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All-optical production of chromium BEC s B essel E ngineering of C hromium

Laboratoire de Physique des Lasers Université Paris Nord Villetaneuse - France. All-optical production of chromium BEC s B essel E ngineering of C hromium. Bruno Laburthe Tolra. Statistical physics at very low T Bose-Einstein condensates Degenerate Fermi gases

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All-optical production of chromium BEC s B essel E ngineering of C hromium

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

  2. 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/r6) • isotropic • Study of dipole-dipole interactions in Quantum Degenerate gases • Dipole-dipole interactions : • ‘long range’ (1/r3) • anisotropic répulsive attractive • chromium: • magnetic moment : 6µB=> dipole dipole interactions x 36 • 1 boson et 1 fermion S=3

  3. First BEC : team of T. Pfau (Stuttgart 2005) Phys. Rev. Lett. 94, 160401 (2005) • 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 edd~1, condensate not stable. Stability depends on trapping geometry. • Collapse of condensate reveals dipolar pattern. Phys. Rev. Lett. 95, 150406 (2005) Nature. 448, 672 (2007) répulsive attractive 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…

  4. All optical production of a Chromium BEC • A Cr BEC in strongrffields • An rf-assisted d-waveFeshbachresonance • Tools, future

  5. 7P4 7P3 650 nm 600 425 nm 550 5S,D (2) (1) 500 427 nm Z 450 500 550 600 650 700 750 7S3 1 10 0 10 -1 10 Phase Sapce Density -2 10 -3 10 -4 10 3 2 4 6 8 10x10 Time (ms) How to make a Chromium BEC in 14s and one slide ? • An atom: 52Cr • An experiment • A small MOT N = 4.106 T=120 μK • A dipole trap • A BEC • An evaporation ramp • A crossed dipole trap

  6. Cr Magneto-optical traps • 52Cr • 53Cr N = 4.106 bosons T=120 μK density = 1.1 1011 atoms /cm3 Loading rate = 3.5 108 atoms/s N = 5.105 fermions T=120 μK density = 2.5 1010 atoms /cm3 Loading rate = 107 atoms/s Very short loading times (10 à 100 ms) and small number of atoms : • A MOT for a mixture (52Cr- 53Cr): N52,53 ~ 105 atoms • decay towards metastable states → repumpers (laser diodes at 663 and 654 nm) • R. Chicireanu et al. • Phys. Rev. A 73, 053406 (2006) • Inelastic collisions (dominant process) 2 to 3 orders of magnitude than alkalis Comparable values for He*. (2005)

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

  8. A mixed optical-magnetictrap for metastable52Cr • up to 1.2 106 atoms at 100 μK • fast accumulation: ~ 100 ms Number of atoms (millions) Loading rate : 107 s-1 Time (ms) Limitations: - Majorana losses - D-D inelastic collisions - loading rate 107 s-1 R Chicireanu et al., Euro Phys J D 45, 189 (2007)

  9. (i) Cancel magnetic forces with an rffield • What for : Load all magneticsublevels, and limitinelastic collisions by reducing the peakatomicdensity • How : Duringloading of the OT, magnetic forces are averaged out by rapidly spin flipping the atoms. RF Sweep m<0 m>0 (similarities Paul trap) Resonant spin flip at E(x) Sweep span to cover size of cloud x

  10. Which rf power? Landau-Zener adiabaticity criterion sets the minimal Rabi frequency: • What sweep rate? Spins must be flipped a large number of times in one oscillation period in the magnetic potential 1/wMT : !!! 150 Watts of rf !!! • Result ? More than 2 million atoms, in 100 ms Q. Beaufils et al., Phys. Rev. A , 77 , 053413 (2008) Loading rate : 2.107 s-1

  11. (ii) Load another metastable state : 5S2 • What we expect : • A lower inelastic loss parameter ? • A larger loading rate ? 7P4 7P3 Doubled laser diode 427 nm (~1 mW) 425nm 633nm 663nm 427nm 5D4 5S2 7S3 • Results? More than de 5 million atoms, in 35 ms • Loading rate = ¼ MOT loading rate ! • Opticallytrappedatoms > NMOT !

