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All-optical formation of a chromium Bose-Einstein Condensate

Joint IFRAF-Holland Workshop – Paris– 19 May 2008. All-optical formation of a chromium Bose-Einstein Condensate. Olivier Gorceix. Laboratoire de Physique des Lasers Université Paris Nord - CNRS - IFRAF. Outline:. Dipolar effects in ultra-cold gases Chromium specificities

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All-optical formation of a chromium Bose-Einstein Condensate

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  1. Joint IFRAF-Holland Workshop – Paris– 19 May 2008 All-optical formation of a chromium Bose-Einstein Condensate Olivier Gorceix Laboratoire de Physique des Lasers Université Paris Nord - CNRS - IFRAF

  2. Outline: • Dipolar effects in ultra-cold gases • Chromium specificities • Cold bosonic and fermionic Cr atoms • Mixed magnetic and optical trapping of metastable Cr* atoms • New (rf-based) stategies to combat inelastic collisions • All-optical Condensation of Cr • RF spectroscopy and association of cold Cr2 molecules

  3. Dipole-dipole interactions Applications range from astrophysics to quantum computing. Hundreds of theoretical papers in recent years. Many theory groups but few experimental demonstrations.  Long range - 1/r3 interaction Anisotropic interaction Attractive   Repulsive      * Trap geometry is important ; * Dipolar interaction can be tailored ; * Feshbach resonances can yield a control of the contact interaction. (Pfau and coll.)

  4. Dipolar effects in ultra-cold gases • Dipolar bosons in optical lattices: • 1D lattice, repulsive interactions : reduction of three body recombination • 2D lattice, attractive interactions: solitons • New quantum phases • Dipolar fermions: • Thermalization in a spin-polarized Fermi gas Magnetic dipole-dipole interaction : long range and anisotropic

  5. Chromium relevant properties: • Dipolar effects in ultra-cold gases which stem from the ground state electronic structure [Ar] 3d5 4s1 S=3 -> magnetic moment of 6 µB • 8% abundant fermionic isotope 53Cr • bosonic and fermionic Cr atoms can be laser cooled But also: • Several metastable states • Large inelastic Collision loss rates -> new strategies

  6. Cr schematic level structure 7 P4 3d5 4p1 G = 3.2 107 s-1 Leaks towards metastable levels ~170 s-1 for 52Cr 7 P3 Repumpers 654 and 633 nm MOT cooling transition 3d4 4s2 5 DJ 6 µ B 5 S2 425.55 nm Isat= 8.5 mW/cm2 6 µ B 7 S3 3d5 4s1

  7. Experimental setup Ti:Sa 1.45W@850nm doubling cavity 350mW@425nm 2 red ECDL to repump metastable atoms 4mW@427nm for spin polarization High temperature oven PSD0 = 10-18 1-meter long Zeeman slower

  8. Laser sources Extended cavity laser diodes few mW around 650 nm Ti:Sa laser :1,6 W at 851 nm Hollow cathode lamp Doubling cavity: 350 mW at 425,5 nm +50 W at 1075 nm fiber laser for optical trapping + 5mW at 427 nm – laser diode+doubling cavity for optical pumping + 18W Verdi laser for pumping the Ti:Sa and for optical lattices

  9. Chromium MOTs Bosonic 52Cr MOT: Fermionic 53Cr MOT: N∞ = 4 106 bosons T=120 μK PSD 5 10-7 Loading rate 4.108 atoms / s Loading time about 20 ms Density = 1. 1011 atoms /cm3 N∞ = 5 105 fermions T=120 μK 107 atoms / s density = 2.5 1010 atoms /cm3 also mixed two-isotope MOTs Fairly limited atom numbers in steady-state MOTs: • decay towards metastable states (halo) • strong inelastic collisions (spring 2005)

  10. Chromium level scheme 7 P4 Isat = 8.5 mW/cm2 3d5 4p G / 2p = 5 MHz t = 32 ns Spontaneous decay 7 P3 ~250 s-1 5D4,3 6 µ B 3d4 4s2 663-654-633 nm Repumpers 425.55 nm 427.60 nm 5S2 3d5 4s [Ar] 3d5 4s 7 S3 6 µ B

