1. All-optical production of chromium BECs Bessel Engineering of Chromium Bruno Laburthe Tolra Laboratoire de Physique des Lasers Université Paris Nord Villetaneuse - France

2.  Dipole-dipole interactions : ‘long range’ (1/r 3 ) anisotropic répulsive attractive  chromium:  Study of dipole-dipole interactions in Quantum Degenerate gases  Statistical physics at very low T  Bose-Einstein condensates  Degenerate Fermi gases  What about interactions ?  In most experiments (alkali) – Van-der-Waals interactions ‘short-range’ (1/r 6 ) isotropic magnetic moment : 6µ B => dipole dipole interactions x 36 1 boson et 1 fermion S=3

3.  Ballistic expansion of the BEC modified by dipole dipole interactions  Tune contact interactions using Feshbach resonances: dipolar interaction larger than Van-der-Waals interaction  When  dd ~1, condensate not stable. Stability depends on trapping geometry. Collapse of condensate reveals dipolar pattern. First BEC : team of T. Pfau (Stuttgart 2005) Phys. Rev. Lett. 94, 160401 (2005) Phys. Rev. Lett. 95, 150406 (2005) Nature. 448, 672 (2007) And… collective excitations, Tc, solitons, vortices, Mott physics, 1D or 2D physics (correlations due to long distance repulsion), spinor physics, dipolar fermions, strong rf fields… répulsive attractive

4.  All optical production of a Chromium BEC  A Cr BEC in strong rf fields  An rf-assisted d-wave Feshbach resonance  Tools, future

5. 10 -4 10 -3 10 -2 10 10 0 1 10x10 3 8642 Time (ms) Phase Sapce Density How to make a Chromium BEC in 14s and one slide ? 425 nm 427 nm 650 nm 7S37S3 5 S,D 7P37P3 7P47P4  An atom: 52 Cr N = 4.10 6 T=120 μK 750700650600550500 600 550 500 450 (1) (2) Z  An experiment  A small MOT  A dipole trap  A crossed dipole trap  An evaporation ramp  A BEC

6. Cr Magneto-optical traps  52 Cr  53 Cr N = 4.10 6 bosons T=120 μK density = 1.1 10 11 atoms /cm 3 Loading rate = 3.5 10 8 atoms/s N = 5.10 5 fermions T=120 μK density = 2.5 10 10 atoms /cm 3 Loading rate = 10 7 atoms/s Very short loading times (10 à 100 ms) and small number of atoms : decay towards metastable states → repumpers (laser diodes at 663 and 654 nm) Inelastic collisions (dominant process) R. Chicireanu et al. Phys. Rev. A 73, 053406 (2006)  A MOT for a mixture ( 52 Cr- 53 Cr): N 52,53 ~ 10 5 atoms 2 to 3 orders of magnitude than alkalis Comparable values for He*. (2005)

7. Our approach: cw accumulation of metastable atoms in an optical trap Depth : ~ 500μK (parametric excitations) The optical trap: The optical trap: IPG fiberized laser – 50W @ 1075 nm Horizontal beam - ~40 µm waist Metastable atoms shielded from light assisted collisions

8. A mixed optical-magnetic trap for metastable 52 Cr up to 1.2 10 6 atoms at 100 μK fast accumulation: ~ 100 ms R Chicireanu et al., Euro Phys J D 45, 189 (2007) Time (ms) Number of atoms (millions) Limitations: - Majorana losses - D-D inelastic collisions - loading rate 10 7 s -1 Loading rate : 10 7 s -1

9. (i) Cancel magnetic forces with an rf field  What for : Load all magnetic sublevels, and limit inelastic collisions by reducing the peak atomic density  How : During loading of the OT, magnetic forces are averaged out by rapidly spin flipping the atoms. RF Sweep m>0 m<0 x E(x) Resonant spin flip at Sweep span to cover size of cloud (similarities Paul trap)

10.  What sweep rate? Spins must be flipped a large number of times in one oscillation period in the magnetic potential 1/   :  Which rf power? Landau-Zener adiabaticity criterion sets the minimal Rabi frequency:  Result ? More than 2 million atoms, in 100 ms Q. BeaufilsQ. Beaufils et al., Phys. Rev. A, 77, 053413 (2008) !!! 150 Watts of rf !!! Loading rate : 2.10 7 s -1