  12. Loading a dipole trap:Summary • Load5D4 et 5D3 : 1,2 million atoms(spring 2007) • (i) RF Sweeps : 2 million atoms(july 2007) • (i)*(ii) Load5D4 et 5S2 and rfsweeps 5 to 6 million atoms(octobre 2007) Loading rate : 107 s-1 Loading rate : 2 107 s-1 Loading rate : 1.5108 s-1 But… phase-space density ~10-6

  13. Suppress two-body inelastic losses : spin polarize into the lowest energy Zeeman state (use the 7S3 → 7P3 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 ( Dph.= n0Λ3dB ) • 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. 1 10 0 10 -1 10 -2 10 -3 10 -4 10 3 2 4 6 8 10x10 Time (ms) Repump and polarize MOT 500 mW ? Horizontal trap Vertical Trap 35 W 100 ms 16 s Loading Evaporation Phase Sapce Density Crossing both OT arms 6s (november 2007) 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.

  15. 17 000 atoms T = 80nK 10 000 atoms Pure BEC Thomas Fermi analysis + Castin-Dum expansion 5 ms -> RTF=19 microns Experimentally : 21 microns Chemical potentential of about 1 kHz  4 kHz (recompressed trap) In situ TF radii 4 and 5 microns Density : 6.1013 at/cm3 2.1014 at/cm3 Condensates lifetime: a few seconds. Q. Beaufils et al., Phys.Rev. A 77, 061601(R) (2008)

  16. All optical production of a Chromium BEC • A Cr BEC in strongrffields • An rf-assisted d-waveFeshbachresonance • Tools, future

  17. Eigenenergies Rf power Control of the Landé factor One canmodify the Landé factor of the atomsgJwithverystrong off resonantrffields. If the RF frequencyωislargerthan the Larmor frequencyω0, gJismodified : • Serge Haroche thesis • S.Haroche, et al., PRL 24 16 (1970) • True in 2D… Generalization in 3D ? 3 2 1 0 -1 Can we use thisdegeneracy for spinorphysics ? See L. Santos et al., PRA 75, 053606 (2007) -2 -3 A spinor is a multicomponent BEC (with degenerate components): the magnetic fields needs to be small (interaction energy > Zeeman energy) < 1 mG !!...

  18. Brf(t) m(t) f(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 onW/w. Good agreement with Bessel function up to 2.4

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

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

  23. x1000 7 6 r e b 5 m u n 4 m o t A 3 50 100 150 200 Time (ms) Inelastic collision properties of off-resonantly rf dressed states : Beware of the lowest energy state argument !! Two timescales : collision time << dressing time. • 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 ?

  24. All optical production of a Chromium BEC • A Cr BEC in strongrffields • An rf-assisted d-waveFeshbachresonance • Tools, future

  25. Superelastic collision A d-wave Feshbach resonance in chromium 0.4 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. 0.3 0.2 Energy (arb.) 0.1 0.0 -0.1 -0.2 1 2 3 4 First seen in J. Werner et al., PRL 94, 183201 (2005) Internuclear distance (arb.) 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

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

  27. Temperature dependence 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 ?

  28. Interpretation 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 • Conclusions: • - « 2-body » three-body losses. • Loss parameter proportionnal to T • -Feshbach coupling measured; very narrow

  29. Can such a resonance be used to tailor anisotropic interactions in a BEC ? Feshbach coupling psd If Gd>>Gm 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 Gm>>w , but then the lifetime of the cloud would be also shorter than the trap frequency !

  30. 0.4 0.3 0.2 0.1 0.0 -0.1 -0.2 1 2 3 4 Rf photon Rf in the vicinity of the Feshbach resonance 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 Resonant losses when w=Eb-Ei 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. 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 1st 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 strongrffields • An rf-assisted d-waveFeshbachresonance • Tools, future

  34. Thanks! PhD: Q. Beaufils (2nd 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) • 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)

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