1. Have left: Q. Beaufils, J. C. Keller, T. Zanon, R. Barbé, A. Pouderous, R. Chicireanu Collaborator: Anne Crubellier (Laboratoire Aimé Cotton) B. Pasquiou (PhD), G. Bismut (PhD), A. de Paz B. Laburthe-Tolra, E. Maréchal, L. Vernac, P. Pedri, M. Efremov (Theory), O. Gorceix (Group leader) Dipolar chromium BECs

2. Dipole-dipole interactions Anisotropic Long range Chromium (S=3): Van-der-Waals plus dipole-dipole interactions R Relative strength of dipole-dipole and Van-der-Waals interactions Cr:

3. Relative strength of dipole-dipole and Van-der-Waals interactions Stuttgart: d-wave collapse, PRL 101, 080401 (2008) Stabilization by confinement arXiv:1105.5015 (2011)arXiv:1105.5015 See also Dy experiment arXiv:1108.5993 (2011)arXiv:1108.5993 Anisotropic explosion pattern reveals dipolar coupling. Stuttgart: Tune contact interactions using Feshbach resonances (Nature. 448, 672 (2007)) BEC collapses Cr: R Parabolic ansatz still good. (Eberlein, PRL 92, 250401 (2004)) BEC stable despite attractive part of dipole-dipole interactions

4. Villetaneuse, PRL 105, 040404 (2010) Stuttgart, PRL 95, 150406 (2005) Collective excitations Striction Anisotropic speed of sound Bragg spectroscopy Villetaneuse Hydrodynamic properties of a BEC with weak dipole-dipole interactions Interesting but weak effects in a scalar Cr BEC

5. Spin degree of freedom coupled to orbital degree of freedom - Spinor physics and magnetization dynamics Dipole-dipole interactions R 0 1 0 1 -2 -3 2 3 without with - Inelastic collisions due to dipole-dipole interactions

6. -3 -2 0 1 2 3 -3 -2 -1 0 1 2 3 B=0: Rabi In a finite magnetic field: Fermi golden rule

7. Important to control magnetic field Rotate the BEC ? Spontaneous creation of vortices ? Einstein-de-Haas effect Angular momentum conservation Dipolar relaxation, rotation, and magnetic field -3 -2 0 1 2 3 Ueda, PRL 96, 080405 (2006) Santos PRL 96, 190404 (2006) Gajda, PRL 99, 130401 (2007) B. Sun and L. You, PRL 99, 150402 (2007)

8. Interpartice distance Energy R c = Condon radius From the molecular physics point of view PRA 81, 042716 (2010) Larger and larger magnetic fields probes smaller and smaller interatomic distances 2-body physics B = 3 GB =.3 mG many-body physics

9. Dipolar relaxation in a Cr BEC Produce BEC m=-3 detect BEC m=-3 Rf sweep 1Rf sweep 2 BEC m=+3, vary time See also Shlyapnikov PRL 73, 3247 (1994) Born approximation Pfau, Appl. Phys. B, 77, 765 (2003) PRA 81, 042716 (2010) Fermi golden rule a 6 = 103 ± 4 a 0. A measurement of scattering length

10. A probe of non-local correlations : here, a mere two-body effect, yet unacounted for in a mean-field « product-ansatz » BEC model Dipolar relaxation: measuring non-local correlations L. H. Y. Phys. Rev. 106, 1135 (1957) Measure dipolar relaxation at magnetic field B = Measure the second order correlation function at:

11. 30 mGauss …spin-flipped atoms go from one band to another 2 3 1 Spin relaxation and band excitation in optical lattices

12. Reduction of dipolar relaxation in optical lattices Load the BEC in a 1D, 2D or 3D Lattice Produce BEC m=-3 detect m=-3 Rf sweep 1Rf sweep 2 BEC m=+3, vary time Load optical lattice One expects a reduction of dipolar relaxation, as a result of the reduction of the density of states in the lattice

13. PRA 81, 042716 (2010) PRL 106, 015301 (2011) 0D 3D lattice Dipolar relaxation in optical lattices

14. 1D Below threshold: a (spin-excited) metastable 1D quantum gas ; Interest for spinor physics, spin excitations in 1D… B. Pasquiou et al., PRL 106, 015301 (2011) (almost) complete suppression of dipolar relaxation in 1D at low field: a threshold consequence of angular momentum conservation B(mG)

