of coupling to the molecular bound state
= Rate of association through the barrier