Laboratoire de Physique des Lasers Université Paris Nord Villetaneuse - France A Chromium BEC in strong RF fields Benjamin Pasquiou, Gabriel Bismut, Paolo Pedri, Bruno Laburthe- Tolra, Etienne Maréchal, Laurent Vernac, Olivier Gorceix Quentin Beaufils
Chromium : S= in the ground state µ = 6µ B Large magnetic dipole-dipole interactions Long range (/r ) Anisotropic Pfau, PRL, 84 (8) d Vdd r r S S S r S r r ( ) = ( )( ). 5.. d-wave collapse in Stuttgart Rich spinor structure Large inelastic collision rate Dipolar relaxation : collisions with change of total magnetization (Einstein-de-Haas effect) m =± m = but E = gµ B S l B
Outline All optical condensation of 5 Cr. A Chromium BEC in a strong off-resonant Radio- Frequency (RF) magnetic field.
Cr Magneto-optical optical traps 5 Cr 5 Cr N = only 4. 6 bosons! N = 5. 5 fermions Very short loading times ( à ms) and small number of atoms : decay towards metastable states Inelastic light assisted collisions (dominant process) to orders of magnitude larger than in alkalis R. Chicireanu et al. Phys. Rev. A 7, 546 (6)
Our approach: accumulation of metastable atoms in an Optical Dipole Trap (ODT) 58 56 54 5 45nm 5 48 46 5 6 7 8 - ODT - - Metastable atoms shielded from light assisted collisions 4 6 8 Plus a few tricks: Dark spot repumpers RF sweeps Q.beaufils et al., Phys.Rev A. 77, 54 (8) 5 million atoms in the single beam OTD (75nm, 5W): More than in the MOT! Loading time : ms Temperature µk.
Evaporation cooling Suppress two-body inelastic losses : spin polarize into the lowest energy Zeeman state (use the 7 S 7 P transition at 47 nm) Loading a crossed optical dipole trap transfert IR power from the horizontal trapping beam to the vertical one (with a motorized λ/ waveplate) MOT Horizontal trap Repump and polarize 5 mw 5 W Vertical Trap ms 6 s Loading Evaporation Crossing ODT arms 6s
A chromium BEC Phase Sapce Density - - - -4 4 6 8 Time (ms) Evaporation ramp x atoms Pure BEC In situ TF radii 4 and 5 microns Density : 6. at/cm. 4 at/cm Condensates lifetime: a few seconds. Q.beaufils et al., Phys.Rev. A 77, 66(R) (8)
Outline All optical condensation of 5 Cr. A Chromium BEC in a strong off-resonant Radio- Frequency (RF) oscillating magnetic field
RF modifies the Landé factor We modify the Landé factor of the atoms g J with very strong off resonant rf fields. For a static field perpendicular to the RF, If the RF frequency ω is larger than the Larmor frequency ω, then: g J Ω ω (, Ω) = g J ω J Serge Haroche thesis S.Haroche, et al., PRL 4 6 (97) True in D Generalization in D? Ω E = mg J µ B ω m J B static Eigenenergies -..4.6.8..4 - - Ω ω Degeneracy in a non zero magnetic field!
We apply a rf such that : ω gµ BB Control magnetism We apply a small gradient. RF modifies the effect of such a gradient: ω J Ω ω = ms g J ( ω, Ω) µ B m B' t Q.beaufils et al., Phys.Rev. A 78, 56 (8)
8 7 6 5 4 8 7 6 5 4 8 7 6 5 4 7 6 5 4 7 6 5 4 8 7 6 5 4 5 5 5 5 5 5 5 5 5 5 5 5 5 Adiabaticity issues Diabatic - - Adiabatic Probability to come back to m=-..8.6.4.. Ω/ω=.8 τ Ω/ω=.6 4 5 6 7 8 4 5 6 7 8 Sweep time ( µ s) - m=- τ =5 µ s τ =8 µ s τ =5 µ s τ = µ s τ =5 µ s τ = µ s..5. -.5 -. B RF Ω ω 5 5 4 τ 5 t
Adiabaticity issues Adiabaticity depends on B// : d dt Ω <<ω //. Probability to stay in m=-.8.6.4.. - B // (mg) 4
Inelastic collision properties of off-resonantly rf dressed states : N+ Beware of the lowest energy state - argument!! - - 4 5 ω N - - - - 4 5 - - 4 5 N- - - - 4 5 Without RF, the lifetime is s
Interpretation: a rf-assisted dipolar relaxation Interatomic potentials Gap ~ Ω J V dd ω in = S = 6, m = 6, l =, m =, N S out = S = 6, m = 6, l =, m =±, N S ω l l Similar mechanism than dipolar relaxation in = S = 6, m =+ 6, l = out = S = 6, m =+ 5, l = S S Interparticle distance Within first order Born approximation: σ rf Ω dipolarrelaxation N N', m m ' = JN N' ( ms ms ') σm m ' ω S S S S Theory : Anne Crubellier (LAC IFRAF) and Paolo Pedri (IFRAF postdoc in our group)
σ Ω = J ( m m ') ω rf dipolarrelaxation N N', m m' N N' S S m m' σ A dipolar relaxation process between dressed states : Control of dipolar relaxation Amplitude: Ω JN N' ( ms ms') ω Outcoming energy: ( ) E = ( m m ') g µ B N N' ω s s J B Proposal with B RF // to B static : E = g µ B ω and j B = Einstein-de Haas m l effect
Summary All optical production of a chromium BEC. Modification of the Landé factor: close to spin degeneracy in a non zero magnetic field. RF-assisted dipolar relaxation.
Future Optical lattices dipolar gases in reduced dimensions. Feshbach resonances pure dipolar gases. Fermions degenerate Fermi sea of polarized atoms with dipole-dipole interactions.
O. Gorceix Q. Beaufils B. Laburthe G. Bismut E. Maréchal L. Vernac P. Pedri B. Pasquiou J. C. Keller Have left: T. Zanon, R. Barbé, A. Pouderous, R. Chicireanu Collaboration: Anne Crubellier (Laboratoire Aimé Cotton)
B rf (t) Classical interpretation µ (t) dµ = gj µ B dt rf (t) B static φ(t) dφ dt = Ω rf cos( ω rf t) T µ x dt cos( Φ( t)) = J T Ω ωrf rf Phase modulation -> Bessel functions e.g. light or matter diffraction; side-bands in frequency modulation; tunneling in modulated lattice (Arimondo 8)
H = H + + + ωs z + ωa a + λsz ( a a) mol + Analytical expression for dressed state (from C. Cohen-Tannoudji) First order perturbation theory: mλ + M, N = exp ( a a ) M, N ω K Ω, J ω ( ω Ω) = K ( ) + H dd Une autre démonstraction (Floquet analysis) Soit un état propre modulé en temps: i dψ dt m = ( H + m H cos( ω ) rf t Ψm e.g. different Zeeman states J N Ω ωrf Resonant coupling between m= and m= with echange of N photons