Condensation du chrome et collisions assistées par champs radio-fréquence

Transcription

1 Laboratoire de Physique des Lasers Université Paris Nord Villetaneuse - France Condensation du chrome et collisions assistées par champs radio-fréquence Q. Beaufils B. Laburthe B. Pasquiou Paolo Pedri E. Maréchal O. Gorceix G. Bismut L. Vernac Have left: J. C. Keller, T. Zanon, R. Barbé, A. Pouderous, R. Chicireanu Collaboration: Anne Crubellier (Laboratoire Aimé Cotton)

2 Chromium : S=3 Large sensitivity to (rf) magnetic fields g = = 3,..., 3 J m S Initial motivation for chromium: strong magnetic traps Doyle, Phys. Rev. A 57, R373 (998) No hyperfine structure Simplification (?) for MOT Purely linear Zeeman effect; simple description of rf-dressed states

3 Large magnetic dipole-dipole interactions ε dd BEC: Stuttgart 004 Villetaneuse 007 = V V dipolaire contact = 0.6 répulsive Stuttgart: modification of self-similar expansion attractive Pfau, PRL 95, (005) Tune contact interactions using Feshbach resonances: dipolar interaction larger than Van-der-Waals interaction Nature. 448, 67 (007) Stuttgart: d-wave collapse Pfau, PRL 0, (008) And collective excitations, Tc, solitons, vortices, Mott physics, D or D physics

4 Large inelastic losses Large dipole-dipole interactions + No hyperfine interactions = V dd μ = S 4π R 0 3cos ( θ ) ( g J μb ) 3 Anisotropic dipole-dipole interactions a nice system to study inelastic collisions Different partial waves are coupled Δl = Control of inelastic collisions (energy of output channel, geometry) - Feshbach resonances due to dipole-dipole interactions Pfau, Appl. Phys. B, 77, 765 (003) Pfau, Nature Physics, 765 (006)

5 Rich spinor physics An new phase diagram: Santos and Pfau PRL 96, (006) ΔE = ΔmSμBB Effect of dipole-dipole interactions: collisions with change of total magnetization (Einstein-de-Haas effect) Need of an extremely good control of B (or of the difference of energy between Zeeman substates) Ueda, PRL 96, (006)

6 I Condensation tout-optique du chrome II Contrôle de collisions inélastiques par champs radio-fréquence -Relaxation dipolaire -Association de molécules III Contrôle du facteur de Landé par champs radiofréquence

7 An atom: 5 Cr 7 P 4 An oven A Zeeman slower 7 P nm Oven at 550 C (Rb 50 C) A small MOT 45 nm (Rb=780 nm) 7 S 3 47 nm 5 S,D 600 () () 550 N = (Rb=0 9 or 0 ) Stuttgart roadmap: Load a magnetic trap And evaporate Z A dipole trap A BEC every 5 s All optical evaporation A crossed dipole trap

8 Cr Magneto-optical traps 5 Cr R. Chicireanu et al.phys. Rev. A 73, (006) 53 Cr N = bosons Loading rate = atoms/s N = fermions Loading rate = 0 7 atoms/s Very short loading times (0 à 00 ms) and small number of atoms : decay towards metastable states repumpers (laser diodes at 663 and 654 nm) Inelastic collisions (dominant process) λ β π v to 3 orders of magnitude than alkalis Comparable values for He*.

9 Our approach: cw accumulation of metastable atoms in an optical trap Metastable atoms shielded from light assisted collisions The optical trap: IPG fiberized laser 075 nm Horizontal beam - ~40 µm waist Depth : ~ 500μK (parametric excitations) R Chicireanu et al., Euro Phys J D 45, 89 (007)

10 Two improvements: (i) Cancel magnetic forces with an rf field What for : Load all magnetic sublevels, and limit inelastic collisions by reducing the peak atomic density!!! 50 Watts of rf!!! How : During loading of the OT, magnetic forces are averaged out by rapidly spin flipping the atoms RF Sweep m>0 m<0 (similarities Paul trap) 7 P 4 (ii) Depump towards metastable state : 5 S What we expect : A lower inelastic loss parameter? A larger loading rate? 7 P 3 45nm 633nm 663nm 47nm 5 S 7 S 3

11 Loading a dipole trap: Summary Load 5 D 4 et 5 D 3 :, million atoms (i) RF Sweeps : million atoms Loading rate : 0 7 s - Loading rate : 0 7 s - Q. Beaufils et al., Phys. Rev. A 77, (008) (i)*(ii) Load 5 D 4 et 5 S and rf sweeps 5 to 6 million atoms Loading rate :.50 8 s - Loading rate = ¼ MOT loading rate But phase-space density ~0-6

