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 CLEO/Europe-EQEC Conference Munich – 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] 3d 5 4s 1 S=3 and magnetic moment of 6 µ B but also: Several metastable states Large inelastic Collision loss rates new strategies to reach BEC

Chromium level scheme 7 S 3 7 P nm nm Spontaneous decay Repumpers  = 5 MHz 7 P 3 5 D 4,3 5S25S2  = 32 ns [Ar] 3d 5 4s 3d 5 4p 3d 4 4s 2 6 µ B ~250 s -1  sat = 8.5 mW/cm nm 3d 5 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 µ 3 ) Sequence : MOT + OT Switch-off MOT beams and field Repump to ground state (  ss <<  dd ) 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 Not to scale Evaporation 100 ms 16 s MOT Horizontal trap Vertical trap Repump Spin polarization 500 mW 35 W Plate rotation 6s !! N init = At the ramp end, in this work, we get T between 2µK and 15µK and N between and 10 5 Ramp end for collision 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 cm -3. ~ BEC transition at ~ 110 nK t = 10 s – pure condensate ~ atoms t= 9.8 s - T = 80nK t=9.2 s - T = 200nK Q. BeaufilsQ. Beaufils, et al, Phys Rev 77, R (2008)

52 Cr Feshbach resonances From Werner PhD dissertation at Stuttgart Uni This work B close to 8.2 G

Pavlovic et al. PRA 69, (2004) Cr 2 molecular potential curves

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, (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 with

Resonance in d-wave collisions Loss 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. Cr 2 * excited molecules decay to more deeply bound states while three atoms are lost Superelastic collision Theory Experiment Q. Beaufils et al., PRA 79, (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. 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  B about 2mG Fit with where  0 =  M g µ B (B-B res )

Unusual T dependence Loss signal width vs B strongly depends on T 3-body loss parameter strongly depends on T

Cr 2 rf-association Rf photon 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 Cr 2 * bound molecular state when a resonance occurs. The loss mechanism then follows the same path as before. rf-peak Bare Feshbach resonance

Cr 2 rf-spectroscopy The rf peak shifts with B. This allows for precise determination of the Feshbach resonance position at G ie for molecular spectroscopy. rf peaks for two values of B rf at max verifies the energy conservation equation signal without rf

Cr 2 rf-association at high power 1050 kHz 900 kHz 700 kHz 500 kHz 400 kHz 300 kHz Q. Beaufils et al., arXiv: arXiv: Association rf of molecules as a Feshbach resonance between dressed states 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  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. BeaufilsQ. Beaufils et al., PRA 77, ® (2008) Q. Beaufils et al., PRA 79, (2009) Q. Beaufils et al., arXiv:

Ph.D students: Quentin Beaufils Gabriel Bismut Benjamin Pasquiou www-lpl.univ-paris13.frPost-docs: 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) 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, OG AND Anne Crubellier (not shown on photo)

Interpretation Thermal averaging, when Feshbach coupling Superelastic rate F. H. Mies et al., PRA, 61, (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) psd Losses = Rate of coupling to the molecular bound state = Rate of association through the barrier