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Magnetism with a Dipolar Condensate: Spin Dynamics and Thermodynamics

Explore the exotic quantum magnetism arising from dipole-dipole interactions in a dipolar condensate, with a focus on spin dynamics and thermodynamics. Investigate the possibilities for quantum simulation and the potential applications in condensed matter physics. Collaborators from Paris North University and other institutions contribute to this research.

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Magnetism with a Dipolar Condensate: Spin Dynamics and Thermodynamics

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  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. 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 magnetismwith large spins arisingfromdipole-dipole interactions - Different exchange mechanismscompete, and maybecontrolled (more or less) independently - Dipolar interactions introducetrue long-range couplings - An interestingplayground for many-body quantum physicswith no analog in solid-state physics

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

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

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

  7. Van-der-Waals (contact) interactions Spinor physics due to contact interactions: scattering length depends on molecular channel Spin oscillations (exchange III) -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

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

  9. 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)

  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 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

  12. 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

  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 spinorphysics 1 Exotic quantum magnetism in opticallattices 2 Thermodynamicsand cooling of a Bose gaswith free magnetization

  15. 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)

  16. 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

  17. 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…

  18. 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

  19. 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)

  20. 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)

  21. 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

  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 -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)

  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 Toy models for singlons (i) (j) 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 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 Superfluid Lower lattice depth: super-exchange may occur and compete Mott Large lattice depth: dynamics dominated by dipolar interactions

  27. 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 (contact)-Exchange (III) Many-body spin dynamics due to intersite couplings GP- mean-field simulation (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 opticallattices: a yetalmostunexploredplayground for many-body physics(evenwithoutdipolar interactions) - Free magnetization. Spin orbitcoupling. 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 spinorphysics 1 Exotic quantum magnetism in opticallattices 2 Thermodynamicsand cooling of a Bose gaswith free magnetization (No Lattice)

  31. 3 2 1 0 -1 -2 -3 Spin temperature equilibriates with mechanical degrees of freedom At low magnetic field: spin thermally activated Magnetization adpats to temperature due to the presence of dipolar interactions -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)

  32. 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 PRL 108, 045307 (2012)

  33. 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 Large B field Only thermal gas depolarizes… get rid of it ? Purify the BEC BEC Thermal ms=-3, -2, -1, … ms=-3 (i) Thermal cloud depolarizes (ii) Kill spin-excited states

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

  35. 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 arXiv (2015) 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

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

  37. 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

  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) 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

  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. 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. 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

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

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