1. Have left: A. Chotia, A. Sharma, B. Pasquiou, G. Bismut, M. Efremov, Q. Beaufils, J. C. Keller, T. Zanon, R. Barbé, A. Pouderous, R. Chicireanu Collaborators: Anne Crubellier, Mariusz Gajda, Johnny Huckans, Perola Milman, Rejish Nath B. Naylor (PhD), A. de Paz (PhD), A. Chotia, A. Sharma, O. Gorceix, B. Laburthe-Tolra, E. Maréchal, L. Vernac, P. Pedri (Theory), L. Santos (Theory, Hannover) Magnetism with a dipolar condensate: spin dynamics and thermodynamics

2. Cold atom activity at Paris North University Rubidium BEC in rf-dressed magnetic traps Hélène Perrin 2D Physics ; BEC in a ring Sodium BEC on a chip (project) Aurélien Perrin Non-equilibrium dynamics Metastable atoms flying by nanostructures Gabriel Dutier Atom interferometry, atom-surface interactions Chromium dipolar gases Laurent Vernac Dipolar BEC Magnetism Fermi gases Strontium (project) Martin Robert-de-Saint-Vincent Magnetism New cooling mechanisms New measurement procedures

3. This talk Exotic quantum magnetism with large spins arising from dipole-dipole interactions - Different exchange mechanisms compete, and may be controlled (more or less) independently - Dipolar interactions introduce true long-range couplings - An interesting playground for many-body quantum physics with no analog in solid-state physics

4. Quantum magnetism, some paradigms, from solid-state physics High-Tc superconductivity Antiferromagnetism Hubbard model Frustrated magnetism ? ? Spin liquids Nanomagnetism Heisenberg model of magnetism (real spins s=1/2, effective spin-spin interaction) Condensed-matter: effective spin-spin interactions arise due to exchange interactions Ising Exchange U (Super-) Exchange (I)

5. Complex Many-body physics Many open questions… Our approach : Study magnetism with strongly magnetic atoms : dipole-dipole interactions between real spins S=3 R Simple two-body Hamiltonian Possibilities for quantum simulation – possibilities for exotic quantum magnetism Dipolar exchange (II)

6. Cold atoms revisit quantum magnetism; from S=1/2 to large Spin Interacting spin-less bosons (effective spin encoded in orbital degrees of freedom) Greiner: Anti-ferromagnetic (pseudo-)spin chains I. Bloch,… Spin ½ interacting Fermions or Bosons Super-exchange interaction Esslinger, Hulet: correlations I. Bloch, T. Porto… Spinor gases: Large spin bosons (or fermions) Stamper-Kurn, Lett, Klempt, Chapman, Sengstock, Shin, Gerbier, …… In all these experiments, an effective spin ½ system is encoded in either the internal or the external degrees of freedom

7. Spinor physics due to contact interactions: scattering length depends on molecular channel  -3 -2 (  250 µs) (period  220 µs) Magnetism… at constant magnetization linear Zeeman effect does not matter -2 -3 0 Spin oscillations (exchange III) Spin-changing collisions have no analog in spin ½ systems Van-der-Waals (contact) interactions

8. Exchange energy Coherent spin oscillation Chapman, Sengstock, Bloch, Villetaneuse… Klempt Stamper- Kurn Domains, spin textures, spin waves, topological states Stamper-Kurn, Chapman, Sengstock, Shin… Quantum phase transitions Stamper-Kurn, Lett, Gerbier Spinor physics due to contact interactions High spin fermions coming up!

9. Dipole-dipole interactions Anisotropic Long range Van-der-Waals (contact) interactions Short range Isotropic Two types of interactions R (only few experiments worldwide with non-negligible dipolar interactions - Stuttgart, Innsbruck, Stanford, Boulder) Chromium: unusually large dipolar interactions (large electronic spin)

10. Two new features introduced by dipolar interactions: Free Magnetization Non-local coupling between spins -3 -2 -1 0 1 2 3

11. 1st main feature : Spinor physics with free magnetization 0 1 Without dipolar interactions 0 1 With anisotropic PRL 106, 255303 (2011) Example: spontaneous demagnetization of a dipolar BEC Occurs when the change in magnetic field energy is smaller than the spin- dependent contact interaction Need a very good control of B (100 µG) Fluxgate sensors

12. Rotate BEC ? Vortex ? Einstein-de-Haas effect Quantum Hall regime with fermions? Spin-orbit coupling (conservation of total angular momentum) 1st main feature : Spinor physics with free magnetization Ueda, PRL 96, 080405 (2006) Santos PRL 96, 190404 (2006) Gajda, PRL 99, 130401 (2007) B. Sun and L. You, PRL 99, 150402 (2007) Buchler, PRL 110, 145303 (2013) Carr, New J. Phys. 17 025001 (2015) Peter Zoller arXiv:1410.3388 (2014) H.P. Buchler, arXiv:1410.5667 (2014) Flat bands, topological insulators XYZ magnetism Frustration engineer Magnetization changing processes write an x+iy intersite phase