11. (ii) Load another metastable state : 5 S 2  What we expect : A lower inelastic loss parameter ? A lower inelastic loss parameter ? A larger loading rate ? A larger loading rate ? 5D45D45D45D4 5S25S25S25S2 7S37S37S37S3 7P37P37P37P3 7P47P47P47P4 425nm 427nm 633nm663nm  Results ? More than de 5 million atoms, in 35 ms  Loading rate = ¼ MOT loading rate !  Optically trapped atoms > N MOT ! Doubled laser diode 427 nm (~1 mW)

12. Loading a dipole trap: Summary  Load 5 D 4 et 5 D 3 : 1,2 million atoms (spring 2007)  (i) RF Sweeps : 2 million atoms (july 2007)  (i)*(ii) Load 5 D 4 et 5 S 2 and rf sweeps 5 to 6 million atoms (octobre 2007) Loading rate : 1.510 8 s -1 Loading rate : 10 7 s -1 Loading rate : 2 10 7 s -1 But… phase-space density ~10 -6

13.   Suppress two-body inelastic losses : spin polarize into the lowest energy Zeeman state (use the 7 S 3 → 7 P 3 transition at 427 nm) Doubled laser diode 427 nm; Polarization pulse : 40 μs  Loading a crossed optical dipole trap remove IR power from the horizontal trapping beam to a vertical one (with a motorized λ/2 waveplate) Result : increase x20 of phase-space density ( D ph. = n 0 Λ 3 dB )  Relative polarization of the laser beams The polarization of all three laser beams must be orthogonal, despite the fact that the optical path difference between the beams is much much larger than the coherence length of the laser !! Atoms in dimple, crossed polarization Parallel polarization Time (ms)

14. 10 -4 10 -3 10 -2 10 10 0 1 10x10 3 8642 Time (ms) LoadingEvaporation 100 ms 16 s MOT Horizontal trap Vertical Trap Repump and polarize 500 mW 35 W Crossing both OT arms 6s ? Phase Sapce Density Densité dans l'espace des phase dans le dimple. On tient compte de rotation de lame et du remplissage du dimple. La lame tourne en 9.2 s de 32 degré à t=-2000, les atomes sont polarisés à t=-2000. (november 2007)

15. Thomas Fermi analysis + Castin-Dum expansion 5 ms -> R TF =19 microns Experimentally : 21 microns Chemical potentential of about 1 kHz  4 kHz (recompressed trap) In situ TF radii 4 and 5 microns Density : 6.10 13 at/cm 3  2.10 14 at/cm 3 Condensates lifetime: a few seconds. Q. BeaufilsQ. Beaufils et al., Phys.Rev. A 77, 061601(R) (2008) 17 000 atoms T = 80nK 10 000 atoms Pure BEC

16.  All optical production of a Chromium BEC  A Cr BEC in strong rf fields  An rf-assisted d-wave Feshbach resonance  Tools, future

17. Control of the Landé factor One can modify the Landé factor of the atoms g J with very strong off resonant rf fields. If the RF frequency ω is larger than the Larmor frequency ω 0, g J is modified : Rf power Eigenenergies Can we use this degeneracy for spinor physics ? See L. Santos et al., PRA 75, 053606 (2007) -3 -2 0 2 1 3 A spinor is a multicomponent BEC (with degenerate components): the magnetic fields needs to be small (interaction energy > Zeeman energy) < 1 mG !!... Serge Haroche thesis S.Haroche, et al., PRL 24 16 (1970) True in 2D… Generalization in 3D ?

18. B rf (t)  (t)  (t) Classical interpretation Phase modulation -> Bessel functions e.g. light or matter diffraction; side-bands in frequency modulation; tunneling in modulated lattice (Arimondo 2008)…

19. Control magnetism  Let us apply blue detuned rf fields to thermal atoms in a one beam optical trap, plus a magnetic field gradient.  B = 0 at the center of the trap. The atoms, all in high field seekers, leave the center of the trap.  RF can erase the effect of such a gradient: Results only depend on  Good agreement with Bessel function up to 

20. Adiabaticity issues One single spin component BEC « diffracted » at 2.4; extreme trajectories represented Adiabaticity depends on B par :

21. A reversible dressing If rf is applied and removed sufficiently slowly, the atoms come back to the initial Zeeman substate state. Very different from the usual resonant regime, with diabatic Rabi flopping.