12 Repump in 7 S 3 and polarize in m=-3 (suppression of all two-body losses) MOT 500 mw Horizontal trap 35 W Vertical Trap ms 6 s Loading Evaporation Crossing both OT arms 6s Relative polarization of the laser beams matters! Phase Sapce Density Time (s) 8 0

13 Thomas Fermi Radii (µm) Tc=50 nk Pure BEC: to atoms Time (ms) Chemical potentential of about khz ö 4 khz (recompressed trap) In situ TF radii 4 and 5 microns Density : at/cm 3 ö.0 4 at/cm 3 Condensates lifetime: a few seconds. Q. Beaufils et al., Phys.Rev. A 77, 0660(R) (008)

14 I Condensation tout-optique du chrome II Contrôle de collisions inélastiques par champs radio-fréquence -Relaxation dipolaire -Association de molécules III Contrôle du facteur de Landé par champs radiofréquence

15 What is dipolar relaxation? ( ),3 3,,3 3 + ( ) 3 0 ). )(. 3(. 4 R u S u S S S g V R R B J dd r r = μ π μ - Only two channels for dipolar relaxation in m=3 (no relaxation in m=-3): ( ) i f i f B J dd k k k k h m g S V + = πh μ μ π,,3 3 ( ) i f i f B J dd k k k k h m g S V + = πh μ μ π B g E B J μ = Δ B g E B J μ = Δ = Δl In the Born approximation Pfau, Appl. Phys. B, 77, 765 (003) Rotate the BEC? (Einstein-de-Haas) ( ) ( ) ( ) S r S r zs S r S r zs S S S S S S z z z z rotation! Dipole-dipole interactions exchange Control of inelastic collisions (energy of final state, geometry) ( ) iy x r + = + = Δl

16 Experimental procedure; typical results BEC m=+3, vary time detect BEC m=-3 Lose BEC x0-3 Atom Number Width (u.a.) Decrease of TF radius (N goes down) 0 dn dt 0 = βn Time (ms) Γn 80 dn dt 00 = ΓN 0 0 /5 5 mω β 4π h a Temps (ms) 6/5 N 7 / Fit gives β

17 Comparison theory / experiment / β exp β Born It has been shown (Pfau, Appl. Phys. B, 77, 765 (003) that the Born approximation is ok for B<G and B> 0 G not in between! (see Shlyapnikov, PRA 53, 447 (996)) Champ magnétique (G)

18 Interpretation Gap ~ V dd a S E f in = = S = 6, m = 6, l = 0 g J μ B B out = S = 6, m = 5, l = R in V eff ( R) = l( l + ) h μr R in = a S Zero coupling Determination of scattering lengths S=6 and S=4 (in progress, Anne Crubellier) NB: two output channels (Δm=, Δm=), with two different output energies. Selective cancellation of a given channel for a given magnetic field!

19 Perspectives: dipolar relaxation in reduced dimension (D gaz) D Lattice (retro-reflected Verdi laser) Cr BEC diffracted by lattice BEC m=+3, vary time Δmg J μ B B < hω L st BZ detect BEC m=-3 Band mapping Dipolar relaxation in reduced dimension (D) Lose BEC (D thermal gas) Stay in first Brillouin zone, i.e., stay in lowest band : no vibrational excitation in lattice!

20 Conclusions: - Rates are well understood. - Typical output (Zeeman) energy much larger than chemical potential 3,3, l = 0 l = ( 3, +,3 ), ΔE = g J μb B 3,3, l = 0,, l = ΔE = g J μb B The spin magnetic moment is transferred into orbital interatomic moment. Can we measure this rotation? Ueda, PRL 96, (006) Can we «store» the produced energy? - Into a vibration excitation of the lattice: apparently not - Use rf-dressed states : dipolar relaxation between manyfolds

21 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. r B rf (t) μ r (t) r dμ r r = g Jμ B rf(t) dt r μ = cste Dipolar interactions: répulsive attractive No rf 3cos( θ) φ θ Rf perpendicular to static field : a new geometrical dependence! Ω Ω 3cos( θ) + J0 3cos( θ)sin( θ)cos( φ) J ω ω 0

22 Inelastic collision properties of off-resonantly rf dressed states : /e lifetime (ms) Beware of the lowest energy state argument!! N+ N ω N- W/w See also Verhaar, PRA, 53, 4343 (996)