13. 2nd main feature of dipolar interactions: Long range-coupling between atoms Implications for lattice magnetism, spin domains… With the contribution of… (Super-) Exchange (I) (dipolar) Exchange (II) (contact)-Exchange (III)

14. 0 Introduction to spinor physics 1 Exotic quantum magnetism in optical lattices 2 Thermodynamics and cooling of a Bose gas with free magnetization

15. Nov 2007 : Chromium BEC April 2014 : Chromium Fermi sea 10 4 atoms 10 3 atoms Experimental system F=9/2 S=3 (from only 3.104 atoms in dipole trap !) Phys. Rev. A 91, 011603(R) (2015)

16. Stern-Gerlach separation: (magnetic field gradient) -2 0 1 2 3 -3 Optical dipole traps equally trap all Zeeman state of a same atom Linear (+ Quadratic) Zeeman effect

17. A 52 Cr BEC in a 3D optical lattice Optical lattice: Perdiodic potential made by a standing wave 3D lattice  Strong correlations, Mott transition… Our lattice architecture: (Horizontal 3-beam lattice) x (Vertical retro-reflected lattice) Rectangular lattice of anisotropic sites

18. Study quantum magnetism with dipolar gases ? Dipole-dipole interactions between real spins Magnetization changing collisions Heisenberg model of magnetism (effective spin model) Tentative model for strongly correlated materials, and emergent phenomena such as high-Tc superconductivity Condensed-matter: effective spin-spin interactions arise due to exchange interactions

19. Control of magnetization-changing collisions: Magnetization dynamics resonance for a Mott state with two atoms per site (~15 mG) -3 -2 0 1 2 3 Dipolar resonance when released energy matches band excitation Mott state locally coupled to excited band Non-linear spin-orbit coupling Phys. Rev. A 87, 051609 (2013) Magnetization changing collisions See also Gajda: Phys. Rev. A 88, 013608 (2013)

20. Magnetization changing collisions Can be suppressed in optical lattices Ressembles but differs from Heisenberg magnetism: From now on : stay away from dipolar magnetization dynamics resonances, Spin dynamics at constant magnetization (<15mG) Related research with polar molecules: A. Micheli et al., Nature Phys. 2, 341 (2006). A.V. Gorshkov et al., PRL, 107, 115301 (2011), See also D. Peter et al., PRL. 109, 025303 (2012) See Jin/Ye group Nature (2013)

21. Initiate spin dynamics by removing quadratic effect vary time Load optical lattice quadratic effect Adiabatic state preparation in 3D lattice quadratic effect -2-3 -2 0 1 2 3 -3

22. Explore spin dynamics in two configurations (i) Mott state with a core of two atomes per site (ii) Empty doublons: singly occupied sites, unit filling

23. Spin dynamics after emptying doubly-occupied sites: A proof of inter-site dipole-dipole interaction Experiment: spin dynamics after the atoms are promoted to ms=-2 Theory: exact diagonalization of the t-J model on a 3*3 plaquette (P. Pedri, L. Santos) Magnetization is constant Phys. Rev. Lett., 111, 185305 (2013) Timescale for spin dynamics = 20 ms Tunneling time = 100 ms Super-exchange > 10s !! Many-body dynamics !! (each atom coupled to many neighbours) Mean-field theories fail -3 -2

24. Spin dynamics in doubly-occupied sites: Faster dynamics due to larger effective dipole (3+3=6 ?) Phys. Rev. Lett., 111, 185305 (2013) Exact diagonalization is excluded with two atoms per site (too many configurations for even a few sites)

25. A toy many-body model for the dynamics at large lattice depth (i) (j ) Toy models for singlons Toy models for doublons: replace S=3 by S=6 Measured frequency: 300 Hz Calculated frequency: 320 Hz Toy models seems to qualitatively reproduce oscillation; see related analysis in Porto, Science (2015) Also related observations in NMR experiments

26. Exotic quantum magnetism of large spin, from Mott to superfluid Superfluid Mott Large lattice depth: dynamics dominated by dipolar interactions Lower lattice depth: super-exchange may occur and compete An exotic magnetism driven by the competition between three types of exchange Dipolar Spin-dependent contact interactions Super-exchange One can tune the relative strength of these processes by tuning lattice depth

27. Observed, and calculated frequencies Two-body spin dynamics in isolated lattice sites (contact)-Exchange (III) Many-body spin dynamics due to intersite couplings GP- mean-field simulation -0.5 0.0 0.5 1.0 6004002000 -3 -2 -0.5 0.0 0.5 1.0 10008006004002000 (Super-) Exchange (I) (dipolar) Exchange (II)

28. Summary: a slow cross-over between two behaviors In the Mott regime: Two well separated oscillating frequencies corresponding to: -On site contact-driven spin-exchange interactions -Many-body intersite dipole-dipole interactions At low lattice depth: Exponential behavior - Gross-Pitaevskii nicely reproduces observations -The dynamics depends on an interplay between contact and dipolar interactions In the intermediate regime: -oscillations survive. - Two frequencies get closer No theoretical model yet A unique and exotic situation!!