  11. Continuous loading of the magnetic trap • Atoms spontaneously decay from the MOT into metastable states • They remain trapped in the MOT gradient (if m<0) • Red repumping yields a ten fold increase in N 52Cr:4.107 atoms at 100 µK ; 53Cr:106 atoms at 100 µK Study of the collisional properties of metastable D states in 52Cr: • elastic cross section : σel=7 10-16 cm2 • DD inelastic collision parameter: βDD=3.3 10-11 cm3/s • PD inelastic collision parameter: βPD=4.9 10-10 cm3/s (summer 2006) • R. Chicireanu et al. • PRA 76 023406 (2007)

  12. !!! 2 to 3 orders of magnitude larger than for the alkalis Light-assisted inelastic collisions in Cr MOTs βSP ~ 4.10-9 cm3/s for the fermion 6.10-10 cm3/s forthe boson about 10-9 cm3/s for the mixed MOT

  13. Outline: • Dipolar effects in ultra-cold gases • Chromium specificities • Cold bosonic and fermionic Cr atoms • Mixed magnetic and optical trapping of metastable Cr* atoms • New (rf-based) stategies to combat inelastic collisions • All-optical Condensation of Cr • RF spectroscopy and association of cold Cr2 molecules

  14. Optical trapping of metastable Cr atoms Condensation of Cr is not possible in a magnetic trap (dipolar relaxation scales as µ3) • S. Hensler et al. • Appl.Phys.B 77 765 (2003) We continuously accumulate Cr* atoms in a mixed magnetic + single-beam optical trap. Sequence : MOT + OT Switch-off MOT beams and field Repump to ground state (bss<<bdd) Spin polarization in lowest-energy sub-state m=-3 Capture an absorption image

  15. Optical trapping of metastable Cr atoms Optical trap depth: 500μK (parametric excitation measurement on retroreflected 35W with waist 40µm) • up to 1.4 106 atoms @ 100μK (TOF) • very fast accumulation ~100 ms • Loading rate on the order of 107 atoms/s • Limitations: • Majorana spin-flips • D-D inelastic collisions • Both worse than in the 3D Mag trap because of the optical radial confinement • R.Chicireanu et al. • arXiv:0705.1479 • (EPJD 45, 189 (2007))

  16. Spin polarization of the trapped atoms • To inhibit the inelastic collisions : • repump the Cr* atoms back to the ground state ( 7S3 ) • polarize them in the lowest-energy sub-state m=-3 (using 7S3 → 7P3 at 427 nm) - along with leaks towards 5S2

  17. A crossed optical-dipole trap • Loading a crossed optical dipole trap • Continuous loading of the dimple: • high peak density ~ 1012 atoms /cm3 • BUT: deleterious inelastic collisions Strategy: form a 1D ODT and then form a dimple since direct loading in the dimple doesn’t work This is performed through a computer controlled rotation of a l/2 plate that induces a dynamical dimple formation • Inhibiting inelastic collisions: • repumping Cr* to the ground state ( 7S3 ) • spin-polarization in the lowest-energy Zeeman sub-state m=-3 • (using the 7S3 - 7P3 transition) • Perform evaporative cooling …through ramping down the IR power

