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. This talk 1 Thermodynamics of a Bose gas with free magnetization Purification of a BEC by spin-filtering 2 Exotic quantum magnetism in optical lattices Intersite spin-spin many-body interactions from Mott to superfluid

3. 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)

4. A “hot” topic : Cold atoms revisit (quantum) magnetism Non-interacting spin-less bosons Sengstock: classical frustration 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: short range anti-correlations I. Bloch, T. Porto, W. Ketterle, R. Hulet… Spinor gases: Large spin bosons (or fermions) Stamper-Kurn, Lett, Klempt, Chapman, Sengstock, Shin, Gerbier, …… Ion traps: spin lattice models with effective long-range interactions C. Monroe Dipolar gases: long range spin-spin interactions J. Ye, this work…

5. This seminar: magnetism with large spin cold atoms 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

6. 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) Spin-changing collisions have no analog in spin ½ systems Van-der-Waals (contact) interactions

7. Klempt Stamper- Kurn Domains, spin textures, spin waves, topological states Stamper-Kurn, Chapman, Sengstock, Shin… Quantum phase transitions Stamper-Kurn, Lett, Gerbier Spinor physics driven by interplay between spin-dependent contact interactions and quadratic Zeeman effect Chapman, Sengstock, Bloch, Lett, Klempt… NB: high spin fermions coming up! third energy scale set by Fermi energy 10 0 1 SU(N) physics, spinor physics (Sengstock, Fallani, Bloch, Ye…)

8. 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)

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

10. 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

11. 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

12. 2nd main feature of dipolar interactions: Long range-coupling between atoms Implications for lattice magnetism, spin domains…

13. 0 Introduction to spinor physics 1 Thermodynamics and cooling of a Bose gas with free magnetization 2 Exotic quantum magnetism in optical lattices

14. 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 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)

15. 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 New magnetism, differs from solid-state PRL 108, 045307 (2012) T>Tc T<Tc a bi-modal spin distribution -3 -2 -1 0 1 2 3

16. 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 ? (Bragg excitations or field gradient) 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

17. 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

18. 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

19. 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)

20. 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

21. 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)

22. 0 Introduction to spinor physics 1 Thermodynamics and cooling of a Bose gas with free magnetization 2 Exotic quantum magnetism in optical lattices

23. 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

24. 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

25. 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)

26. 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)

27. 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

28. 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

29. 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

30. Spin dynamics in doubly-occupied sites: Faster dynamics due to larger effective dipole (3+3=6 ?) Magnetization is constant Phys. Rev. Lett., 111, 185305 (2013)

31. A toy many-body model for the dynamics at large lattice depth (i) (j ) Exact diagonalization is excluded with two atoms per site (too many configurations for even a few sites) Toy models for singlons Toy models for doublons: replace S=3 by S=4 or S=6 Measured frequency: 300 Hz Calculated frequency: S=4: 220 Hz S=6: 320 Hz Toy models seems to qualitatively reproduce oscillation; see related analysis in Porto, arXiv:1411.7036 (2015)arXiv:1411.7036

32. Observed spin dynamics, from superfluid to Mott 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

33. 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?

34. Observed, and calculated frequencies Two-body spin dynamics in isolated lattice sites 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 superexchange

35. 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: - GP-simulations predict long-lived oscillations (not seen on the experiment) Temperature effect ? -Drift in spin dynamics qualitatively reproduced by simulation -The dynamics depends on an interplay between contact and dipolar interactions Time (ms) In the intermediate regime: -oscillations survive. - Two frequencies get closer No theoretical model yet

36. More probes to caracterize both regimes (1) Hamiltonian should create entanglement (collaboration Perola Milman; Paris 7 University) We are looking for an entanglement witness based on measurements of global spin variables. (e.g. for any mixture of separable states) Idea: adapt this criterion to our observations, measure spin fluctuations Entanglement may only arrise at high lattice depth (otherwise BEC-like state) When does entanglement appear/disappear? (i) (j )

37. More probes to caracterize both regimes (2) Mean-field vs « many-body » dynamics At the mean-field level, dipolar interactions cancel out for an homogeneous system Spin dynamics is a border effect (low lattice depth) True many-body Hamiltonian predicts non-vanishing spin dynamics (i) (j ) Deep lattices: spin dynamics occurs in the core Measure locally could differentiate between regimes

38. What have we learned (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

39. What have we learned (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 ?

40. What have we learned ? (3) Truly new phenomena arrise due to dipolar interactions when the spin degrees of freedom are released. - Free magnetization. Spin orbit coupling. Also an interesting challenge from the theoretical point of view. - Effective Hamiltonians relevant for quantum magnetism. Some of the physics is specific to high spin atoms (no analog with electrons or with heteronuclear molecules) - Large spin atoms in optical lattices: a yet almost unexplored playground for many-body physics (even without dipolar interactions) Carr, New J. Phys. 17 025001 (2015) Peter Zoller arXiv:1410.3388 (2014) H.P. Buchler, arXiv:1410.5667 (2014) See M. Wall et al., arXiv 1305.1236

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. This is not the whole picture: the (small but interesting) effect of demagnetization cooling Our theoretical results predict that depolarization may induce an increase of the BEC atom number!! How is it compatible with the fact that the entropy must increase? Entropy of a saturated cloud: Entropy of a non-saturated cloud: is… larger The entropy can therefore be stored in the non-saturated gas, and the BEC atom number increase, without filtering! For a fully saturated gas, the entropy is given by the condensate fraction: you cannot increase the condensate fraction and entropy at the same time ! NB: this effect is associated to demagnetization cooling T. Pfau, Nature Physics 2, 765 (2006)

43. How to characterize the cooling efficiency: use entropy per particle 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 7,5 0 2,55 Magnetic field (mG) Entropy (given by BEC fraction)

44. Complex Many-body physics Many open questions… Our approach : Study magnetism with strongly magnetic atoms : dipole-dipole interactions between real spins R Simple two-body Hamiltonian Possibilities for quantum simulation – possibilities for exotic quantum magnetism

45. Quantum magnetism, some paradigms, from solid-state physics High-Tc superconductivity Antiferromagnetism Hubbard model Frustrated magnetism ? ? Spin liquids Heisenberg model of magnetism (real spins, effective spin-spin interaction) Condensed-matter: effective spin-spin interactions arise due to exchange interactions Ising Exchange Our experiment: real spin-spin interactions due to dipole-dipole interactions

46. This is not the whole picture: the (small but interesting) effect of demagnetization cooling m s =-3 m s =-3, -2, -1, … At finite magnetic field, depolarization implies a conversion of kinetic energy in magnetic energy T. Pfau, Nature Physics 2, 765 (2006) At finite magnetic field, depolarization may induce an increase of the BEC atom number!! How is it compatible with the fact that the entropy must increase? Entropy of a saturated cloud: Entropy of a non-saturated cloud: is… larger The entropy can therefore be stored in the non- saturated gas, and the BEC atom number increase, without filtering! For a fully saturated gas, the entropy is given by the condensate fraction: you cannot increase the condensate fraction and entropy at the same time !