Magnetism with a Dipolar Condensate: Spin Dynamics and Thermodynamics

1. Magnetismwith a dipolarcondensate: spin dynamics and thermodynamics 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) 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

2. This talk 1 Thermodynamics of a Bose gaswith free magnetization Purification of a BEC by spin-filtering 2 Exotic quantum magnetism in opticallattices Intersite spin-spin many-body interactions fromMott to superfluid

3. Experimental system Nov 2007 : Chromium BEC S=3 104 atoms April 2014 : Chromium Fermi sea F=9/2 103 atoms (from only 3.104 atoms in dipole trap !) Phys. Rev. A 91, 011603(R) (2015)

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

5. This seminar: magnetism with large spin cold atoms Optical dipole traps equally trap all Zeeman state of a same atom Linear (+ Quadratic) Zeeman effect 3 2 1 Stern-Gerlach separation: (magnetic field gradient) 0 -1 -2 -3

6. Van-der-Waals (contact) interactions Spinor physics due to contact interactions: scattering length depends on molecular channel Spin oscillations (exchange) -1 -2 -2 -3 -3 -1 G= 0 ( 250 µs) (period  220 µs) Magnetism… at constant magnetization linear Zeeman effect does not matter Spin-changing collisions have no analog in spin ½ systems

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

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

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

11. 1st main feature : Spinor physics with free magnetization Spin-orbit coupling (conservation of total angular momentum) Magnetization changing processes write an x+iy intersite phase Rotate BEC ? Vortex ? Einstein-de-Haas effect Quantum Hall regime with fermions? Flat bands, topological insulators XYZ magnetism Frustration Carr, New J. Phys. 17 025001 (2015) Peter Zoller arXiv:1410.3388 (2014) H.P. Buchler, arXiv:1410.5667 (2014) 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) engineer

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

13. 0 Introduction to spinorphysics 1 Thermodynamics and cooling of a Bose gaswith free magnetization 2 Exotic quantum magnetism in opticallattices

14. 3 2 1 0 -1 -2 -3 Spin temperature equilibriates with mechanical degrees of freedom At low magnetic field: spin thermally activated -3 -2 -1 0 1 2 3 We measure spin-temperature by fitting the mS population (separated by Stern-Gerlach technique) Related to Demagnetization Cooling expts, T. Pfau, Nature Physics 2, 765 (2006)

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

16. 3 2 1 0 -1 -2 -3 A new cooling method using the spin degrees of freedom? A BEC component only in the ms=-3 state Optical depth ms=-1 ms=-2 ms=-3 Only thermal gas depolarizes… get rid of it ? (Bragg excitations or field gradient) Purify the BEC BEC Thermal ms=-3 ms=-3, -2, -1, … (i) Thermal cloud depolarizes (ii) Kill spin-excited states

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

18. A competition between two mechanisms At high T/Tc, BEC melts (too few atoms in the BEC to cool the thermal gas back to saturation) B=1,5mG At low T/Tc, 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

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

20. Theoretical limits for cooling 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 Process can be repeated Entropy compression There does not seem to be any limit other than practical In principle, cooling is efficient as long as depolarization is efficient Initial entropy per atom

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) 1 Proposal: use Na or Rb at zero magnetization. Spin dynamics occurs at constant magnetization 0 -1 Related to collision-assisted Zeeman cooling, J. Roberts, EPJD, 68, 1, 14 (2014) F=1, mF=-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

22. 0 Introduction to spinorphysics 1 Thermodynamics and cooling of a Bose gaswith free magnetization 2 Exotic quantum magnetism in opticallattices

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

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

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

26. From now on : stay away from dipolar magnetization dynamics resonances, Spin dynamics at constant magnetization (<15mG) Magnetization changing collisions Can be suppressed in optical lattices Ressembles but differs from Heisenberg magnetism: 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. Adiabatic state preparation in 3D lattice Load optical lattice 3 quadratic effect 2 quadratic effect vary time 1 0 -1 -2 -3 -3 -2 Initiate spin dynamics by removing quadratic effect

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 -3 -1 -2 -2 Magnetization is constant Timescale for spin dynamics = 20 ms Tunneling time = 100 ms Super-exchange > 10s 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) !! Many-body dynamics !! (each atom coupled to many neighbours) Mean-field theories fail Phys. Rev. Lett., 111, 185305 (2013)

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 Exact diagonalization is excluded with two atoms per site (too many configurations for even a few sites) Toy models for singlons (i) (j) 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)

32. Observed spin dynamics, from superfluid to Mott An exotic magnetism driven by the competition between three types of exchange Dipolar Spin-dependent contact interactions Super-exchange Superfluid Lower lattice depth: super-exchange may occur and compete Mott Large lattice depth: dynamics dominated by dipolar interactions

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

34. 1.0 1.0 0.5 0.5 0.0 0.0 -0.5 -0.5 -1.0 -1.0 0 0 200 200 400 400 600 600 800 1000 -3 -2 Observed, and calculated frequencies -2 -1 Two-body spin dynamics in isolated lattice sites Many-body spin dynamics due to intersite couplings GP- mean-field simulation superexchange

35. Time (ms) Summary: a slow cross-over between two behaviors 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 In the Mott regime: Two well separated oscillating frequencies corresponding to: • On site contact-driven spin-exchange interactions • Many-body intersite dipole-dipole interactions 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) (i) (j) 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?

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. Thankyou 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) Bruno Naylor Post-doctoral position available Arijit Sharma Aurélie De Paz Amodsen Chotia

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 Entropy (given by BEC fraction) Entropy compression 2,5 5 7,5 0 Magnetic field (mG) Initial entropy per atom

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

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

46. This is not the whole picture: the (small but interesting) effect of demagnetization cooling At finite magnetic field, depolarization implies a conversion of kinetic energy in magnetic energy T. Pfau, Nature Physics 2, 765 (2006) ms=-3, -2, -1, … ms=-3 Entropy of a saturated cloud: At finite magnetic field, depolarization may induce an increase of the BEC atom number!! 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 ! How is it compatible with the fact that the entropy must increase? 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!