  18. Fast RF sweeps to cancel magnetic forces Fast RF sweeps to cancel magnetic forces Fast RF sweeps to cancel magnetic forces Fast RF sweeps to cancel magnetic forces Fast RF sweeps to cancel magnetic forces Fast RF sweeps to cancel magnetic forces Fast RF sweeps to cancel magnetic forces Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. In situ images: No sweep Sweeped In situ images: No sweep Sweeped In situ images: No sweep Sweeped In situ images: No sweep Sweeped In situ images: No sweep Sweeped In situ images: No sweep Sweeped In situ images: No sweep Sweeped • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping How Fast ? Many times per oscillation frequency in the magnetic trap MT How Fast ? Many times per oscillation frequency in the magnetic trap MT How Fast ? Many times per oscillation frequency in the magnetic trap MT How Fast ? Many times per oscillation frequency in the magnetic trap MT How Fast ? Many times per oscillation frequency in the magnetic trap MT How Fast ? Many times per oscillation frequency in the magnetic trap MT How Fast ? Many times per oscillation frequency in the magnetic trap MT How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth. How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth. How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth. How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth. How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth. How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth. How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth. First attempts to reach BEC: Evaporative cooling in a crossed optical trap Spring 2007 Evaporative cooling down to degeneracy By lowering the overall optical power (AOM control) Still unsuccessful despite a gain in phase space density (up to 5.10-4) (spring 2007 –Ninit =1.2 million – 5D4 and 5D3 accumulation and the optimal dimple formation time) Need for better starting conditions Since the gain in phase space density follows a (Ninit)4 power law see K. O’Hara et al PRA 64, 051403 Absorption image of Cr atoms in a crossed optical trap. 150 000 atoms at T=16µK. Scientific goals Scientific goals Scientific goals Scientific goals Fast RF sweeps to cancel magnetic forces Fast RF sweeps to cancel magnetic forces Fast RF sweeps to cancel magnetic forces Fast RF sweeps to cancel magnetic forces Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. Fast RF sweeps to cancel magnetic forces Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. Fast RF sweeps to cancel magnetic forces Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. In situ images: No sweep Sweeped Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. In situ images: No sweep Sweeped Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. In situ images: No sweep Sweeped Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. In situ images: No sweep Sweeped In situ images: No sweep Sweeped In situ images: No sweep Sweeped • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping How Fast ? Many times per oscillation frequency in the magnetic trap MT • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping How Fast ? Many times per oscillation frequency in the magnetic trap MT • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth. How Fast ? Many times per oscillation frequency in the magnetic trap MT • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth. How Fast ? Many times per oscillation frequency in the magnetic trap MT • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth. How Fast ? Many times per oscillation frequency in the magnetic trap MT How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth. How Fast ? Many times per oscillation frequency in the magnetic trap MT How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth. How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth.

  19. Outline: • Dipolar effects in ultra-cold gases • Chromium specificities • Cold bosonic and fermionic Cr atoms • Mixed magnetic and optical trapping of metastable Cr* atoms • New (rf-based) stategies to combat inelastic collisions • All-optical Condensation of Cr • RF spectroscopy and association of cold Cr2 molecules

  20. Fast RF sweeps to cancel magnetic forces Fast RF sweeps to cancel magnetic forces Fast RF sweeps to cancel magnetic forces Fast RF sweeps to cancel magnetic forces Fast RF sweeps to cancel magnetic forces Fast RF sweeps to cancel magnetic forces Fast RF sweeps to cancel magnetic forces Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. In situ images: No sweep Sweeped In situ images: No sweep Sweeped In situ images: No sweep Sweeped In situ images: No sweep Sweeped In situ images: No sweep Sweeped In situ images: No sweep Sweeped In situ images: No sweep Sweeped • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping How Fast ? Many times per oscillation frequency in the magnetic trap MT How Fast ? Many times per oscillation frequency in the magnetic trap MT How Fast ? Many times per oscillation frequency in the magnetic trap MT How Fast ? Many times per oscillation frequency in the magnetic trap MT How Fast ? Many times per oscillation frequency in the magnetic trap MT How Fast ? Many times per oscillation frequency in the magnetic trap MT How Fast ? Many times per oscillation frequency in the magnetic trap MT How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth. How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth. How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth. How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth. How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth. How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth. How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth. Fast RF sweeps to improve the optical trap loading Motivation : In the mixed “Mag+Opt” trap, accumulation is hampered by inelastic collisions, Majorana losses and limited by state selective loading. The trap is strongly confining in all three directions, as the magnetic trap dominates along the axis of the laser beam. High-field seekers (m>0) are lost along the axis. In addition, the magnetic trap is switched off anyway in the end… Main Idea : • Average magnetic forces to zero by sweeping the frequency of an intense rf fields to rapidly flip the spin of the atoms. Sequence : MOT + OT + rf sweeps (100ms) switch-off MOT Repump to ground state Capture an absorption image Absorption images and cuts of Cr atom clouds in a dressed optico-magnetic trap ((1) without the rf and (2) with a frequency swept rf field). Scientific goals Scientific goals Scientific goals Scientific goals Fast RF sweeps to cancel magnetic forces Fast RF sweeps to cancel magnetic forces Fast RF sweeps to cancel magnetic forces Fast RF sweeps to cancel magnetic forces Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. Fast RF sweeps to cancel magnetic forces Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. Fast RF sweeps to cancel magnetic forces Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. In situ images: No sweep Sweeped Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. In situ images: No sweep Sweeped Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. In situ images: No sweep Sweeped Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. In situ images: No sweep Sweeped In situ images: No sweep Sweeped In situ images: No sweep Sweeped • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping How Fast ? Many times per oscillation frequency in the magnetic trap MT • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping How Fast ? Many times per oscillation frequency in the magnetic trap MT • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth. How Fast ? Many times per oscillation frequency in the magnetic trap MT • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth. How Fast ? Many times per oscillation frequency in the magnetic trap MT • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth. How Fast ? Many times per oscillation frequency in the magnetic trap MT How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth. How Fast ? Many times per oscillation frequency in the magnetic trap MT How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth. How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth.

