All-optical formation of a chromium Bose-Einstein Condensate

1. SFB SEMINAR Stuttgart – 28 jan. 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 • Work in progress and outlook

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 • Dipolar fermions: • Thermalization in a spin-polarized Fermi gas Magnetic dipole-dipole interaction : long range and anisotropic

5. 52Cr (boson) 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 D4 6 µ B 5 S2 425.55 nm Isat= 8.5 mW/cm2 53Cr (fermion) F=3/2 6 µ B 7 S3 F=5/2 800 MHz 3d5 4s1 F=7/2 F=9/2 Chromium electronic structure

6. Experimental setup

7. 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

8. Chromium MOTs Bosonic 52Cr MOT: Fermionic 53Cr MOT: N∞ = 4 106 bosons T=120 μK 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 Fairly limited atom numbers in steady-state MOTs: • decay towards metastable states (halo) • strong inelastic collisions (spring 2005)

9. 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

10. 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)

11. Dual-isotope boson-fermion Cr MOT 52+53 N∞52 = 7 104 atoms N∞53 = 5 105atoms 52 52 Recipe: sequential accumulation of 53Cr and 52Cr in the metastable D states followed by optical pumping back into the ground state Up to 40 106 bosons and 106 fermions • R. Chicireanu et al., Phys. Rev. A 73, 053406 (2006)

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. !!! 2 to 3 orders of magnitude larger than for the alkalis Light-assisted inelastic collisions in Cr MOTs βSP ~ 10-9 cm3/s both for the fermion and for the boson • Light-assisted collisions: • Cr: βSP is close to classical unitary limit, i.e. the maximal PA rate: βLangevin = (λ/2π)2 · v (flux of particles through a sphere of radius RC=λ/2π) • This points towards an unknown loss mechanism, affecting many collision channels, which expels excited pairs, with a probability close to 1. • first: excitation of a pair on an attractive molecular potential • then: various loss mechanisms • in most cases P « 1: few collision channels lead to losses (alkalis) BUT : βSP still small enough to cool atoms down to Doppler temperature !!!

14. 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 • Work in progress and outlook

15. 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 Repump to ground state (bss<<bdd) Spin polarization in lowest-energy sub-state m=-3 Capture an absorption image

16. 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))

17. Optical trapping of metastable Cr atoms Optical trap depth: 500μK (parametric excitation measurement) • up to 1.4 106 atoms @ 100μK (TOF) • very fast accumulation ~100 ms • Peak density 1012 atoms/cm3 • Loading rate 107 atoms/s • Limitations: • Majorana spin-flips and DD collisions • (worse than in the 3D Mag trap) • (EPJD 45, 189 (2007))

18. 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)

19. 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

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. 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.

21. 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 • Work in progress and outlook

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 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 beams 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.

23. 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) 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 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.

24. 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 for improved OT loading (b) How to choose the frequency span ? nmin : not 0 ! At high rf power and close to B=0, RWA breaks down at low rf frequencies. nmin such that nmin ~ (rf Rabi frequency ~500 kHz) nmax : ~ 7 MHzas 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.

25. 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.

26. 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 more than 5 106 atoms in 50 ms • Loading rate = ¼ of the MOT loading rate! • N optical trap > NMOT !

27. Succesful (?) procedure and time sequence : summary 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

28. Dimple loading • Importance of the trapping beam polarizations : They must be orthogonal. (15 november 2007)

29. Evaporation optimization Still in progress… Very important is an unperfect gravity compensation ! (Oort cloud)

30. 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, submitted to PRL arXiv:0712.3521 (dec. 2007)

31. Early measurements on the Cr BEC Alternative pictures of the BEC transition Lifetime about 3s Anisotropic expansion in TOF + Castin-Dum analysis. Elementary excitations measurements searching for dipolar induced effects in progress…

32. A new tool to control atomic magnetism ? • Many applications (spinors, …) require an exquisite control of the magnetic field. • gJ the Landé factor can be tailored (« renormalized ») using strong rf fields : When the RF frequency ω exceeds the Larmor frequency ω0 ,gJ is modified : • Serge Haroche PhD thesis • S.Haroche, et al., PRL 24 16 (1970)

33. Brf(t) m(t) f(t) Classical picture

34. Controlling the atom magnetism • A strong RF field out of resonance is applied to a thermal m=+3 Cr atom cloud trapped in the 1D optical trap plus a magnetic gradient with B=0 at the cloud center. • The RF field can null the gradient induced cloud explosion: Atom cloud at 100μK Longitudinal potential 3 gJ Rf power

35. Adiabatic dressing If the rf switch-on/off is slow enough, the initial state is coherently recovered

36. Open questions : How are modified the elastic and inelastic collisions ? What about the ac Stark shifts ?

37. Summary Cold fermionic 53 Cr dipolar atoms available Dipolar 52 Cr Bose Einstein Condensate produced using innovative methods New means to tackle with inelastic collisions

38. 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

39. 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 Past members Arnaud Pouderous René Barbé Collaborations Laboratoire Aimé Cotton in Orsay NIST Gaithersburg Friendly advices: • T. Pfau and coworkers • J. Mc Clelland 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, submitted to PRL and arXiv:0711.0663 (nov. 2007) Q. Beaufils, et al, submitted to PRL arXiv:0712.3521 (dec. 2007)

40. Group members : The Cold Atom Group in Paris Nord Laboratoire de Physique des Lasers – CNRS -IFRAF Université Paris Nord, Villetaneuse, France Ph.D students: Quentin Beaufils Radu Chicireanu (now at SYRTE) – defense October 25th 2007 Post-doc: Thomas Zanon Permanent staff: Bruno Laburthe-Tolra, Etienne Maréchal, Laurent Vernac, Jean-Claude Keller and O. G. www-lpl.univ-paris13.fr