1. Collaborations: L. Santos (Hannover) Former members: R. Chicireanu, Q. Beaufils, B. Pasquiou, G. Bismut A.de Paz (PhD), A. Sharma (post-doc), A. Chotia (post doc) J. Huckans (visitor), O. Gorceix, E. Maréchal, L. Vernac, P. Pedri, B. Laburthe-Tolra Quantum magnetism with a chromium BEC in a 3D lattice

2. Quantum Magnetism with a chromium BEC in a 3D lattice long range interactions = beyond the next neighbor direct spin-spin interaction real spin magnetic dipole moment S=3 quantum regime, high filling factor V dd = 10-20 Hz T < 1 nK Spin dynamics in an out of equilibrium system = Jila experiment V dd to reach ground state

3. different spin dynamics induced by dipole-dipole interactions in a Cr BEC loaded in a 3D lattice measurement of the evolution of the Zeeman states populations -2 0 1 2 3 -3 2 1 Mott state Quantum Magnetism with a chromium BEC in a 3D lattice

4. different spin dynamics induced by dipole-dipole interactions in a Cr BEC loaded in a 3D lattice measurement of the evolution of the Zeeman states populations -2 0 1 2 3 -3 spin exchange constant magnetization 2 1 Mott state the atoms stay in the lowest band intrasite (contact) + intersite (dipole-dipole) spin exchange magnetization = Quantum Magnetism with a chromium BEC in a 3D lattice

5. Quantum magnetism with a dipolar BEC: Villetaneuse experiment different spin dynamics induced by dipole-dipole interactions in a Cr BEC loaded in a 3D lattice measure of the evolution of the Zeeman states populations -2 0 1 2 3 -3 dipolar relaxationchange of the magnetization 2 1 Mott state spin orbit coupling - band excitations intrasite dipole interactions magnetization =

6. Quantum magnetism with a dipolar BEC: Villetaneuse experiment different spin dynamics induced by dipole-dipole interactions in a Cr BEC loaded in a 3D lattice measure of the evolution of the Zeeman states populations -2 0 1 2 3 -3 dipolar relaxation spin exchange change of the magnetization constant magnetization 2 1 Mott state

7. Dipolar relaxation in a 3D lattice - observation of resonances width of the resonances: tunnel effect + B field, lattice fluctuations n x, n y, n z kHz 1 mG = 2.8 kHz (Larmor frequency)

8. Initial Final pair orbital momentum spin state kHz Dipolar relaxation in a 3D lattice – study of the first resonance

9. B (kHz) Atomic Fraction in m=+3 2 1 probe of the Mott distribution good agreement between theory for two atoms per site and experiment both for the shape and position of the resonance Dipolar relaxation in a 3D lattice – effect of onsite contact interactions de Paz et al, Phys Rev A 87 (2013) theory including intrasite contact interactions

10. -3 -2 Spin exchange dynamics in a 3D lattice vary time Load optical lattice state preparation in -2 B dipolar relaxation suppressed evolution at constant magnetization experimental sequence: spin exchange from -2 first resonance 0 10 mG Stern Gerlach analysis

11. expected Mott distribution Different Spin exchange dynamics in a 3D lattice Contact interaction (intrasite)

12. expected Mott distribution doublons removed = only singlons Different Spin exchange dynamics in a 3D lattice dipolar relaxation with Contact interaction (intrasite) Dipole-dipole interaction (intersite) without spin changing term

13. Spin exchange dynamics in a 3D lattice: with only singlons the spin populations change! comparison with a plaquette model (Pedri, Santos) 3*3 sites, 8 sites containing one atom + 1 hole quadratic light shift and tunneling taken into account Proof of intersite dipolar coupling Many Body system E(m s ) = q m S 2 measured with interferometry

14. Spin exchange dynamics in a 3D lattice with doublons at short time scale initial spin state onsite contact interaction: spin oscillations with the expected period strong damping contact spin exchange in 3D lattice: Bloch PRL 2005, Sengstock Nature Physics 2012

15. result of a two site model: Spin exchange dynamics in a 3D lattice with doublons at longer time scale two sites with two atoms dipolar rate raised (quadratic sum of all couplings) our experiment allows the study of molecular Cr2 magnets with larger magnetic moments than Cr atoms, without the use of a Feshbach resonance intersite dipolar coupling not fast enough: the system is many body

16. Spin exchange dynamics in a 3D lattice with doublons: strong reduction by a magnetic gradient amplitude if the spin dynamics results from intersite coupling it should disappear when: dipolar coupling rate Proof of intersite coupling

17. -3 -2 expected Mott distribution doublons removed = only singlons Different Spin exchange dynamics with a dipolar quantum gas in a 3D lattice intrasite contact intersite dipolar Heisenberg like hamiltonian quantum magnetism with S=3 bosons and true dipole-dipole interactions de Paz et al, Arxiv (2013)

18. thank you for your attention!