23 Interpretation: an rf-assisted dipolar relaxation Gap ~ Ω J V dd ω in = S = 6, m = 6, l = 0, N Similar mechanism than dipolar relaxation in = S = 6, m = + 6, l = 0 E f = hω g rf J μ B B out = S = 6, m = 5, l =, N out = S = 6, m = + 5, l = σ Within first order Born approximation: rf N N ', m m' Ω dipolarrelaxation = J N N ' ( m m') σ m m' ω In collaboration with Anne Crubellier (LAC Ifraf) and Paolo Pedri (Ifraf postdoc in our group) ( E = ( m m') g μ B ( N N' ) hω ) f J B (B rf parallel to B) rf

24 σ rf N N ', m m'.0x0-8 Ω dipolarrelaxation = J N N ' ( m m') σ m m' ω ( E = ( m m') g μ B ( N N' ) hω ) f Analytic calculation by Paolo Pedri, no adjustable parameter J B rf Tw o body loss parameter (m^3/s) Dipolar relaxation between dressed states: Control: Coupling Output energy: E f J Ω ( ω N N ' m m' ) = ( m m') g μ B J B ( N N' ) hωrf 0 Ω/ω 3 4

25 Why Bessel functions? r B rf r // B 0 H = H Analytical expression for dressed state (from C. Cohen-Tannoudji) hω0s z + hωa a + λsz ( a a) mol + mλ + M, N = exp ( a a ) M, N hω First order perturbation theory: Another equivalent approach (Floquet analysis) K Ω, J ω ( ω Ω) = K ( ) 0 + H dd Modulate the eigenenergy of an eigenstate: ih dψ dt m = ( H + mδh cos( ω ) rf t Ψm e.g. different Zeeman states t i Ω Ω Ψ ω t ωrf t ( ) = Ψ exp = Ψ n sin( ) ω exp rf n ω 0 rf Resonant coupling between m= and m=0 with echange of N photons n () i J ( i( ( ω nω) t) ) J N Ω ωrf

26 Une proposition pour voir l effet Einstein de Haas: Mettre en rotation le condensat par relaxation dipolaire assistée par photons rf! On sait faire des condensats de chrome La relaxation dipolaire crée du moment orbital, mais aussi une énergie magnétique >> μ On sait contrôler la relaxation dipolaire par champs rf: -l amplitude de transition Ω J N N ' ( m m' ) ω -l énergie dans le canal de sortie! E f = ( m m') g μ B J B ( N N' ) hωrf On veut E f μ Contrôle de B au voisinage de 0 au khz près (difficile) Contrôle de B au voisinage de 00 khz au khz près (facile) + rf

27 I Condensation tout-optique du chrome II Contrôle de collisions inélastiques par champs radio-fréquence -Relaxation dipolaire -Association de molécules III Contrôle du facteur de Landé par champs radiofréquence

28 (digression) Un autre cas de collision inélastique en présence de champ rf: l association rf de molécules Un champ magnétique est modulé au voisinage d une résonance de Feshbach Production résonante de molécules froides quand hω rf = E b Énergie de liaison Mais la rf ne couple pas deux potentiels moléculaires différents! (règle de sélection) Ni deux états vibrationnels d un même potentiel (orthogonalité) C est l opérateur qui couple les spins (dipôle-dipôle, hyperfin) qui couple les états. La résonance est assurée par l émission ou l absorption d un photon rf. See also: S. T. Thomson et al., PRL (005), C. Ospelkaus et al., PRL 97, 040 (006), F. Lang et al., Nature Physics 4, 3 (008), T. M. Hanna et al., PRA, (007), C. Weber et al., PRA 78, 0660(R) (008), C. Klempt et al., PRA 78, 0660(R) (008) Notre contribution : une interprétation en terme d atomes habillés, et une formule universelle pour l association de molécules.