29. What have we learned ? Truly new phenomena arrise due to dipolar interactions when the spin degrees of freedom are released. - Effective Hamiltonians relevant for quantum magnetism. -Large spin atoms in optical lattices: a yet almost unexplored playground for many-body physics (even without dipolar interactions) - Free magnetization. Spin orbit coupling. Also an interesting challenge from the theoretical point of view. Carr, New J. Phys. 17 025001 (2015) Peter Zoller arXiv:1410.3388 (2014) H.P. Buchler, arXiv:1410.5667 (2014)

30. 0 Introduction to spinor physics 1 Exotic quantum magnetism in optical lattices 2 Thermodynamics and cooling of a Bose gas with free magnetization (No Lattice)

31. Spin temperature equilibriates with mechanical degrees of freedom We measure spin-temperature by fitting the m S population (separated by Stern-Gerlach technique) At low magnetic field: spin thermally activated Magnetization adpats to temperature due to the presence of dipolar interactions 0 1 -2 -3 2 3 -3 -2 -1 0 1 2 3 Related to Demagnetization Cooling expts, T. Pfau, Nature Physics 2, 765 (2006)

32. Spontaneous magnetization due to BEC BEC only in m S =-3 (lowest energy state) Cloud spontaneously polarizes ! Thermal population in Zeeman excited states A non-interacting BEC is ferromagnetic PRL 108, 045307 (2012) T>Tc T<Tc a bi-modal spin distribution -3 -2 -1 0 1 2 3

33. m s =-3 m s =-1 Optical depth m s =-2 -3 -2 0 2 1 3 Only thermal gas depolarizes… get rid of it ? Purify the BEC A new cooling method using the spin degrees of freedom? A BEC component only in the m s =-3 state BEC Thermal m s =-3 m s =-3, -2, -1, … (i) Thermal cloud depolarizes (ii) Kill spin-excited states Large B field

34. A competition between two mechanisms BEC Thermal m s =-3 m s =-3, -2, -1, … (i) Thermal cloud depolarizes (ii) BEC melts to re- saturate m s =-3 thermal gas (and cools it) (iii) Kill spin-excited states Losses in thermal cloud due to depolarization BEC melts (a little) ? Who Wins ? BEC fraction B-field Atom Number B-field

35. A competition between two mechanisms At high T/T c, BEC melts (too few atoms in the BEC to cool the thermal gas back to saturation) At low T/T c, spin filtering of excited thermal atoms efficiently cools the gas Theoretical model: rate equation based on the thermodynamics of Bosons with free magentization. Interactions are included within Bogoliubov approximation B=1,5mG arXiv (2015)

36. Summary of the experimental results as a function of B 7,5 0 2,55 Magnetic field (mG) Final condensat fraction (large field, no effect) arXiv (2015)

37. Theoretical limits for cooling There does not seem to be any limit other than practical In principle, cooling is efficient as long as depolarization is efficient Process can be repeated As T→0, less and less atoms are in the thermal cloud, therefore less and less spilling However, all the entropy lies in the thermal cloud Therefore, the gain in entropy is high at each spilling provided T~B Initial entropy per atom Entropy compression

38. Proposal: Extension to ultra-low temperatures for non-dipolar gases In our scheme, limitation around 25 nK, limited by (difficult to control below 100 µG) Proposal: use Na or Rb at zero magnetization. Spin dynamics occurs at constant magnetization 0 1 F=1, m F =-1, 0, 1 We estimate that temperatures in the pK regime may be reached Nota: the spin degrees of freedom may also be used to measure temperature then Related to collision-assisted Zeeman cooling, J. Roberts, EPJD, 68, 1, 14 (2014)

39. Conclusion (1)? Bulk Magnetism: spinor physics with free magnetization New spinor phases at extremely low magnetic fields New cooling mechanism to reach very low entropies (in bulk): Use spin to store and remove entropy Should be applicable to non-dipolar species pK regime possible

40. Conclusion (2)? Lattice Magnetism: Magnetization dynamics is resonant Intersite dipolar spin-exchange Exotic quantum magnetism, from Mott to superfluid Different types of exchange contribute Consequences for magnetic ordering ?

41. Bruno Naylor A. de Paz (PhD), A. Sharma, A. Chotia, B. Naylor (PhD) E. Maréchal, L. Vernac,O. Gorceix, B. Laburthe P. Pedri (Theory), L. Santos (Theory, Hannover) Thank you Aurélie De Paz Amodsen Chotia Arijit Sharma Post-doctoral position available

42. Amplitude of exponential behaviour Amplitude of oscillatory behaviour Empirical description, from superfluid to Mott Spin dynamics mostly exponential at low lattice depth Dynamics shows oscillation at larger lattice depth Slow cross-over between two regimes?

43. High Spin Fermions coming up… Spin oscillations Pomeranchuk-like cooling New SU(N) symmetry (alkaline-earth atoms) (F=9/2 K atoms, Sengstock) (Yb atoms) Rey, Gorshkov, Gurarie, Ye… Dipolar Fermi gases (spin may « store » some entropy)