  21. Fast RF sweeps to cancel magnetic forces Fast RF sweeps to cancel magnetic forces Fast RF sweeps to cancel magnetic forces Fast RF sweeps to cancel magnetic forces Fast RF sweeps to cancel magnetic forces Fast RF sweeps to cancel magnetic forces Fast RF sweeps to cancel magnetic forces Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. In situ images: No sweep Sweeped In situ images: No sweep Sweeped In situ images: No sweep Sweeped In situ images: No sweep Sweeped In situ images: No sweep Sweeped In situ images: No sweep Sweeped In situ images: No sweep Sweeped • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping How Fast ? Many times per oscillation frequency in the magnetic trap MT How Fast ? Many times per oscillation frequency in the magnetic trap MT How Fast ? Many times per oscillation frequency in the magnetic trap MT How Fast ? Many times per oscillation frequency in the magnetic trap MT How Fast ? Many times per oscillation frequency in the magnetic trap MT How Fast ? Many times per oscillation frequency in the magnetic trap MT How Fast ? Many times per oscillation frequency in the magnetic trap MT How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth. How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth. How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth. How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth. How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth. How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth. How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth. Fast RF sweeps to improve OT loading (a and b) How powerful should be the rf ? L-Z criterion for adiabatic crossing W rf Rabi frequency, nmin , nmax sweep interval, tsweep sweep period: RF power 150W How to choose the frequency span ? nmin ~ (rf Rabi frequency ~ 500 kHz) nmin ~ 7 MHz as set by the Zeeman effect at the trap Rayleigh length Scientific goals Scientific goals Scientific goals Scientific goals Fast RF sweeps to cancel magnetic forces Fast RF sweeps to cancel magnetic forces Fast RF sweeps to cancel magnetic forces Fast RF sweeps to cancel magnetic forces Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. Fast RF sweeps to cancel magnetic forces Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. Fast RF sweeps to cancel magnetic forces Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. In situ images: No sweep Sweeped Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. In situ images: No sweep Sweeped Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. In situ images: No sweep Sweeped Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. In situ images: No sweep Sweeped In situ images: No sweep Sweeped In situ images: No sweep Sweeped • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping How Fast ? Many times per oscillation frequency in the magnetic trap MT • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping How Fast ? Many times per oscillation frequency in the magnetic trap MT • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth. How Fast ? Many times per oscillation frequency in the magnetic trap MT • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth. How Fast ? Many times per oscillation frequency in the magnetic trap MT • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth. How Fast ? Many times per oscillation frequency in the magnetic trap MT How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth. How Fast ? Many times per oscillation frequency in the magnetic trap MT How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth. How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth.

