Ultracold collisions in chromium d wave feshbach resonance and rf assisted molecule association
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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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Ultracold collisions in chromium: d-wave Feshbach resonance and rf-assisted molecule association

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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

A. Crubellier (theory)

Laboratoire Aimé-Cotton

Université Paris Sud - Orsay

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

Repulsive interaction

Attractive interaction

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 P4

Isat = 8.5 mW/cm2

3d5 4p

G / 2p = 5 MHz

t = 32 ns

Spontaneous decay

7 P3

~250 s-1


6 µ B

3d4 4s2

663-654-633 nm


425.55 nm

427.60 nm


3d5 4s

[Ar] 3d5 4s

7 S3

6 µ B

Optical trapping of Cr atoms

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

Sequence :


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

time sequence for Cr-BEC and collision studies

Ninit = 6 106

At the ramp end, in this work, we get

T between 2µK and 15µK and N between 3 104 and 105


Spin polarization

Ramp end for collision studies


35 W

500 mW


Horizontal trap

Vertical trap

100 ms

16 s

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

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 .

t= 9.8 s - T = 80nK

t = 10 s – pure condensate

~20 000 atoms

Q. Beaufils, et al, Phys Rev 77, 061601 R (2008)

This work

B close to 8.2 G

52Cr Feshbach resonances

From Werner

PhD dissertation

at Stuttgart Uni

Cr2 molecular potential curves

Pavlovic et al. PRA 69, 030701 (2004)

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)

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


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.

Superelastic collision



Cr2* excited molecules decay to more deeply bound states

while three atoms are lost

Q. Beaufils et al., PRA 79, 032706 (2009)

Atom losses near resonance

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.

Fit with

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

Unusual T dependence

Loss signal width vs B strongly depends on T

3-body loss parameter strongly depends on T












Rf photon

Cr2 rf-association


Bare Feshbach


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.

Cr2 rf-spectroscopy

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

Cr2 rf-association at high power

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 !

1050 kHz

900 kHz

700 kHz

500 kHz

400 kHz

400 kHz

300 kHz

Q. Beaufils et al., arXiv:0812.4355

Association rf of molecules as a Feshbach resonance between dressed states


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)


  • 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

Group members : The Cold Atom Group in Paris Nord

Ph.D students:

Quentin Beaufils

Gabriel Bismut

Benjamin Pasquiouwww-lpl.univ-paris13.fr


Paolo Pedri

Thomas Zanon (now at LNE-CNAM)

Permanent staff:

Bruno Laburthe-Tolra, Etienne Maréchal, Laurent Vernac and O. G.

Former members

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)


Superelastic rate

Feshbach coupling

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

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