29 Feshbach resonances in chromium Pfau, J. Mod Opt. 54, 647 (007), Phys. Rev. Lett. 94, 830 (005) This talk

30 0.4 A Feshbach resonance in d-wave collisions Energy (arb.) S = 6; m = 5; l = 0 > S g μ B S = 6; m = 6; l = ; m =+ > S B l 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 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 Superelastic collision

31 Interpretation Γm ( ε ) = π Ψbound Vdd Ψ ε Thermal averaging, when Γ ) m ( ε 0 << Γ d << π Γm ( ε ) Γd σ ( k) = k ( ε ε ) + ( Γ ( ε ) + Γ ) Feshbach coupling ε k B T 0 (l+ ) / m d / 4 Γd = nγ d Superelastic rate F. H. Mies et al., PRA, 6, 07 (000) P. S. Julienne and F. H. Mies, J. Opt. Soc. Am. B. 6, 57 (989). π (l + ) ε 0 K T = Γ ( ) m( ε 0) exp hqt kbt Calculation with no adjustable parameter (adiabatic elimination of Γ d ) (Anne Crubellier LAC) Γ m (ε) n& = αγ ( 3 nλ ) n m db psd Losses = Rate of coupling to the molecular bound state = Rate of association through the barrier

32 00 40x0 80 x0 - Γ Γ m m Theory 5 ( ε ) = k B T = 8μK Experiment 5 ( 5.5 ± 3) 0 k B T = μk ( ε ) = K (m s ) Three-body losse parameter strongly depends on T Width of resonant losses strongly depends on T Magnetic field (MHz) Q. Beaufils et al., arxiv:08.48

33 Rf in the vicinity of the Feshbach resonance gμ B B Rf photon We modulate the magnetic field close to the 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 ω=e b -E i

34 Loss analysis in the dressed molecule approach: K Ω, J ω ( ω Ω) = K ( ) Analogy with dipolar collisions of Rydberg atoms in a micro-wave field Pillet Phys. Rev. A, 36, 3 (987) Gallagher Phys. Rev. A, 45, 358 (99) K /K (0) khz khz khz khz khz 400 khz khz Ω /ω 4 5 Q. Beaufils et al., arxiv: Association rf of molecules = a Feshbach resonance between dressed states

35 I Condensation tout-optique du chrome II Contrôle de collisions inélastiques par champs radio-fréquence -Relaxation dipolaire -Association de molécules III Contrôle du facteur de Landé par champs radiofréquence

36 Another use of rf for spinor physics: rf control of the Landé factor A spinor is a multicomponent BEC (with degenerate components): the magnetic fields needs to be small (interaction energy > Zeeman energy) < mg!!... 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, then: g J Ω ω (, Ω) = g J ω J 0 Serge Haroche thesis S.Haroche, et al., PRL 4 6 (970) True in D Generalization in 3D? Eigenenergies Rf power Can we use this degeneracy for spinor physics?

37 r B rf (t) φ(t) μ r (t) r dμ r r = gjμ B dt dφ dt Classical interpretation rf (t) = Ω rf cos( ω rf t) T dt cos( Φ( t)) = μx 0 T 0 J Ωrf ωrf Phase modulation -> Bessel functions e.g. side-bands in frequency modulation; tunneling in modulated lattice (Arimondo PRL (007)) light or matter diffraction

38 We apply blue detuned rf fields to a Cr BEC in a one beam optical trap, plus a magnetic field gradient. B = 0 at the center of the trap. The atoms, high field seekers, leave the center of the trap. RF modifies the effect of such a gradient: Control magnetism B (t) rf V(r) Δ = m S g J ( ω, Ω) μbb' m t Rf dressing is reversible (adiabatic) Q. Beaufils et al., Phys. Rev. A 78, (008)

39 Adiabaticity issues Adiabaticity depends on B par : dω <<ω dt par

40 A reversible dressing Probability to come back to m= Ω/ω=.8 Ω/ω=3.6 τ=500 μs τ=80 μs τ=50 μs τ=3 μs τ=5 μs τ=0 μs Sweep time ( μs) m= If rf is applied and removed sufficiently slowly, the atoms come back to the initial Zeeman substate state. Q. Beaufils et al., Phys. Rev. A 78, (008) NB see also Phys. Rev. Lett. 4, 974 (970) : Control Rb-Cs spin exchange Perspectives for spinor physics: Be B-independent 3D control inelastic collisions

41 Conclusion On sait produire des condensats de chrome On a analysé la relaxation dipolaire (contrôle par champ magnétique et par confinement) On sait contrôler par champs rf la relaxation dipolaire Les champs rf peuvent aussi modifier le facteur de Landé des atomes On a analysé l association rf de molécules Perspectives Vers l observation de l effet Einstein-de-Haas Expériences dans les réseaux optiques Produire des champs magnétiques élevés pour contrôler la longueur de diffusion Annulation du facteur de Landé à trois dimensions, et physique des spinors Fermions

42 Have left: T. Zanon, R. Barbé, A. Pouderous, R. Chicireanu Collaboration: Anne Crubellier (Laboratoire Aimé Cotton)