  22. Fast RF sweeps to cancel magnetic forces Fast RF sweeps to cancel magnetic forces Fast RF sweeps to cancel magnetic forces Fast RF sweeps to cancel magnetic forces Fast RF sweeps to cancel magnetic forces Fast RF sweeps to cancel magnetic forces Fast RF sweeps to cancel magnetic forces Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. In situ images: No sweep Sweeped In situ images: No sweep Sweeped In situ images: No sweep Sweeped In situ images: No sweep Sweeped In situ images: No sweep Sweeped In situ images: No sweep Sweeped In situ images: No sweep Sweeped • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping How Fast ? Many times per oscillation frequency in the magnetic trap MT How Fast ? Many times per oscillation frequency in the magnetic trap MT How Fast ? Many times per oscillation frequency in the magnetic trap MT How Fast ? Many times per oscillation frequency in the magnetic trap MT How Fast ? Many times per oscillation frequency in the magnetic trap MT How Fast ? Many times per oscillation frequency in the magnetic trap MT How Fast ? Many times per oscillation frequency in the magnetic trap MT How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth. How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth. How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth. How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth. How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth. How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth. How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth. Fast RF sweeps to improve OT loading (c) How fast should be the frequency sweep ? Spin flip should occur many time during an oscillation period in the Mag trap Experiment status in oct. 2007 Accumulation in 5D4 state before dimple formation and evaporation 2.2 106 atoms at 100µK (july 2007) gathered in <100ms in the (retrorefl. longitudinal) optical trap No rf heating !! Scientific goals Scientific goals Scientific goals Scientific goals Fast RF sweeps to cancel magnetic forces Fast RF sweeps to cancel magnetic forces Fast RF sweeps to cancel magnetic forces Fast RF sweeps to cancel magnetic forces Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. Fast RF sweeps to cancel magnetic forces Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. Fast RF sweeps to cancel magnetic forces Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. In situ images: No sweep Sweeped Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. In situ images: No sweep Sweeped Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. In situ images: No sweep Sweeped Main Idea : In the mixed trap, accumulation is limited by inelastic collisions. The trap is strongly confining in three directions, as the magnetic trap dominates along the axis of the laser beam. In addition, the magnetic trap is switched off anyway in the end… Average magnetic forces to zero by sweeping rf fields to rapidly flip the spin of the atoms. In situ images: No sweep Sweeped In situ images: No sweep Sweeped In situ images: No sweep Sweeped • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping How Fast ? Many times per oscillation frequency in the magnetic trap MT • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping How Fast ? Many times per oscillation frequency in the magnetic trap MT • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth. How Fast ? Many times per oscillation frequency in the magnetic trap MT • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth. How Fast ? Many times per oscillation frequency in the magnetic trap MT • How Strong ? • The usual Landau Zener critrion for adiabatic crossing ( rf Rabi frequency, max and min define span of sweep, tsweep is the time for one linear sweep): • Also: beat the effective quadratic Zeeman effect related to optical trapping How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth. How Fast ? Many times per oscillation frequency in the magnetic trap MT How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth. How Fast ? Many times per oscillation frequency in the magnetic trap MT How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth. How Wide ? min : not 0 ! Not very well understood. For our rf power, Rotating Wave Approximation breaks down for low rf frequencies. min such that min ~ min (500 kHz) ? (the rf field dominates the static field at the center of the trap  all atoms adressed ?) max : sets the trap depth. 7 MHz corresponds to a trap depth of ~4/5 of the pure optical trap depth.

  23. Next decisive step: switch to another metastable state : 5S2 • Less unfavorable inelastic collision rate ? • Improved loading rate ? 7P4 7P3 425nm 633nm 663nm 427nm 5D4 5S2 7S3 • Outcome up to 6 106 atoms in 50 ms • Loading rate = ¼ of the MOT loading rate! • N optical trap > NMOT !

  24. Successful procedure and time sequence for Cr-BEC Accumulation in 5S2 and 5D4 + rf sweeps -> Ninit = 6 106 Spin polarization Repump 500 mW MOT 35 W !! Horizontal trap Vertical trap 100 ms 16 s Not to scale Evaporation Plate rotation 6s

  25. Evaporation ramp

  26. Cr Bose-Einstein Condensation BEC transition at 110 nK t=9.2 s - 28 000 atoms at T = 200nK t= 9.8 s - 17 000 atoms at T = 80nK All-optical evaporation After « dimple » formation, the trapping beam power is lowered from 35W to 500mW within 10 s. The complete cycle time is below 20s. BEC in situ dimensions are on the order of 4 to 5 µm, The peak density is 6. 1013 cm-3 The chemical potential is 800Hz. The trapping frequency are 110Hz, 100Hz et 150 Hz. t = 10 s – pure condensate ~10 000 atomes (first results - 17 nov. 2007) Q. Beaufils, et al, PhysRev in press, arXiv:0712.3521

  27. Early measurements on the Cr BEC Alternative pictures of the BEC transition Lifetime about 3s Anisotropic expansion in TOF + Castin-Dum analysis.