22. répulsive attractive Elastic s-wave collisions: Rf does not couple different molecular potentials -> s-wave elastic collisions should be unchanged. Collision properties of off-resonantly rf dressed states : Dipolar interactions: « geometrical averaging ? » (non calculated) 

23. No emission of rf photons during a collision An inelastic collision in a fixed (rf) field -> Dipolar relaxation Roughly ok for thermalization ? Other atoms ? See something at 2.4 ? Inelastic collision properties of off-resonantly rf dressed states : Two timescales : collision time << dressing time. Beware of the lowest energy state argument !! x1000 3 4 5 6 7 20015 0 10050 A t o m n u m b e r Time (ms)

24.  All optical production of a Chromium BEC  A Cr BEC in strong rf fields  An rf-assisted d-wave Feshbach resonance  Tools, future

25. At ultra-low temperature scattering is inhibited in l>0, because atoms need to tunnel through a centrifugal barrier to collide: collisions are « s-wave ». In a « d-wave » Feshbach resonance, tunneling is resonantly increased by the presence of a bound molecular state. Superelastic collision To probe a feshbach resonance: 3 body losses Tunneling to short internuclear distance is increased by a Feshbach resonance. A third atom triggers superelastic collisions, leading to three-body losses, as the kinetic gained greatly exceeds the trap depth A d-wave Feshbach resonance in chromium 0.4 0.3 0.2 0.1 0.0 -0.1 -0.2 4321 Internuclear distance (arb.) Energy (arb.) First seen in J. Werner et al., PRL 94, 183201 (2005)

26. Three-body losses observed Non exponential decay; Deduce three-body loss parameter

27. Three-body losse parameter strongly depends on T Width of resonant losses strongly depends on T A very original Feshbach resonance: Strong dependence on T. Very narrow. Outlook : tailor anisotropic interactions in a BEC ? Temperature dependence

28. Interpretation Thermal averaging, when Feshbach coupling Superelastic rate Conclusions: - « 2-body » three-body losses. -Loss parameter proportionnal to T -Feshbach coupling measured; very narrow F. H. Mies et al., PRA, 61, 022721 (2000) P. S. Julienne and F. H. Mies, J. Opt. Soc. Am. B. 6, 2257 (1989).

29. Can such a resonance be used to tailor anisotropic interactions in a BEC ? psd Feshbach coupling If  d   m it is not likely to use such Feshbach resonances in a BEC to tailor anisotropic interactions: for the interactions to have a substantial effect on the trapped atoms, one would need to have  m , but then the lifetime of the cloud would be also shorter than the trap frequency !

30. Rf in the vicinity of the Feshbach resonance Resonant losses when  =E b -E i Rf photon 0.4 0.3 0.2 0.1 0.0 -0.1 -0.2 4321 We modulate the magnetic field close tothe Feshbach resonance. The colliding pair of atoms emits a photon while it is colliding, and the pair of atoms is transfered into a bound molecule See also: S. T. Thomson et al., PRL 190404 (2005), C. Ospelkaus et al., PRL 97, 120402 (2006), F. Lang et al., Nature Physics 4, 223 (2008), T. M. Hanna et al., PRA, 013606 (2007).

31. Rf spectroscopy: not so high precision The resonance shifts with the position of the molecular level. This allows for spectroscopy. The width of the resonance is limited by temperature. Also: interesting power shifting of the Feshbach resonance

32. A radio-frequency assisted d-wave Feshbach resonance in the strong field regime Amplitude of losses analysis: A radio-frequency assisted d-wave Feshbach resonance in the strong field regime In the modulation technique, the eigenstates are sinusoidally modulated in energy. The Feshbach resonance may happen between the dressed states. The loss rate is then qualitatively related to the population in the first Bessel function, i.e. to the population in the 1 st dressed state. See P. Pillet et al., Phys. Rev. A, 36, 1132 (1987) The rf assisted three-body loss parameter only depends on the ration of the rabi frequency to the rf frequency: we describe a four body process (three atoms and one photon) by a simple analytical Bessel function !

33.  All optical production of a Chromium BEC  A Cr BEC in strong rf fields  An rf-assisted d-wave Feshbach resonance  Tools, future

34. Fermions: Phys. Rev. A 73, 053406 (2006) Cr Metastable: Phys. Rev. A 76, 023406 (2007) Optical trapping metastable: Eur. Phys. J. D 45 189 (2007) Rf sweeps: Phys. Rev. A, 77, 053413 (2008) BEC: Phys.Rev. A 77, 061601(R) (2008) Thanks! PhD: Q. Beaufils (2 nd year) ATER: T. Zanon (leaving) Permanent people: B. Laburthe-Tolra, E. Maréchal, L. Vernac, (R. Barbé), J.C. Keller O. Gorceix Former PhDs: A. Pouderous R. Chicireanu Next year Paolo Pedri (post-doc, theory) P. Bismut, B. Pasquiou (PhD) Collaboration Anne Crubellier (Laboratoire Aimé Cotton)