15. 0D At resonance should produce vortices in each lattice site (EdH effect) (problem of tunneling) Towards coherent excitation of pairs into higher lattice orbitals ? (Rabi oscillations) Mott state locally coupled to excited band 0D: a resonance due to energy conservation Collab. Group of Mariusz Gajda

16. .3 mGauss -2 0 1 2 3 -3 -2 0 2 1 3 Similar to M. Fattori et al., Nature Phys. 2, 765 (2006) at large fields and in the thermal regime Spontaneous demagnetization of the condensate Magnetic field control below.5 mG (dynamic lock, fluxgate sensors) (.1mG stability) (no magnetic shield…)

17. S=3 Spinor physics with free magnetization - Up to now, spinor physics with S=1 and S=2 only - Up to now, all spinor physics at constant magnetization (exchange interactions, no dipole-dipole interactions) - They investigate the ground state for a given magnetization -> Linear Zeeman effect irrelavant 0 1 New features with Cr - First S=3 spinor (7 Zeeman states, four scattering lengths, a 6, a 4, a 2, a 0 ) - Dipole-dipole interactions free total magnetization - Can investigate the true ground state of the system (need very small magnetic fields) 0 1 -2 -3 2 3

18. BEC at low magnetic field: BEC only in m S =-3 (lowest energy state) Cloud spontaneously polarizes ! Thermal population in Zeeman excited states 0 1 -2 -3 2 3 Non-interacting multicomponent Bose thermodynamics: a BEC is ferromagnetic

19. Below a critical magnetic field: the BEC ceases to be ferromagnetic ! -Magnetization remains small even when the condensate fraction approaches 1 !! Observation of a depolarized condensate !! Necessarily an interaction effect B=100 µG B=900 µG

20. Santos PRL 96, 190404 (2006) -2 -3 -2 0 2 1 3 Phases set by contact interactions (a 6, a 4, a 2, a 0 ) – differ by total magnetization -2 0 1 2 3 -3 Large magnetic field : ferromagneticLow magnetic field : polar/cyclic Ho PRL. 96, 190405 (2006) -2 -3 Cr spinor properties at low field

21. Mean-field effect BECLattice Critical field0.26 mG1.25 mG 1/e fitted0.3 mG1.45 mG Load into deep 2D optical lattices to boost density. Field for depolarization depends on density Phys. Rev. Lett. 106, 255303 (2011)

22. Dynamics analysis Meanfield picture : Spin(or) precession (Majorana flips) Ueda, PRL 96, 080405 (2006) Natural timescale for depolarization: PRL 106, 255303 (2011) Produce BEC m=-3 Rapidly lower magnetic field

23. A quench through a zero temperature phase transition Santos and Pfau PRL 96, 190404 (2006) Diener and Ho PRL. 96, 190405 (2006) Phases set by contact interactions, magnetization dynamics set by dipole-dipole interactions - Operate near B=0. Investigate absolute many-body ground-state -We do not (cannot ?) reach those new ground state phases -Quench should induce vortices… -Role of thermal excitations ? Also new physics in 1D: Polar phase is a singlet-paired phase Shlyapnikov-Tsvelik NJP, 13, 065012 (2011) !! Depolarized BEC likely in metastable state !! See also Demler PRL 97, 180412 (2006) Polar Cyclic

24. Thermodynamics: phase diagram Measure T c (B) and M(T c,B) for different magnetic fields B Get T c (M) Quasi- Boltzmann distribution Bi-modal spin distribution Phase diagram adapted from J. Phys. Soc. Jpn, 69, 12, 3864 (2000) See also PRA, 59, 1528 (1999)

25. Dipolar relaxation in BEC can be used as a non- local probe: new measurement of Cr scattering lengths non-local correlations 0D Control of dipolar relaxation in optical lattices can be made resonant could be made coherent ? towards Einstein-de-Haas (rotation in lattice sites) spin dynamics in optical lattices Magnetization changing collisions reveal new spinor phases at extremely low magnetic fields Conclusions

26. G. Bismut (PhD), B. Pasquiou (PhD), A. de Paz B. Laburthe, E. Maréchal, L. Vernac, P. Pedri, M. Efremov, O. Gorceix