  28. Anisotropic expansion and profiles

  29. Outline: • Dipolar effects in ultra-cold gases • Chromium specificities • Cold bosonic and fermionic Cr atoms • Mixed magnetic and optical trapping of metastable Cr* atoms • New (rf-based) stategies to combat inelastic collisions • All-optical Condensation of Cr • RF spectroscopy and association of cold Cr2 molecules

  30. 52Cr resonances From Werner PhD dissertation at Stuttgart Uni

  31. Cr2 molecular potential curves Pavlovic et al. PRA 69, 0)30701 (2004)

  32. Magnetic field tuning : above resonance

  33. Feshbach resonance at low field • Several Feshach resonance have been observed at Stuttgart Uni in Tilman Pfau’s group J.Werner et al. Phys. Rev. Lett. 94, 183201 (2005) We work close to the Feshbach resonance at 8.2 G

  34. Feshbachresonanceat 8.2 G We have monitoredlosses vs the magneticfieldstregthattwotemperaturesbelow the Wigner threshold for d-waveresonances but above BEC transition.

  35. Magnetic field tuning : below resonance

  36. Cr2 RF-association Collaboration with Anne Crubellier (LAC)

  37. Feshbach resonance : rf induced « new » peak A 350 kHz rf-field shifts the resonance and triggers a new losschannel 350 kHz below the FR

  38. More convincing evidence for rf-association 900 kHz hold time 8s – T= 8µK

  39. RF-association spectroscopy In a given B0, the « new peak » location isresonant vs the rf-frequency. nrf-max

  40. rf-resonancefrequency vs magneticstrength Weverifiedthatnrf-maxsatisifies the energy conservation equation:

  41. Summary Cold fermionic 53 Cr dipolar atoms available 52 Cr BEC produced using innovative methods New means to tackle with inelastic collisions Preliminary evidence for formation of cold Cr2 molecules

  42. Perspectives Cooling the fermionic 53 Cr isotope down to the degenerate regime Thermalization in polarized dipolar fermionic gases Collisional properties Study of Dipolar Fermi seas and ofboson-fermion mixtures involving dipolar species MOT 53 Transfer into optical lattices Demonstrating new quantum phases and strongly correlated systems + studies in lower dimensions models for solid state physics

  43. 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 Collaborations Laboratoire Aimé Cotton in Orsay NIST Gaithersburg • Publications: • R. Chicireanu et al., Phys. Rev. A 73, 053406 (2006) • R. Chicireanu et al., Phys. Rev. A 76, 023406 (2007) • R. Chicireanu et al., EPJD 45,189 (2007) • Q. Beaufils et al, PRA in press and arXiv:0711.0663 (2008) • Q. Beaufils et al, PRA in press arXiv:0712.3521 (2008) • E. Maréchal et al, Appl. Phys B (2008) – IFRAF MOCA project

  44. Group members : The Cold Atom Group in Paris Nord Université Paris Nord, Villetaneuse, France Ph.D students: Quentin Beaufils RaduChicireanu(now at SYRTE) – defense October 25th 2007 www-lpl.univ-paris13.fr Post-doc: Thomas Zanon Permanent staff: Bruno Laburthe-Tolra, Etienne Maréchal, Laurent Vernac, Jean-Claude Keller and O. G. Pastmembers Arnaud Pouderous René Barbé

  45. THANKS! Radu Chicireanu, Arnaud Pouderous and René Barbé Laurent Vernac, Etienne Maréchal, Thomas Zanon, Jean-Claude Keller, Bruno Laburthe, Quentin Beaufils, OG

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