1. Have left: B. Pasquiou (PhD), G. Bismut (PhD), M. Efremov, Q. Beaufils, J. C. Keller, T. Zanon, R. Barbé, A. Pouderous, R. Chicireanu Collaborators: Anne Crubellier (Laboratoire Aimé Cotton), J. Huckans, M. Gajda A.de Paz (PhD), A. Chotia, A. Sharma, B. Laburthe-Tolra, E. Maréchal, L. Vernac, P. Pedri (Theory), O. Gorceix (Group leader) Magnetization dynamics of a dipolar BEC in a 3D optical lattice

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) See also Er PRL, 108, 210401 (2012) See also Dy, PRL, 107, 190401 (2012) … and Dy Fermi sea PRL, 108, 215301 (2012) … and heteronuclear molecules… Anisotropic explosion pattern reveals dipolar coupling. Stuttgart: Tune contact interactions using Feshbach resonances (Nature. 448, 672 (2007)) BEC collapses Cr: R 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 arXiv: 1205.6305 (2012) Hydrodynamic properties of a BEC with weak dipole-dipole interactions Interesting but weak effects in a scalar Cr BEC Saddle shape

5. Polarized (« scalar ») BEC Hydrodynamics Collective excitations, sound, superfluidity Anisotropic Long-ranged R Hydrodynamics: non-local mean-field Magnetism: Atoms are magnets Chromium (S=3): involve dipole-dipole interactions Multicomponent (« spinor ») BEC Magnetism Phases, spin textures…

6. Focus on : Magnetization dynamics in a 3D optical lattice : - 3 regimes : - B is of the order of the lattice band excitations. Observation of dipolar resonances and of band excitations mediated by dipole interactions. Resonances line-shape is sensitive to the interaction energy in each lattice site, and therefore to on-site number distribution. - B is below the first excitation band : Observation of intersite dynamics, with constant magnetization. -B is very low : spontaneous depolarization.

7. Observation of spin changing collisions resonances and band excitations: - BEC atom number N=10^4 atoms. - Loaded adiabatically in a 3 D anisotropic optical lattice. Lattice in horizontal plane Typical frequencies:  x = 2  kHz  y = 2  kHz  z = 2  kHz BEC In m=-3 Rf sweep 20 ms T V0 ≈ 25 Er Time sequence : m=+3 +B amplitude and direction is set Stern Gerlach analysis 2 1 Mott distribution With our parameters

8. -3 -2 0 1 2 3 Two dipolar relaxation channels for two atoms in m=+3, sharing a same lattice site Here, z is fixed by the B field orientation.

9. time Atoms remaining in m=-3 If B is higher than the lattice depth (25 Er), dipolar relaxation leads to losses. This case allows to measure the number of site with single occupancy. B is higher than the trap depth B is lower than the trap depth Mott distribution 2 1 Simple measure of site with two atoms or more

10. If B is lower than the lattice depth : magnetization dynamics with no loss. Dynamics very sensitive to the magnetic field orientation and value.

11. Observation of resonances due to dipolar relaxation (fixed time T=12 ms) Anisotropic lattice sites

12. -Two particles in a harmonic anisotropic potential with frequencies  x,  y and  z. - Consider the relative orbital motion -Initial relative orbital motion |n X =0, n Y =0, n Z =0> -Coupling to final relative orbital motion of the atomic pair |nx,ny,nz> Initial Final For channel 2 : B along OX Predication of the resonances position:

13. Width of the resonances enlarged by the tunneling Lower energy resonance around 50 kHz : -Tunneling very small (100 Hz) -Focus on this lowest energy resonance. Red curve : Lowest energy resonance at  L =  Y Typical frequencies:  x = 2  kHz  y = 2  kHz  z = 2  kHz With (n Y +n Z ) even

14. Lower energy resonance. Probe of the atom number distribution. Black curve : two atoms / site. Contact interaction : shift and splitting of the resonance. Shift due to contact interactions Molecular Basis :

15. Note: Lineshape of dipolar resonances probes number of atoms per site 3 and more atoms per sites loaded in lattice for faster loading B(kHz) Fraction in m=+3 Few-body physics ! The 3-atom state which is reached has entangled spin and orbital degrees of freedom Probe of atom squeezing in Mott state spin orbit

16. Focus on : Magnetization dynamics in a 3D optical lattice : - 3 regimes : - B is of the order of the lattice depth. Observation of dipolar resonances and of band excitations mediated by dipole interactions. Resonances line-shape is sensitive to the interaction energy in each lattice site, and therefore to on-site number distribution. - B is below the first excitation band : Observation of intersite dynamics, with constant magnetization. -B is very low : spontaneous depolarization.

17. From now on : stay away from dipolar magnetization dynamics resonances, Spin dynamics at constant magnetization (<15mG) New tool : Control the initial state by a tensor light-shift A  polarized laser Close to a J  J transition (100 mW 427.8 nm) In practice, a  component couples m S states 0 1 -2 -3 -3 -2 -1 0 1 2 3 Energy  m S 2 Quadratic light shift effect allows state preparation

18. Adiabatic state preparation in 3D lattice t quadratic effect -2 -3  Initiate spin dynamics by removing quadratic effect (2 atomes / site)

19.  On-site spin oscillations -3 -2 (  250 µs) vary time Load optical lattice quadratic effect (due to contact oscillations) (period  220 µs) Up to now unknown source of damping

20. Long time-scale spin dynamics in lattice vary time Load optical lattice quadratic effect Sign for intersite dipolar interaction ? (two orders of magnitude slower than on-site dynamics)

21. Coherent spin oscillations at lower lattice depth The very long time scale excludes on-site oscillations where spin-exchange collisions dominate

22. Probing spin oscillations from superfluid to Mott Intersite coherent spin oscillation seems to need phase coherence between sites Superfluid more robust Probes magnetism from superfluid to insulator (Probes coherence length) (probes coherent spin oscillations)

23. Focus on : Magnetization dynamics in a 3D optical lattice : - 3 regimes : - B is of the order of the lattice depth. Observation of dipolar resonances and of band excitations mediated by dipole interactions. Resonances line-shape is sensitive to the interaction energy in each lattice site, and therefore to on-site number distribution. - B is below the first excitation band : Observation of intersite dynamics, with constant magnetization. -B is very low : spontaneous depolarization.

24. At extremely low magnetic field (<1.5 mG): Spontaneous demagnetization of atoms in a 3D lattice 3D lattice Critical field 4kHz Threshold seen 5kHz -3 -2 PRL 106, 255303 (2011) ( in bulk BEC)

25. Summary - Magnetism in lattice Away from resonances: spin oscillations Spin-exchange : intrasite and inter site dynamics Not robust in Mott regime Resonant magnetization dynamics Few body vs many body physics Spontaneous depolarization at low magnetic field Towards low-field phase diagram

26. A.de Paz, A. Chotia, A. Sharma B. Pasquiou, G. Bismut, B. Laburthe-Tolra, E. Maréchal, L. Vernac, P. Pedri, M. Efremov, O. Gorceix Thanks for your attention!.

27. A.de Paz, A. Chotia, A. Sharma B. Pasquiou, G. Bismut, B. Laburthe-Tolra, E. Maréchal, L. Vernac, P. Pedri, M. Efremov, O. Gorceix